Class 12 • Physics

Atoms & Nuclei

Chapter-12

680 Questions

0 Video Solutions

129 Easy542 Medium9 Hard

Practice Questions

Click on any question to view the complete question with options and detailed solution.

Options:

A) 26.8 MeV

B) 8.1 MeV

C) 23.6 MeV

D) 5.9 MeV

100

EasyJEE Mains2025

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of \mathrm{Li}^{++} ion in its ground state is given by \frac{1}{X} a_0, where X= __________ (Where \mathrm{a}_0 is the first Bohr's radius.)

Options:

A) 2

B) 9

C) 1

D) 3

101

MediumJEE Mains2025

Considering Bohr's atomic model for hydrogen atom : (A) the energy of H atom in ground state is same as energy of \mathrm{He}^{+}ion in its first excited state. (B) the energy of H atom in ground state is same as that for \mathrm{Li}^{++} ion in its second excited state. (C) the energy of H atom in its ground state is same as that of \mathrm{He}^{+}ion for its ground state. (D) the energy of \mathrm{He}^{+}ion in its first excited state is same as that for \mathrm{Li}^{++}ion in its ground state. Choose the correct answer from the options given below :

Options:

A) (A), (B) only

B) (A), (D) only

C) (A), (C) only

D) (B), (D) only

102

EasyJEE Mains2025

The number of spectral lines emitted by atomic hydrogen that is in the 4th energy level, is

Options:

A) 3

B) 6

C) 1

D) 0

103

EasyJEE Mains2025

The frequency of revolution of the electron in Bohr's orbit varies with n , the principal quantum number as:

Options:

A) \frac{1}{n^4}

B) \frac{1}{n^2}

C) \frac{1}{n^3}

D) \frac{1}{n}

104

EasyJEE Mains2025

Choose the correct nuclear process from the below options [ p : proton, n : neutron, \mathrm{e}^{-}: electron, \mathrm{e}^{+}: positron, v: neutrino, \bar{v}: antineutrino]

Options:

A) n \rightarrow p+e^{+}+{v}

B) \mathrm{n} \rightarrow \mathrm{p}+\mathrm{e}^{-}+\bar{v}

C) \mathrm{n} \rightarrow \mathrm{p}+\mathrm{e}^{+}+\bar{v}

D) \mathrm{n} \rightarrow \mathrm{p}+\mathrm{e}^{-}+v

105

EasyJEE Mains2025

The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation

Options:

A) \mathrm{E}^2=\mathrm{pc}^2+\mathrm{m}^2 \mathrm{c}^4

B) \mathrm{E}^2=\mathrm{pc}^2+\mathrm{m}^2 \mathrm{c}^2

C) \mathrm{E}^2=\mathrm{p}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^4

D) \mathrm{E}^2=\mathrm{p}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^2

106

MediumJEE Mains2025

During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is 2000 \mathop A\limits^o and it becomes 6000 \mathop A\limits^o when the electron jumps from state B to state C. Then the wavelength of the radiation emitted during the transition of electrons from state A to state B is

Options:

A) 4000 \mathop A\limits^o

B) 6000 \mathop A\limits^o

C) 2000 \mathop A\limits^o

D) 3000 \mathop A\limits^o

107

EasyJEE Mains2025

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number A , for nuclei with mass numbers between 30 and 170 . Reason (R) : Nuclear force is long range. In the light of the above statements, choose the correct answer from the options given below :

Options:

A) (A) is true but (R) is false

B) Both (A) and (R) are true and (R) is the correct explanation of (A)

C) (A) is false but (R) is true

D) Both (A) and (R) are true but (R) is NOT the correct explanation of (A)

108

MediumJEE Mains2025

A radioactive nucleus \mathrm{n}_2 has 3 times the decay constant as compared to the decay constant of another radioactive nucleus n_1. If initial number of both nuclei are the same, what is the ratio of number of nuclei of n_2 to the number of nuclei of n_1, after one half-life of n_1 ?

Options:

A) 1/4

B) 1/8

C) 4

D) 8

109

EasyJEE Mains2024

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $2: 1$. After disintegration they will move :

Options:

A) in opposite directions with speed in the ratio of $1: 2$ respectively.

B) in the same direction with same speed.

C) in opposite directions with speed in the ratio of $2: 1$ respectively.

D) in opposite directions with the same speed.

110

MediumJEE Mains2024

The energy released in the fusion of $2 \mathrm{~kg} of hydrogen deep in the sun is E_H and the energy released in the fission of 2 \mathrm{~kg} of { }^{235} \mathrm{U} is E_U. The ratio \frac{E_H}{E_U} is approximately: (Consider the fusion reaction as 4_1^1H+2 \mathrm{e}^{-} \rightarrow{ }_2^4 \mathrm{He}+2 v+6 \gamma+26.7 \mathrm{~MeV}, energy released in the fission reaction of { }^{235} \mathrm{U} is 200 \mathrm{~MeV} per fission nucleus and \mathrm{N}_{\mathrm{A}}= 6.023 \times 10^{23})

Options:

A) 7.62

B) 25.6

C) 9.13

D) 15.04

111

MediumJEE Mains2024

A hydrogen atom in ground state is given an energy of $10.2 \mathrm{~eV}$. How many spectral lines will be emitted due to transition of electrons?

Options:

A) 3

B) 6

C) 10

D) 1

112

EasyJEE Mains2024

The energy equivalent of $1 \mathrm{~g}$ of substance is :

Options:

A) 5.6 \times 10^{26} \mathrm{~MeV}

B) 5.6 \times 10^{12} \mathrm{~MeV}

C) 5.6 \mathrm{~eV}

D) 11.2 \times 10^{24} \mathrm{~MeV}

113

EasyJEE Mains2024

If $M_0 is the mass of isotope { }_5^{12} B, M_p and M_n$ are the masses of proton and neutron, then nuclear binding energy of isotope is:

Options:

A) (5 M_p+7 M_n-M_o) C^2

B) (M_o-5 M_p-7 M_n) C^2

C) (M_o-5 M_p) C^2

D) (M_0-12 M_n) C^2

114

EasyJEE Mains2024

In a hypothetical fission reaction ${ }_{92} X^{236} \rightarrow{ }_{56} \mathrm{Y}^{141}+{ }_{36} Z^{92}+3 R$ The identity of emitted particles (R) is :

Options:

A) Proton

B) Neutron

C) Electron

D) \gamma$-radiations

115

EasyJEE Mains2024

Binding energy of a certain nucleus is $18 \times 10^8 \mathrm{~J}$. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

Options:

A) 20 $\mu$g

B) 2 $\mu$g

C) 10 $\mu$g

D) 0.2 $\mu$g

116

EasyJEE Mains2024

The longest wavelength associated with Paschen series is : (Given $\mathrm{R}_{\mathrm{H}}=1.097 \times 10^7 \mathrm{SI}$ unit)

Options:

A) 2.973 \times 10^{-6} \mathrm{~m}

B) 1.876 \times 10^{-6} \mathrm{~m}

C) 1.094 \times 10^{-6} \mathrm{~m}

D) 3.646 \times 10^{-6} \mathrm{~m}

117

EasyJEE Mains2024

The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :

Options:

A) 1: 2

B) 1: 4

C) 2: 1

D) 4: 1

118

EasyJEE Mains2024

The angular momentum of an electron in a hydrogen atom is proportional to : (Where $\mathrm{r}$ is the radius of orbit of electron)

Options:

A) \frac{1}{\mathrm{r}}

B) \frac{1}{\sqrt{\mathrm{r}}}

C) \sqrt{\mathrm{r}}

D) r

119

EasyJEE Mains2024

An electron rotates in a circle around a nucleus having positive charge $\mathrm{Ze}$. Correct relation between total energy (E) of electron to its potential energy (U) is :

Options:

A) 2 \mathrm{E}=3 \mathrm{U}

B) \mathrm{E}=\mathrm{U}

C) 2 \mathrm{E}=\mathrm{U}

D) \mathrm{E}=2 \mathrm{U}

120

EasyJEE Mains2024

According to Bohr's theory, the moment of momentum of an electron revolving in $4^{\text {th }}$ orbit of hydrogen atom is:

Options:

A) 2 \frac{h}{\pi}

B) \frac{h}{2 \pi}

C) \frac{h}{\pi}

D) 8 \frac{h}{\pi}

121

EasyJEE Mains2024

Which of the following nuclear fragments corresponding to nuclear fission between neutron $\left({ }_0^1 \mathrm{n}\right) and uranium isotope \left({ }_{92}^{235} \mathrm{U}\right)$ is correct :

Options:

A) { }_{56}^{140} \mathrm{Xe}+{ }_{38}^{94} \mathrm{Sr}+3{ }_0^1 \mathrm{n}

B) { }_{51}^{153} \mathrm{Sb}+{ }_{41}^{99} \mathrm{Nb}+3{ }_0^1 \mathrm{n}

C) { }_{56}^{144} \mathrm{Ba}+{ }_{36}^{89} \mathrm{Kr}+4{ }_0^1 \mathrm{n}

D) { }_{56}^{144} \mathrm{Ba}+{ }_{36}^{89} \mathrm{Kr}+3{ }_0^1 \mathrm{n}

122

MediumJEE Mains2024

From the statements given below : (A) The angular momentum of an electron in n^{\text {th }} orbit is an integral multiple of \hbar. (B) Nuclear forces do not obey inverse square law. (C) Nuclear forces are spin dependent. (D) Nuclear forces are central and charge independent. (E) Stability of nucleus is inversely proportional to the value of packing fraction. Choose the correct answer from the options given below :

Options:

A) (B), (C), (D), (E) only

B) (A), (C), (D), (E) only

C) (A), (B), (C), (E) only

D) (A), (B), (C), (D) only

123

MediumJEE Mains2024

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly :

Options:

A) 13.6 \mathrm{eV}

B) 1.5 \mathrm{eV}

C) 12.1 \mathrm{eV}

D) 1.9 \mathrm{eV}

124

EasyJEE Mains2024

The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is :

Options:

A) 32

B) 24

C) 20

D) 40

125

EasyJEE Mains2024

If the wavelength of the first member of Lyman series of hydrogen is $\lambda$. The wavelength of the second member will be

Options:

A) \frac{27}{5} \lambda

B) \frac{5}{27} \lambda

C) \frac{27}{32} \lambda

D) \frac{32}{27} \lambda

126

MediumJEE Mains2024

An electron revolving in $n^{\text {th }} Bohr orbit has magnetic moment \mu_n. If \mu_n \propto n^x, the value of x$ is

Options:

A) 2

B) 0

C) 3

D) 1

127

MediumJEE Mains2024

In a nuclear fission reaction of an isotope of mass $M, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect \Delta M$ will be :

Options:

A) c \sqrt{\frac{3 \Delta M}{M}}

B) \frac{\Delta M c^2}{3}

C) c \sqrt{\frac{2 \Delta M}{M}}

D) \sqrt{\frac{2 c \Delta M}{M}}

128

EasyJEE Mains2024

The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the 5 th excited state of a hydrogen atom is :

Options:

A) 4

B) 1

C) \frac{1}{2}

D) \frac{1}{4}

129

EasyJEE Mains2024

Given below are two statements: Statement I : Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford's model. Statement II : An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford's model. In the light of the above statements, choose the most appropriate from the options given below

Options:

A) Both Statement I and Statement II are true

B) Statement I is true but Statement II is false

C) Statement I is false but Statement II is true

D) Both statement I and statement II are false

130

MediumJEE Mains2024

The explosive in a Hydrogen bomb is a mixture of ${ }_1 \mathrm{H}^2,{ }_1 \mathrm{H}^3 and { }_3 \mathrm{Li}^6 in some condensed form. The chain reaction is given by \begin{aligned} & { }_3 \mathrm{Li}^6+{ }_0 \mathrm{n}^1 \rightarrow{ }_2 \mathrm{He}^4+{ }_1 \mathrm{H}^3 \\ & { }_1 \mathrm{H}^2+{ }_1 \mathrm{H}^3 \rightarrow{ }_2 \mathrm{He}^4+{ }_0 \mathrm{n}^1 \end{aligned} During the explosion the energy released is approximately [Given ; \mathrm{M}(\mathrm{Li})=6.01690 \mathrm{~amu}, \mathrm{M}\left({ }_1 \mathrm{H}^2\right)=2.01471 \mathrm{~amu}, \mathrm{M}\left({ }_2 \mathrm{He}^4\right)=4.00388 \mathrm{amu}, and 1 \mathrm{~amu}=931.5 \mathrm{~MeV}]

Options:

A) 22.22 MeV

B) 28.12 MeV

C) 16.48 MeV

D) 12.64 MeV

131

EasyJEE Mains2024

The atomic mass of ${ }_6 \mathrm{C}^{12} is 12.000000 \mathrm{~u} and that of { }_6 \mathrm{C}^{13} is 13.003354 \mathrm{~u}. The required energy to remove a neutron from { }_6 \mathrm{C}^{13}, if mass of neutron is 1.008665 \mathrm{~u}$, will be :

Options:

A) 62.5 MeV

B) 6.25 MeV

C) 4.95 MeV

D) 49.5 MeV

132

EasyJEE Mains2024

The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth stationary orbit will be:

Options:

A) \frac{4}{3} \mathrm{R}

B) \frac{16}{9} R

C) \frac{3}{4} R

D) \frac{9}{16} \mathrm{R}

133

EasyJEE Mains2023

The half-life of a radioactive nucleus is 5 years. The fraction of the original sample that would decay in 15 years is:

Options:

A) \frac{1}{8}

B) \frac{3}{4}

C) \frac{7}{8}

D) \frac{1}{4}

134

EasyJEE Mains2023

Given below are two statements: one is labelled as Assertion $\mathbf{A} and the other is labelled as Reason \mathbf{R}$ Assertion A : The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range 30 to 170 . Reason R : Nuclear force is short ranged. In the light of the above statements, choose the correct answer from the options given below

Options:

A) \mathrm{A} is false but \mathbf{R}$ is true

B) \mathrm{A} is true but \mathbf{R}$ is false

C) Both $\mathbf{A} and \mathbf{R} are true and \mathbf{R} is the correct explanation of \mathbf{A}

D) Both $\mathbf{A} and \mathbf{R} are true but \mathbf{R} is NOT the correct explanation of \mathbf{A}

135

EasyJEE Mains2023

_{92}^{238}A \to _{90}^{234}B + _2^4D + Q In the given nuclear reaction, the approximate amount of energy released will be: [Given, mass of { }_{92}^{238} \mathrm{~A}=238.05079 \times 931.5 ~\mathrm{MeV} / \mathrm{c}^{2}, mass of { }_{90}^{234} B=234 \cdot 04363 \times 931 \cdot 5 ~\mathrm{MeV} / \mathrm{c}^{2}, mass of \left.{ }_{2}^{4} D=4 \cdot 00260 \times 931 \cdot 5 ~\mathrm{MeV} / \mathrm{c}^{2}\right]

Options:

A) 2.12 MeV

B) 4.25 MeV

C) 3.82 MeV

D) 5.9 MeV

136

MediumJEE Mains2023

A $12.5 \mathrm{~eV}$ electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:

Options:

A) 2

B) 4

C) 3

D) 1

137

EasyJEE Mains2023

The energy of $\mathrm{He}^{+} ion in its first excited state is, (The ground state energy for the Hydrogen atom is -13.6 ~\mathrm{eV})$ :

Options:

A) -13.6 ~\mathrm{eV}

B) -27.2 ~\mathrm{eV}

C) -3.4 ~\mathrm{eV}

D) -54.4 ~\mathrm{eV}

138

EasyJEE Mains2023

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If $\lambda_{A} and \lambda_{B}$ are decay constants of A and B respectively, then choose the correct relation from the given options.

Options:

A) \lambda_{\mathrm{A}}=\lambda_{\mathrm{B}} \ln 2

B) \lambda_{\mathrm{A}} \ln 2=\lambda_{\mathrm{B}}

C) \lambda_{\mathrm{A}}=2 \lambda_{\mathrm{B}}

D) \lambda_{\mathrm{A}}=\lambda_{\mathrm{B}}

139

EasyJEE Mains2023

The half life of a radioactive substance is T. The time taken, for disintegrating $\frac{7}{8}$th part of its original mass will be:

Options:

A) 8T

B) 3T

C) T

D) 2T

140

EasyJEE Mains2023

The angular momentum for the electron in Bohr's orbit is L. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be

Options:

A) L

B) \frac{L}{2}

C) zero

D) 2 L

141

EasyJEE Mains2023

A radio active material is reduced to $1 / 8 of its original amount in 3 days. If 8 \times 10^{-3} \mathrm{~kg}$ of the material is left after 5 days the initial amount of the material is

Options:

A) 64 g

B) 256 g

C) 32 g

D) 40 g

142

EasyJEE Mains2023

The waves emitted when a metal target is bombarded with high energy electrons are

Options:

A) Infrared rays

B) Radio Waves

C) Microwaves

D) X-rays

143

HardJEE Mains2023

For a nucleus ${ }_{\mathrm{A}}^{\mathrm{A}} \mathrm{X} having mass number \mathrm{A} and atomic number \mathrm{Z} A. The surface energy per nucleon \left(b_{\mathrm{s}}\right)=-a_{1} A^{2 / 3}. B. The Coulomb contribution to the binding energy \mathrm{b}_{\mathrm{c}}=-a_{2} \frac{Z(Z-1)}{A^{4 / 3}} C. The volume energy \mathrm{b}_{\mathrm{v}}=a_{3} A D. Decrease in the binding energy is proportional to surface area. E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( a_{1}, a_{2} and a_{3}$ are constants) Choose the most appropriate answer from the options given below:

Options:

A) C, D only

B) B, C, E only

C) B, C only

D) A, B, C, D only

144

MediumJEE Mains2023

A small particle of mass $m moves in such a way that its potential energy U=\frac{1}{2} m ~\omega^{2} r^{2} where \omega is constant and r is the distance of the particle from origin. Assuming Bohr's quantization of momentum and circular orbit, the radius of n^{\text {th }}$ orbit will be proportional to,

Options:

A) \sqrt{n}

B) n^{2}

C) \frac{1}{n}

D) n

145

EasyJEE Mains2023

The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is :

Options:

A) A

B) C

C) B

D) D

146

EasyJEE Mains2023

An electron of a hydrogen like atom, having $Z=4, jumps from 4^{\text {th }} energy state to 2^{\text {nd }} energy state. The energy released in this process, will be : (Given Rch = 13.6~\mathrm{eV}$) Where R = Rydberg constant c = Speed of light in vacuum h = Planck's constant

Options:

A) 10.5 ~\mathrm{eV}

B) 40.8 ~\mathrm{eV}

C) 13.6 ~\mathrm{eV}

D) 3.4 ~\mathrm{eV}

147

EasyJEE Mains2023

The mass of proton, neutron and helium nucleus are respectively $1.0073~u,1.0087~u and 4.0015~u$. The binding energy of helium nucleus is :

Options:

A) 28.4~\mathrm{MeV}

B) 56.8~\mathrm{MeV}

C) 7.1~\mathrm{MeV}

D) 14.2~\mathrm{MeV}

148

EasyJEE Mains2023

The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd orbit will be

Options:

A) 2.25R

B) 3 \mathrm{R}

C) \frac{\mathrm{R}}{3}

D) 9 \mathrm{R}

149

EasyJEE Mains2023

A free neutron decays into a proton but a free proton does not decay into neutron. This is because

Options:

A) neutron is an uncharged particle

B) neutron has larger rest mass than proton

C) neutron is a composite particle made of a proton and an electron

D) proton is a charged particle

150

MediumJEE Mains2023

Given below are two statements: one is labelled as Assertion \mathbf{A} and the other is labelled as Reason \mathbf{R} Assertion A: The nuclear density of nuclides { }_{5}^{10} \mathrm{~B},{ }_{3}^{6} \mathrm{Li},{ }_{26}^{56} \mathrm{Fe},{ }_{10}^{20} \mathrm{Ne} and { }_{83}^{209} \mathrm{Bi} can be arranged as \rho_{\mathrm{Bi}}^{\mathrm{N}}>\rho_{\mathrm{Fe}}^{\mathrm{N}}>\rho_{\mathrm{Ne}}^{\mathrm{N}}>\rho_{\mathrm{B}}^{\mathrm{N}}>\rho_{\mathrm{Li}}^{\mathrm{N}} Reason R: The radius R of nucleus is related to its mass number A as R=R_{0} A^{1 / 3}, where R_{0} is a constant. In the light of the above statements, choose the correct answer from the options given below

Options:

A) {Both ~\mathbf{A}} and \mathbf{R} are true and \mathbf{R} is the correct explanation of \mathbf{A}

B) Both \mathbf{A} and \mathbf{R} are true but \mathbf{R} is NOT the correct explanation of \mathbf{A}

C) \mathbf{A} is false but \mathbf{R} is true

D) \mathbf{A} is true but \mathbf{R} is false

151

EasyJEE Mains2023

Speed of an electron in Bohr's $7^{\text {th }} orbit for Hydrogen atom is 3.6 \times 10^{6} \mathrm{~m} / \mathrm{s}. The corresponding speed of the electron in 3^{\text {rd }} orbit, in \mathrm{m} / \mathrm{s}$ is :

Options:

A) \left(1.8 \times 10^{6}\right)

B) \left(7.5 \times 10^{6}\right)

C) \left(8.4 \times 10^{6}\right)

D) \left(3.6 \times 10^{6}\right)

152

MediumJEE Mains2023

Substance A has atomic mass number 16 and half life of 1 day. Another substance B has atomic mass number 32 and half life of $\frac{1}{2}$ day. If both A and B simultaneously start undergo radio activity at the same time with initial mass 320 g each, how many total atoms of A and B combined would be left after 2 days.

Options:

A) 1.69\times10^{24}

B) 3.38\times10^{24}

C) 6.76\times10^{23}

D) 6.76\times10^{24}

153

EasyJEE Mains2023

If a radioactive element having half-life of $30 \mathrm{~min} is undergoing beta decay, the fraction of radioactive element remains undecayed after 90 \mathrm{~min}$. will be

Options:

A) \frac{1}{16}

B) \frac{1}{4}

C) \frac{1}{8}

D) \frac{1}{2}

154

EasyJEE Mains2023

The energy levels of an atom is shown in figure. Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm? Given (h = 6.62 $\times 10^{-34}$ Js)

Options:

A) C

B) B

C) A

D) D

155

EasyJEE Mains2023

The ratio of the density of oxygen nucleus ($_8^{16}O) and helium nucleus (_2^{4}\mathrm{He}$) is

Options:

A) 4 : 1

B) 1 : 1

C) 2 : 1

D) 8 : 1

156

EasyJEE Mains2023

A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The corresponding wavelength for this transition is (given, h = 4 $\times 10^{-15}$ eVs) :

Options:

A) 99.3 nm

B) 94.1 nm

C) 974 nm

D) 941 nm

157

EasyJEE Mains2023

Consider the following radioactive decay process $_{84}^{218}A\buildrel \alpha \over \longrightarrow {A_1}\buildrel {{\beta ^ - }} \over \longrightarrow {A_2}\buildrel \gamma \over \longrightarrow {A_3}\buildrel \alpha \over \longrightarrow {A_4}\buildrel {{\beta ^ + }} \over \longrightarrow {A_5}\buildrel \gamma \over \longrightarrow {A_6} The mass number and the atomic number of A_6$ are given by :

Options:

A) 210 and 84

B) 210 and 80

C) 211 and 80

D) 210 and 82

158

EasyJEE Mains2022

Read the following statements : (A) Volume of the nucleus is directly proportional to the mass number. (B) Volume of the nucleus is independent of mass number. (C) Density of the nucleus is directly proportional to the mass number. (D) Density of the nucleus is directly proportional to the cube root of the mass number. (E) Density of the nucleus is independent of the mass number. Choose the correct option from the following options.

Options:

A) (A) and (D) only.

B) (A) and (E) only.

C) (B) and (E) only.

D) (A) and (C) only.

159

EasyJEE Mains2022

Find the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) second permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted level.

Options:

A) 3 : 4

B) 4 : 3

C) 1 : 4

D) 4 : 1

160

EasyJEE Mains2022

A radioactive sample decays $\frac{7}{8}$ times its original quantity in 15 minutes. The half-life of the sample is

Options:

A) 5 min

B) 7.5 min

C) 15 min

D) 30 min

161

MediumJEE Mains2022

The half life period of a radioactive substance is 60 days. The time taken for $\frac{7}{8}$th of its original mass to disintegrate will be :

Options:

A) 120 days

B) 130 days

C) 180 days

D) 20 days

162

EasyJEE Mains2022

The activity of a radioactive material is $6.4 \times 10^{-4} curie. Its half life is 5 days. The activity will become 5 \times 10^{-6}$ curie after :

Options:

A) 7 days

B) 15 days

C) 25 days

D) 35 days

163

EasyJEE Mains2022

What is the half-life period of a radioactive material if its activity drops to $1 / 16^{\text {th }}$ of its initial value in 30 years?

Options:

A) 9.5 years

B) 8.5 years

C) 7.5 years

D) 10.5 years

164

EasyJEE Mains2022

A nucleus of mass $M at rest splits into two parts having masses \frac{M^{\prime}}{3} and {{2M'} \over 3}(M' < M)$. The ratio of de Broglie wavelength of two parts will be :

Options:

A) 1 : 2

B) 2 : 1

C) 1 : 1

D) 2 : 3

165

EasyJEE Mains2022

Mass numbers of two nuclei are in the ratio of $4: 3$. Their nuclear densities will be in the ratio of

Options:

A) 4 : 3

B) \left(\frac{3}{4}\right)^{\frac{1}{3}}

C) 1 : 1

D) \left(\frac{4}{3}\right)^{\frac{1}{3}}

166

EasyJEE Mains2022

The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is : $\left(\right.Take \left.\log _{10} 1.88=0.274\right)

Options:

A) 0.02 \min ^{-1}

B) 2.7 \min ^{-1}

C) 0.063 \min ^{-1}

D) 6.3 \min ^{-1}

167

EasyJEE Mains2022

Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength $\lambda. The value of principal quantum number 'n' of the excited state will be : (\mathrm{R}:$ Rydberg constant)

Options:

A) \sqrt{\frac{\lambda \mathrm{R}}{\lambda-1}}

B) \sqrt{\frac{\lambda \mathrm{R}}{\lambda \mathrm{R}-1}}

C) \sqrt{\frac{\lambda}{\lambda \mathrm{R}-1}}

D) \sqrt{\frac{\lambda R^{2}}{\lambda R-1}}

168

EasyJEE Mains2022

The momentum of an electron revolving in $\mathrm{n}^{\text {th }}$ orbit is given by : (Symbols have their usual meanings)

Options:

A) \frac{\mathrm{nh}}{2 \pi \mathrm{r}}

B) \frac{n h}{2 r}

C) \frac{\mathrm{nh}}{2 \pi}

D) \frac{2 \pi r}{\mathrm{nh}}

169

EasyJEE Mains2022

The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by :

Options:

A) \vec{\mu}_{\mathrm{L}}=\frac{\overrightarrow{\mathrm{eL}}}{2 \mathrm{~m}}

B) \vec{\mu}_{\mathrm{L}}=-\frac{\overrightarrow{\mathrm{eL}}}{2 \mathrm{~m}}

C) \vec{\mu}_{l}=-\frac{\overrightarrow{e L}}{\mathrm{~m}}

D) \vec{\mu}_{l}=\frac{2 \overrightarrow{\mathrm{eL}}}{\mathrm{m}}

170

MediumJEE Mains2022

A hydrogen atom in ground state absorbs 12.09 eV of energy. The orbital angular momentum of the electron is increased by :

Options:

A) 1.05 $\times 10 -$34 Js

B) 2.11 $\times 10 -$34 Js

C) 3.16 $\times 10 -$34 Js

D) 4.22 $\times 10 -$34 Js

171

EasyJEE Mains2022

In the following nuclear reaction, $D\buildrel \alpha \over \longrightarrow {D_1}\buildrel {{\beta ^ - }} \over \longrightarrow {D_2}\buildrel \alpha \over \longrightarrow {D_3}\buildrel \gamma \over \longrightarrow {D_4}$ Mass number of D is 182 and atomic number is 74. Mass number and atomic number of D 4 respectively will be _________.

Options:

A) 174 and 71

B) 174 and 69

C) 172 and 69

D) 172 and 71

172

EasyJEE Mains2022

The activity of a radioactive material is 2.56 $\times 10 -3 Ci. If the half life of the material is 5 days, after how many days the activity will become 2 \times 10 -$5 Ci ?

Options:

A) 30 days

B) 35 days

C) 40 days

D) 25 days

173

EasyJEE Mains2022

Following statements related to radioactivity are given below : (A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions. (B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time. (C) Slope of the graph of log e (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time ($\tau). (D) Product of decay constant (\lambda$) and half-life time (T 1/2 ) is not constant. Choose the most appropriate answer from the options given below :

Options:

A) (A) and (B) only

B) (B) and (D) only

C) (B) and (C) only

D) (C) and (D) only

174

EasyJEE Mains2022

The Q-value of a nuclear reaction and kinetic energy of the projectile particle, K p are related as :

Options:

A) Q = K p

B) (K p + Q) < 0

C) Q < K p

D) (K p + Q) > 0

175

EasyJEE Mains2022

Given below are two statements : Statement I : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit (E 1 ) to higher energy orbit (E 2 ), is given as hf = E 1 $- E 2 Statement II : The jumping of electron from higher energy orbit (E 2 ) to lower energy orbit (E 1 ) is associated with frequency of radiation given as f = (E 2 -$ E 1 )/h This condition is Bohr's frequency condition. In the light of the above statements, choose the correct answer from the options given below :

Options:

A) Both Statement I and Statement II are true.

B) Both Statement I and Statement II are false.

C) Statement I is correct but Statement II is false.

D) Statement I is incorrect but Statement II is true.

176

MediumJEE Mains2022

A hydrogen atom in its ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of : (Given, Planck's constant = 6.6 $\times 10 -$34 Js).

Options:

A) 2.10 $\times 10 -$34 Js

B) 1.05 $\times 10 -$34 Js

C) 3.15 $\times 10 -$34 Js

D) 4.2 $\times 10 -$34 Js

177

MediumJEE Mains2022

A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process. The effective half-life of the nucleus will be:

Options:

A) 3.75 hours

B) 0.56 hours

C) 0.26 hours

D) 1.80 hours

178

EasyJEE Mains2022

How many alpha and beta particles are emitted when Uranium 92 U 238 decays to lead 82 Pb 206 ?

Options:

A) 3 alpha particles and 5 beta particles

B) 6 alpha particles and 4 beta particles

C) 4 alpha particles and 5 beta particles

D) 8 alpha particles and 6 beta particles

179

EasyJEE Mains2022

Which of the following figure represents the variation of ${l_n}\left( {{R \over {{R_0}}}} \right) with {l_n}A$ (if R = radius of a nucleus and A = its mass number)

Options:

180

EasyJEE Mains2022

The ratio for the speed of the electron in the 3 rd orbit of He + to the speed of the electron in the 3 rd orbit of hydrogen atom will be :

Options:

A) 1 : 1

B) 1 : 2

C) 4 : 1

D) 2 : 1

181

MediumJEE Mains2022

In Bohr's atomic model of hydrogen, let K, P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level :

Options:

A) All K, P and E increase.

B) K decreases, P and E increase.

C) P decreases, K and E increase.

D) K increases, P and E decrease.

182

EasyJEE Mains2022

Choose the correct option from the following options given below :

Options:

A) In the ground state of Rutherford's model electrons are in stable equilibrium. While in Thomson's model electrons always experience a net-force.

B) An atom has a nearly continuous mass distribution in a Rutherford's model but has a highly non-uniform mass distribution in Thomson's model.

C) A classical atom based on Rutherford's model is doomed to collapse.

D) The positively charged part of the atom possesses most of the mass in Rutherford's model but not in Thomson's model.

183

EasyJEE Mains2022

Nucleus A is having mass number 220 and its binding energy per nucleon is 5.6 MeV. It splits in two fragments 'B' and 'C' of mass numbers 105 and 115. The binding energy of nucleons in 'B' and 'C' is 6.4 MeV per nucleon. The energy Q released per fission will be :

Options:

A) 0.8 MeV

B) 275 MeV

C) 220 MeV

Options:

A) A, B, C, D and E

B) A, B and E only

C) B and D only

D) A, C and E only

190

EasyJEE Mains2021

If 'f' denotes the ratio of the number of nuclei decayed (N d ) to the number of nuclei at t = 0 (N 0 ) then for a collection of radioactive nuclei, the rate of change of 'f' with respect to time is given as : [$\lambda$ is the radioactive decay constant]

Options:

A) - \lambda (1 - e -\lambda$t )

B) \lambda (1 - e -\lambda$t )

C) \lambdae -\lambda$t

D) - \lambdae -\lambda$t

191

MediumJEE Mains2021

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as : (where $\lambda$ is the decay constant)

Options:

A) {1 \over 2}{{\ln 2} \over \lambda }

B) {{\ln 2} \over \lambda }

C) {{2\ln 2} \over \lambda }

D) {{\ln {3 \over 2}} \over \lambda }

192

MediumJEE Mains2021

The half-life of ${}^{198}Au is 3 days. If atomic weight of {}^{198}Au is 198 g/mol then the activity of 2 mg of {}^{198}Au$ is [in disintegration/second] :

Options:

A) 2.67 $\times$ 10 12

B) 6.06 $\times$ 10 18

C) 32.36 $\times$ 10 12

D) 16.18 $\times$ 10 12

193

MediumJEE Mains2021

A nucleus with mass number 184 initially at rest emits an $\alpha-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the \alpha$-particle.

Options:

A) 5.5 MeV

B) 5.0 MeV

C) 5.38 MeV

D) 0.12 MeV

194

MediumJEE Mains2021

For a certain radioactive process the graph between In R and t(sec) is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately :

Options:

A) 9.15 sec

B) 6.93 sec

C) 2.62 sec

D) 4.62 sec

195

MediumJEE Mains2021

A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the time after which one third of the material remains ? (Take ln 3 = 1.1)

Options:

A) 740 years

B) 1110 years

C) 700 years

D) 340 years

196

MediumJEE Mains2021

A nucleus of mass M emits $\gamma$ -ray photon of frequency 'v'. The loss of internal energy by the nucleus is : [Take 'c' as the speed of electromagnetic wave]

Options:

A) hv

B) hv\left[ {1 + {{hv} \over {2M{c^2}}}} \right]

C) hv\left[ {1 - {{hv} \over {2M{c^2}}}} \right]

D) 0

197

MediumJEE Mains2021

The decay of a proton to neutron is :

Options:

A) always possible as it is associated only with $\beta$ + decay

B) possible only inside the nucleus

C) not possible as proton mass is less than the neutron mass

D) not possible but neutron to proton conversation is possible

198

MediumJEE Mains2021

Imagine that the electron in a hydrogen atom is replaced by a muon ($\mu$). The mass of muon particle is 207 times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be :

Options:

A) 13.6 eV

B) 2815.2 eV

C) 331.2 eV

D) 27.2 eV

199

MediumJEE Mains2021

A radioactive sample disintegrates via two independent decay processes having half lives $T_{1/2}^{(1)} and T_{1/2}^{(2)}$ respectively. The effective half-life T 1/2 of the nuclei is :

Options:

A) None of the above

B) {T_{1/2}} = T_{1/2}^{(1)} + T_{1/2}^{(2)}

C) {T_{1/2}} = {{T_{1/2}^{(1)}T_{1/2}^{(2)}} \over {T_{1/2}^{(1)} + T_{1/2}^{(2)}}}

D) {T_{1/2}} = {{T_{1/2}^{(1)} + T_{1/2}^{(2)}} \over {T_{1/2}^{(1)} - T_{1/2}^{(2)}}}

200

EasyJEE Mains2021

The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region?

Options:

A) Brackett series

B) Balmer series

C) Paschen series

D) Lyman series

201

EasyJEE Mains2021

If an electron is moving in the n th orbit of the hydrogen atom, then its velocity (v n ) for the n th orbit is given as :

Options:

A) {v_n} \propto {1 \over n}

B) v n $ \propto $ n 2

C) v n $ \propto $ n

D) {v_n} \propto {1 \over {{n^2}}}

202

EasyJEE Mains2021

Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?

Options:

A) 8

B) 6

C) 1

D) 4

203

MediumJEE Mains2021

Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.

Options:

A) 40 minutes

B) 60 minutes

C) 13 minutes

D) 20 minutes

204

MediumJEE Mains2021

The half-life of Au 198 is 2.7 days. The activity of 1.50 mg of Au 198 if its atomic weight is 198 g mol $-1 is, (N a = 6 \times$ 10 23 /mol).

Options:

A) 240 Ci

B) 357 Ci

C) 252 Ci

D) 535 Ci

205

MediumJEE Mains2021

A radioactive sample is undergoing $\alpha decay. At any time t 1 , its activity is A and another time t 2 , the activity is {A \over 5}$. What is the average life time for the sample?

Options:

A) {{\ln 5} \over {{t_2} - {t_1}}}

B) {{\ln ({t_2} + {t_1})} \over 2}

C) {{{t_1} - {t_2}} \over {\ln 5}}

D) {{{t_2} - {t_1}} \over {\ln 5}}

206

MediumJEE Mains2021

If $\lambda 1 and \lambda 2 are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of \lambda 1 : \lambda$ 2 is :

Options:

A) 7 : 135

B) 7 : 108

C) 1 : 9

D) 1 : 3

207

EasyJEE Mains2021

The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n = 2 to n = 1 state is :

Options:

A) 194.8 nm

B) 490.7 nm

C) 913.3 nm

D) 121.8 nm

208

MediumJEE Mains2021

Two radioactive substances X and Y originally have N 1 and N 2 nuclei respectively. Half life of X is half of the half life of Y. After three half lives of Y, number of nuclei of both are equal. The ratio ${{{N_1}} \over {{N_2}}}$ will be equal to :

Options:

A) {1 \over 8}

B) {3 \over 1}

C) {1 \over 3}

D) {8 \over 1}

209

EasyJEE Mains2021

According to Bohr atomic model, in which of the following transitions will the frequency be maximum?

Options:

A) n = 2 to n = 1

B) n = 3 to n = 2

C) n = 4 to n = 3

D) n = 5 to n = 4

210

MediumJEE Mains2021

In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A, B, C, D and E. The transitions A, B and C respectively represent :

Options:

A) The series limit of Lyman series, second member of Balmer series and second member of Paschen series.

B) The ionization potential of hydrogen, second member of Balmer series and third member of Paschen series.

C) The series limit of Lyman series, third member of Balmer series and second member of Paschen series.

D) The first member of the Lyman series, third member of Balmer series and second member of Paschen series.

211

MediumJEE Mains2020

Given the masses of various atomic particles m p = 1.0072 u, m n = 1.0087 u, m e = 0.000548 u, ${m_{\overline v }} = 0, m d = 2.0141 u, where p \equiv proton, n \equiv neutron, e \equiv electron, \overline v \equiv antineutrino and d \equiv $ deuteron. Which of the following process is allowed by momentum and energy conservation?

Options:

A) n + n $ \to $ deuterium atom (electron bound to the nucleus)

B) n + p $ \to d + \gamma

C) p $ \to n + e + + \overline v

D) e + + e - $ \to \gamma

212

MediumJEE Mains2020

You are given that Mass of ${}_3^7Li = 7.0160u, Mass of {}_2^4He = 4.0026u and Mass of {}_1^1H = 1.0079u. When 20 g of {}_3^7Li is converted into {}_2^4He$ by proton capture, the energy liberated, (in kWh), is : [Mass of nucleon = 1 GeV/c 2 ]

Options:

A) 6.82 $ \times $ 10 5

B) 4.5 $ \times $ 10 5

C) 8 $ \times $ 10 6

D) 1.33 $ \times $ 10 6

213

MediumJEE Mains2020

A radioactive nucleus decays by two different processes. The half life for the first process is 10 s and that for the second is 100 s. The effective half life of the nucleus is close to :

Options:

A) 12 sec

B) 9 sec

C) 55 sec

D) 6 sec

214

MediumJEE Mains2020

Activities of three radioactive substances A, B and C are represented by the curves A, B and C, in the figure. Then their half-lives ${T_{{1 \over 2}}}\left( A \right) : {T_{{1 \over 2}}}\left( B \right) : {T_{{1 \over 2}}}\left( C \right)$ are in the ratio :

Options:

A) 3 : 2 : 1

B) 2 : 1 : 1

C) 4 : 3 : 1

D) 2 : 1 : 3

215

MediumJEE Mains2020

Find the Binding energy per neucleon for ${}_{50}^{120}Sn$. Mass of proton m p = 1.00783 U, mass of neutron m n = 1.00867 U and mass of tin nucleus m Sn = 119.902199 U. (take 1U = 931 MeV)

Options:

A) 9.0 MeV

B) 8.5 MeV

C) 8.0 MeV

D) 7.5 MeV

216

MediumJEE Mains2020

Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to :

Options:

A) 2 : 1

B) 1 : 2

C) 5 : 7

D) 10 : 7

217

MediumJEE Mains2020

The radius R of a nucleus of mass number A can be estimated by the formula R = (1.3 $ \times 10 –15 )A 1/3 m. It follows that the mass density of a nucleus is of the order of : (M prot. \cong M neut \simeq 1.67 \times $ 10 –27 kg)

Options:

A) 10 24 kg m –3

B) 10 10 kg m –3

C) 10 17 kg m –3

D) 10 3 kg m –3

218

MediumJEE Mains2020

In a radioactive material, fraction of active material remaining after time t is 9/16. The fraction that was remaining after t/2 is

Options:

A) {3 \over 4}

B) {4 \over 5}

C) {3 \over 5}

D) {7 \over 8}

219

MediumJEE Mains2020

In a hydrogen atom the electron makes a transition from (n + 1) th level to the n th level. If n >> 1, the frequency of radiation emitted is proportional to :

Options:

A) {1 \over n}

B) {1 \over {{n^2}}}

C) {1 \over {{n^3}}}

D) {1 \over {{n^4}}}

220

MediumJEE Mains2020

In a reactor, 2 kg of 92 U 235 fuel is fully used up in 30 days. The energy released per fission is 200 MeV. Given that the Avogadro number, N = 6.023 $ \times $ 10 26 per kilo mole and 1 eV = 1.6 × 10 –19 J. The power output of the reactor is close to

Options:

A) 125 MW

B) 60 MW

C) 54 MW

D) 35 MW

221

MediumJEE Mains2020

The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state ?

Options:

A) 35.8 nm

B) 11.4 nm

C) 8.6 nm

D) 24.2 nm

222

MediumJEE Mains2020

The graph which depicts the results of Rutherford gold foil experiment with $\alpha -particales is : \theta : Scattering angle Y : Number of scattered \alpha $-particles detected (Plots are schematic and not to scale)

Options:

223

MediumJEE Mains2020

The activity of a radioactive sample falls from 700 s –1 to 500 s –1 in 30 minutes. Its half life is close to:

Options:

A) 62 min

B) 66 min

C) 72 min

D) 52 min

224

MediumJEE Mains2020

The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 $ \times $ 10 -16 s. The frequency of revolution of the electron in its first excited state (in s -1 ) is :

Options:

A) 5.6 $ \times $ 10 12

B) 1.6 $ \times $ 10 14

C) 7.8 $ \times $ 10 14

D) 6.2 $ \times $ 10 15

225

MediumJEE Mains2019

Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively, If initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be :

Options:

A) 9 : 8

B) 1 : 8

C) 8 : 1

D) 3 : 8

226

MediumJEE Mains2019

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, ${{{\lambda _1}} \over {{\lambda _2}}}$, of the photons emitted in this process is :

Options:

A) {{22} \over 5}

B) {7 \over 5}

C) {9 \over 7}

D) {{20} \over 7}

227

MediumJEE Mains2019

Consider an electron in a hydrogen atom revolving in its second excited state (having radius 4.65 $\mathop A\limits^o $). The de-Broglie wavelength of this electron is :

Options:

A) 6.6 $\mathop A\limits^o

B) 3.5 $\mathop A\limits^o

C) 9.7 $\mathop A\limits^o

D) 12.9 $\mathop A\limits^o

228

MediumJEE Mains2019

An excited He + ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a transition to ground state. The quantum number n, corresponding to its initial excited state is (for photon of wavelength $\lambda , energy E = {{1240\,eV} \over {\lambda (in\,nm)}}$) :

Options:

A) n = 4

B) n = 7

C) n = 5

D) n = 6

229

MediumJEE Mains2019

In Li + + , electron in first Bohr orbit is excited to a level by a radiation of wavelength $\lambda . When the ion gets deexcited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines are observed. What is the value of \lambda $? (Given : H = 6.63 × 10 –34 Js; c = 3 × 10 8 ms –1 )

Options:

A) 10.8 nm

B) 12.3 nm

C) 9.4 nm

D) 11.4 nm

230

MediumJEE Mains2019

Two radioactive substances A and B have decay constants 5$\lambda and \lambda respectively. At t = 0, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become {\left( {{1 \over e}} \right)^2}$ will be :

Options:

A) {2 \over \lambda }

B) {1 \over {4\lambda }}

C) {1 \over {2\lambda }}

D) {1 \over {\lambda }}

231

MediumJEE Mains2019

Two radioactive materials A and B have decay constants 10$\lambda and \lambda $, respectively. It initially they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time :

Options:

A) 1/9$\lambda

B) 11/10$\lambda

C) 1/10$\lambda

D) 1/11$\lambda

232

MediumJEE Mains2019

A He + ion is in its first excited state. Its ionization energy is :-

Options:

A) 13.60 eV

B) 6.04 eV

C) 48.36 eV

D) 54.40 eV

233

MediumJEE Mains2019

Taking the wavelength of first Balmer line in hydrogen spectrum (n = 3 to n = 2) as 660 nm, the wavelength of the 2nd Balmer line (n = 4 to n = 2) will be :

Options:

A) 642.7 nm

B) 488.9 nm

C) 889.2 nm

D) 388.9 nm

234

MediumJEE Mains2019

The ratio of mass densities of nuclei of 40 Ca and 16 O is close to :-

Options:

A) 1

B) 5

C) 0.1

D) 2

235

MediumJEE Mains2019

Radiation coming from transitions n = 2 to n = 1 of hydrogen atoms fall on He + ions in n = 1 and n = 2 states. The possible transition of helium ions as they absorb energy from the radiation is :

Options:

A) n = 1 $ \to $ n = 4

B) n = 2 $ \to $ n = 5

C) n = 2 $ \to $ n = 4

D) n = 2 $ \to $ n = 3

236

MediumJEE Mains2019

In a radioactive decay chain, the initial nucleus is ${}_{90}^{232}Th. At the end there are 6 \alpha -particles and 4 \beta -particles which are emitted. If the end nucleus is {}_Z^A$X, A and Z are given by :

Options:

A) A = 208; Z = 80

B) A = 208; Z = 82

C) A = 200; Z = 81

D) A = 202; Z = 80

237

MediumJEE Mains2019

A particle of mass m moves in a circular orbit in a central potential field U(r) = ${1 \over 2}$ kr 2 . If Bohr 's quantization conditions are applied, radii of possible orbitls and energy levels vary with quantum number n as :

Options:

A) r n $ \propto \sqrt n , E n \propto $ n

B) r n $ \propto \sqrt n , E n \propto {1 \over n}

C) r n $ \propto n, E n \propto $ n

D) r n $ \propto n 2 , E n \propto {1 \over {{n^2}}}

238

MediumJEE Mains2019

In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is $\lambda $. If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation will be:

Options:

A) {{25} \over {16}} \lambda

B) {{27} \over {20}} \lambda

C) {{16} \over {25}} \lambda

D) {{20} \over {27}} \lambda

239

MediumJEE Mains2019

A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980$\mathop A\limits^ \circ . The radius of the atom in the excited state, in terms of Bohr radius a 0 will be : (hc = 12500 eV\mathop A\limits^ \circ $)

Options:

A) 4a 0

B) 9a 0

C) 25a 0

D) 16a 0

240

MediumJEE Mains2019

Consider the nuclear fission Ne 20 $ \to $ 2He 4 + C 12 Given that the binding energy/ nucleon of Ne 20 , He 4 and C 12 are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement -

Options:

A) 8.3 MeV energy will be released

B) energy of 11.9 MeV has to be supplied

C) energy of 12.4 MeV will be supplied

D) energy of 3.6 MeV will be released

241

MediumJEE Mains2019

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = 6 seconds is close to -

Options:

A) 200

B) 150

C) 400

D) 360

242

MediumJEE Mains2019

At a given instant, say t = 0, two radioactive substance A and B have equal activities. the ratio ${{{R_B}} \over {{R_A}}} of their activities after time t itself decays with time t as e -$3t . If the half-life of A is ln 2 , the half-life of B is :

Options:

A) 4ln2

B) {{\ln 2} \over 2}

C) {{\ln 2} \over 4}

D) 2ln2

243

MediumJEE Mains2019

A sample of radioactive material A, that has an activity of 10 mCi(1 Ci = 3.7 $ \times $ 10 10 decays/s), has twice the number of nuclei as another sample of a different radioactive materail B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be respectively :

Options:

A) 5 days and 10 days

B) 10 days and 40 days

C) 20 days and 5 days

D) 20 days and 10 days

244

MediumJEE Mains2018

At some instant, a radioactive sample S 1 having an activity 5 $\mu Ci has twice the number of nuclei as another sample S 2 which has an activity of 10 \mu $Ci. The half lives of S 1 and S 2 are :

Options:

A) 20 years and 5 years, respectively

B) 20 years and 10years, respectively

C) 5 years and 20 years, respectively

D) 10 years and 20 years, respectively

245

MediumJEE Mains2018

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let ${\lambda _n}, {\lambda _g} be the de Broglie wavelength of the electron in the n th state and the ground state respectively. Let {\Lambda _n}$ be the wavelength of the emitted photon in the transition from the n th state to the ground state. For large n, (A, B are constants)

Options:

A) {\Lambda _n} \approx A + {B \over {\lambda _n^2}}

B) {\Lambda _n} \approx A + B{\lambda _n}

C) \Lambda _n^2 \approx A + B\lambda _n^2

D) \Lambda _n^2 \approx \lambda

246

MediumJEE Mains2018

If the series limit frequency of the Lyman series is ${\nu _L}$, then the series limit frequency of the Pfund series is:

Options:

A) {\nu _L}/25

B) 25{\nu _L}

C) 16{\nu _L}

D) {\nu _L}/16

247

MediumJEE Mains2018

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is p d ; while for its similar collision with carbon nucleus at rest, fractional loss of energy is p c . The values of p d and p c are respectively :

Options:

A) (0, 1)

B) (0.89, 0.28)

C) (0.28, 0.89)

D) (0, 0)

248

MediumJEE Mains2018

Muon ($\mu - ) is a negatively charged (|q| = |e|) particle with a mass m \mu = 200 m e , where m e is the mass of the electron and e is the electronic charge. If \mu - is bond to a proton to form a hydrogen like atom, identify the correct statements. (A) Radis of the muonic orbit is 200 times smaller than that of the electron. (B) The speed of the \mu - in the n th orbit is {1 \over {200}}$ times that of the electron in the n th orbit. (C) The ionization energy of muonic atom is 200 timesmore than of an hydroen atom. (D) The momentum of the muon in the n th orbit is 200 times more than that of the electron.

Options:

A) (A), (B), (D)

B) (A), (C), (D)

C) (B), (D)

D) (C), (D)

249

MediumJEE Mains2018

An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei (assumed to be spherical) is :

Options:

A) 8 : 27

B) 4 : 9

C) 3 : 2

D) 2 : 3

250

MediumJEE Mains2018

The energy required to remove the electron from a singly ionized Helium atom is $2.2$ times the energies required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is :

Options:

A) 20 eV

B) 34 eV

C) 79 eV

D) 109 eV

251

MediumJEE Mains2018

A solution containing active cobalt ${^{60}_{27}}Co having activity of 0.8 \mu Ci and decay constant \lambda is injected in an animal's body. If 1\,c{m^3} of blood is drawn from the animal's body after 10 hrs of injection, the activity found was 300 decays per minute What is the volume of blood that is flowing in the body ? \left( {\,\,Ci = 3.7 \times {{10}^{10}}\,} \right. decays per second and at t=10 hrs \left. {{e^{ - \lambda t}} = 0.84} \right)

Options:

A) 6$ liters

B) 7$ liters

C) 4$ liters

D) 5$ liters

252

MediumJEE Mains2017

The acceleration of an electron in the first orbit of the hydrogen atom (n = 1) is :

Options:

A) {{{h^2}} \over {{\pi ^2}{m^2}{r^3}}}

B) {{{h^2}} \over {{8\pi ^2}{m^2}{r^3}}}

C) {{{h^2}} \over {{4\pi ^2}{m^2}{r^3}}}

D) {{{h^2}} \over {{4\pi }{m^2}{r^3}}}

253

MediumJEE Mains2017

Imagine that a reactor converts all given mass into energy and that it operates at a power level of 10 9 watt. The mass of the fuel consumed per hour in the reactor will be : (velocity of light, c is 3×10 8 m/s)

Options:

A) 0.96 gm

B) 0.8 gm

C) 4 $ \times 10 -$2 gm

D) 6.6 $ \times 10 -$5 gm

254

MediumJEE Mains2017

Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is : (given binding energy per nucleon for deuteron = 1.1 MeV and for helium = 7.0 MeV)

Options:

A) 30.2 MeV

B) 32.4 MeV

C) 23.6 MeV

D) 25.8 MeV

255

MediumJEE Mains2017

According to Bohr’s theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the n th orbit is proportional to : (n = principal quantum number)

Options:

A) {n^{ - 4}}

B) {n^{ - 5}}

C) n $-$3

D) n $-$2

256

MediumJEE Mains2017

A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by :

Options:

A) t = {T \over {\log (1.3)}}

B) t = T\log (1.3)

C) t = {T \over 2}{{\log 2} \over {\log 1.3}}

D) t = T{{\log 1.3} \over {\log 2}}

257

MediumJEE Mains2017

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = ${{\lambda _1}}/{{\lambda _2}}$, is given by:

Options:

A) r = 1/3

B) r = 4/3

C) r = 2/3

D) r = 3/4

258

MediumJEE Mains2016

A hydrogen atom makes a transition from n = 2 to n = 1 and emits a photon. This photon strikes a doubly ionized lithium atom (z = 3) in excited state and completely removes the orbiting electron. The least quantum number for the excited state of the ion for the process is :

Options:

A) 2

B) 3

C) 4

D) 5

259

MediumJEE Mains2016

Half-lives of two radioactive elements $A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed number of A and B$ nuclei will be:

Options:

A) 1:4

B) 5:4

C) 1:16

D) 4:1

260

MediumJEE Mains2015

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :

Options:

A) kinetic energy decreases, potential energy increases but total energy remains same

B) kinetic energy and total energy decrease but potential energy increases

C) its kinetic energy increases but potential energy and total energy decrease

D) kinetic energy, potential energy and total energy decrease

261

MediumJEE Mains2014

The radiation corresponding to $3 \to 2 transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field 3 \times {10^{ - 4}}\,T. If the radius of the larger circular path followed by these electrons is 10.0 mm$, the work function of the metal is close to:

Options:

A) 1.8 eV

B) 1.1 eV

C) 0.8 eV

D) 1.6 eV

262

MediumJEE Mains2014

Hydrogen $\left( {{}_1{H^1}} \right), Deuterium \left( {{}_1{H^2}} \right), singly ionised Helium {\left( {{}_2H{e^4}} \right)^ + } and doubly ionised lithium {\left( {{}_3L{i^6}} \right)^{ + + }} all have one electron around the nucleus. Consider an electron transition from n=2 to n=1. If the wavelengths of emitted radiation are {\lambda _1},{\lambda _2},{\lambda _3} and {\lambda _4}$ respectively then approximately which one of the following is correct?

Options:

A) 4{\lambda _1} = 2{\lambda _2} = 2{\lambda _3} = {\lambda _4}

B) {\lambda _1} = 2{\lambda _2} = 2{\lambda _3} = {\lambda _4}

C) {\lambda _1} = {\lambda _2} = 4{\lambda _3} = 9{\lambda _4}

D) {\lambda _1} = 2{\lambda _2} = 3{\lambda _3} = 4{\lambda _4}

263

MediumJEE Mains2013

In a hydrogen like atom electron make transition from an energy level with quantum number $n to another with quantum number \left( {n - 1} \right). If n > > 1,$ the frequency of radiation emitted is proportional to :

Options:

A) {1 \over n}

B) {1 \over {{n^2}}}

C) {1 \over {{n^{{3 \over 2}}}}}

D) {1 \over {{n^3}}}

264

MediumJEE Mains2012

Assume that a neutron breaks into a proton and an electron. The energy released during this process is : (mass of neutron $ = 1.6725 \times {10^{ - 27}}kg, mass of proton = 1.6725 \times {10^{ - 27}}\,kg, mass of electron = 9 \times {10^{ - 31}}\,kg$ ).

Options:

A) 0.51 MeV

B) 7.10\,MeV

C) 6.30\,MeV

D) 5.4\,MeV

265

MediumJEE Mains2012

A diatomic molecule is made of two masses ${m_1} and {m_2} which are separated by a distance r. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by: (n$ is an integer)

Options:

A) {{{{\left( {{m_1} + {m_2}} \right)}^2}{n^2}{h^2}} \over {2m_1^2m_2^2{r^2}}}

B) {{{n^2}{h^2}} \over {2\left( {{m_1} + {m_2}} \right){r^2}}}

C) {{2{n^2}{h^2}} \over {\left( {{m_1} + {m_2}} \right){r^2}}}

D) {{\left( {{m_1} + {m_2}} \right){n^2}{h^2}} \over {2{m_1}{m_2}{r^2}}}

266

MediumJEE Mains2012

Hydrogen atom is excited from ground state to another state with principal quantum number equal to $4.$ Then the number of spectral lines in the emission spectra will be :

Options:

A) 2

B) 3

C) 5

D) 6

267

MediumJEE Mains2011

Energy required for the electron excitation in $L{i^{ + + }}$ from the first to the third Bohr orbit is :

Options:

A) 36.3 eV

B) 108.8 eV

C) 122.4 eV

D) 12.1 eV

268

MediumJEE Mains2011

The half life of a radioactive substance is $20 minutes. The approximate time interval \left( {{t_2} - {t_1}} \right) between the time {{t_2}} when {2 \over 3} of it had decayed and time {{t_1}} when {1 \over 3}$ of it had decayed is :

Options:

A) 14$ min

B) 20$ min

C) 28$ min

D) 7$ min

269

MediumJEE Mains2010

A nucleus of mass $M+\Delta m is at rest and decays into two daughter nuclei of equal mass {M \over 2} each. Speed of light is c. The binding energy per nucleon for the parent nucleus is {E_1} and that for the daughter nuclei is {E_2}.$ Then

Options:

A) {E_2} = 2{E_1}

B) {E_1} > {E_2}

C) {E_2} > {E_1}

D) {E_1} = 2{E_2}

270

MediumJEE Mains2010

A radioactive nucleus (initial mass number $A and atomic number Z emits 3\,\alpha - particles and 2$ positrons. The ratio of number of neutrons to that of protons in the final nucleus will be

Options:

A) {{A - Z - 8} \over {Z - 4}}

B) {{A - Z - 4} \over {Z - 8}}

C) {{A - Z - 12} \over {Z - 4}}

D) {{A - Z - 4} \over {Z - 2}}

271

MediumJEE Mains2010

A nucleus of mass $M+\Delta m is at rest and decays into two daughter nuclei of equal mass {M \over 2} each. Speed of light is c.$ The speed of daughter nuclei is

Options:

A) c{{\Delta m} \over {M + \Delta m}}

B) c\sqrt {{{2\Delta m} \over M}}

C) c\sqrt {{{\Delta m} \over M}}

D) c\sqrt {{{\Delta m} \over {M + \Delta m}}}

272

MediumJEE Mains2009

The transition from the state $n=4 to n=3$ in a hydrogen like atom result in ultra violet radiation. Infrared radiation will be obtained in the transition from :

Options:

A) 3 \to 2

B) 4 \to 2

C) 5 \to 4

D) 2 \to 1

273

MediumJEE Mains2009

The above is a plot of binding energy per nucleon ${E_b}, against the nuclear mass M;A,B,C,D,E,F correspond to different nuclei. Consider four reactions : \eqalign{ & \left( i \right)\,\,\,\,\,\,\,\,\,\,A + B \to C + \varepsilon \,\,\,\,\,\,\,\,\,\,\left( {ii} \right)\,\,\,\,\,\,\,\,\,\,C \to A + B + \varepsilon \,\,\,\,\,\,\,\,\,\, \cr & \left( {iii} \right)\,\,\,\,\,\,D + E \to F + \varepsilon \,\,\,\,\,\,\,\,\,\,\left( {iv} \right)\,\,\,\,\,\,\,\,\,F \to D + E + \varepsilon ,\,\,\,\,\,\,\,\,\,\, \cr} where \varepsilon is the energy released? In which reactions is \varepsilon $ positive?

Options:

A) (i) and (iii)

B) (ii) and (iv)

C) (ii) and (iii)

D) (i) and (iv)

274

MediumJEE Mains2008

This question contains Statement- 1 and Statement- 2. Of the four choices given after the statements, choose the one that best describes the two statements: Statement- 1: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion and Statement- 2: For heavy nuclei, binding energy per nucleon increases with increasing $Z while for light nuclei it decreases with increasing Z.

Options:

A) Statement - $1 is false, Statement - 2$ is true

B) Statement - $1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1

C) Statement - $1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1

D) Statement - $1 is true, Statement - 2$ is false

275

MediumJEE Mains2008

Suppose an electron is attracted towards the origin by a force ${k \over r} where 'k' is a constant and 'r' is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the {n^{th}} orbital of the electron is found to be '{r_n}' and the kinetic energy of the electron to be '{T_n}'.$ Then which of the following is true?

Options:

A) {T_n} \propto {1 \over {{n^2}}},{r_n} \propto {n^2}

B) {T_n} independent of n,{r_n} \propto n

C) {T_n} \propto {1 \over n},{r_n} \propto n

D) {T_n} \propto {1 \over n},{r_n} \propto {n^2}

276

MediumJEE Mains2007

The half-life period of a ratio-active element $X is same as the mean life time of another ratio-active element Y.$ Initially they have the same number of atoms. Then

Options:

A) X and Y$ decay at same rate always

B) X will decay faster than Y

C) Y will decay faster than X

D) X and Y$ have same decay rate initially

277

MediumJEE Mains2007

Which of the following transitions in hydrogen atoms emit photons of highest frequency ?

Options:

A) n = 1 to n=2

B) n = 2 to n=6

C) n = 6 to n=2

D) n = 2 to n=1

278

MediumJEE Mains2007

In gamma ray emission from a nucleus

Options:

A) only the proton number changes

B) both the neutron number and the proton number change

C) there is no change in the proton number and the neutron number

D) only the neutron number changes

279

MediumJEE Mains2007

If ${M_O} is the mass of an oxygen isotope {}_8{O^{17}} , {M_p} and {M_N}$ are the masses of a proton and neutron respectively, the nuclear binding energy of the isotope is

Options:

A) \left( {{M_O} - 17{M_N}} \right){C^2}

B) \left( {{M_O} - 8{M_P}} \right){C^2}

C) \left( {{M_O} - 8{M_P} - 9{M_N}} \right){C^2}

D) {{M_O}{c^2}}

280

MediumJEE Mains2006

An alpha nucleus of energy ${1 \over 2}m{v^2} bombards a heavy nuclear target of charge Ze$. Then the distance of closest approach for the alpha nucleus will be proportional to

Options:

A) {v^2}

B) {1 \over m}

C) {1 \over {{v^2}}}

D) {1 \over {Ze}}

281

MediumJEE Mains2006

The energy spectrum of $\beta -particles [ number N(E) as a function of \beta -energy E$ ] emitted from a radioactive source is

Options:

282

MediumJEE Mains2006

The $'rad'$ is the correct unit used to report the measurement of

Options:

A) the ability of a beam of gamma ray photons to produce ions in a target

B) the energy delivered by radiation to a target

C) the biological effect of radiation

D) the rate of decay of radioactive source

283

MediumJEE Mains2006

When ${}_3L{i^7} nuclei are bombarded by protons, and the resultant nuclei are {}_4B{e^8}$, the emitted particles will be

Options:

A) alpha particles

B) beta particles

C) gamma photons

D) neutrons

284

MediumJEE Mains2006

If the binding energy per nucleon in ${}_3^7Li and {}_2^4He nuclei are 5.60 MeV and 7.06 MeV respectively, then in the reaction p + {}_3^7Li \to 2\,{}_2^4He$$ energy of proton must be

Options:

A) 28.24 MeV

B) 17.28 MeV

C) 1.46 MeV

D) 39.2 MeV

285

MediumJEE Mains2005

The intensity of gamma radiation from a given source is $L. On passing through 36 mm of lead, it is reduced to {{\rm I} \over 8}. The thickness of lead which will reduce the intensity to {{\rm I} \over 2}$ will be

Options:

A) 9mm

B) 6mm

C) 12mm

D) 18mm

286

MediumJEE Mains2005

The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?

Options:

A) iv

B) iii

C) ii

D) i

287

MediumJEE Mains2005

Starting with a sample of pure ${}^{66}Cu,{7 \over 8} of it decays into Zn in 15$ minutes. The corresponding half life is

Options:

A) 15$ minutes

B) 10$ minutes

C) 7{1 \over 2}$ minutes

D) 5$ minutes

288

MediumJEE Mains2005

A nuclear transformation is denoted by $X\left( {n,\alpha } \right)\matrix{ 7 \cr 3 \cr } Li. Which of the following is the nucleus of element X$ ?

Options:

A) {}_5^{10}B

B) {}^{12}{C_6}

C) {}_4^{11}Be

D) {}_5^9B

289

MediumJEE Mains2005

If radius of the $\matrix{ {27} \cr {13} \cr } Al nucleus is estimated to be 3.6 fermi then the radius of \matrix{ {125} \cr {52} \cr } \,Te$ nucleus is estimated to be nearly

Options:

A) 8$ fermi

B) 6$ fermi

C) 5$ fermi

D) 4$ fermi

290

MediumJEE Mains2004

A nucleus disintegrated into two nuclear parts which have their velocities in the ratio of $2:1.$ The ratio of their nuclear sizes will be

Options:

A) {3^{{\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}}}:1

B) 1:{2^{1/3}}

C) {2^{1/3}}:1

D) 1:{3^{{\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}}}

291

MediumJEE Mains2004

The binding energy per nucleon of deuteron $\left( {{}_1^2\,H} \right) and helium nucleus \left( {{}_2^4\,He} \right) is 1.1 MeV and 7 MeV$ respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is

Options:

A) 23.6\,\,MeV

B) 26.9\,\,MeV

C) 13.9\,\,MeV

D) 19.2\,\,MeV

292

MediumJEE Mains2004

An $\alpha -particle of energy 5 MeV is scattered through {180^ \circ }$ by a fixed uranium nucleus. The distance of closest approach is of the order of

Options:

A) {10^{ - 12}}\,cm

B) {10^{ - 10}}\,cm

C) 1A

D) {10^{ - 15a}}\,cm

293

MediumJEE Mains2003

In the nuclear fusion reaction $${}_1^2H + {}_1^3H \to {}_2^4He + n given that the repulsive potential energy between the two nuclei is \sim 7.7 \times {10^{ - 14}}J, the temperature at which the gases must be heated to initiate the reaction is nearly [ Boltzmann's Constant k = 1.38 \times {10^{ - 23}}\,J/K$ ]

Options:

A) {10^7}\,\,K

B) {10^5}\,\,K

C) {10^3}\,\,K

D) {10^9}\,\,K

294

MediumJEE Mains2003

Which of the following cannot be emitted by radioactive substances during their decay ?

Options:

A) Protons

B) Neutrinoes

C) Helium nuclei

D) Electrons

295

MediumJEE Mains2003

A radioactive sample at any instant has its disintegration rate $5000 disintegrations per minute. After 5 minutes, the rate is 1250$ disintegrations per minute. Then, the decay constant (per minute) is

Options:

A) 0.4 ln2

B) 0.2 ln2

C) 0.1 ln2

D) 0.8 ln2

296

MediumJEE Mains2003

If the binding energy of the electron in a hydrogen atom is $13.6eV, the energy required to remove the electron from the first excited state of L{i^{ + + }}$ is

Options:

A) 30.6 eV

B) 13.6 eV

C) 3.4 eV

D) 122.4 eV

297

MediumJEE Mains2003

Which of the following atoms has the lowest ionization potential ?

Options:

A) {}_7^{14}N

B) {}_{55}^{133}\,Cs

C) {}_{18}^{40}\,Ar

D) {}_8^{16}\,O

298

MediumJEE Mains2003

Which of the following radiations has the least wavelength ?

Options:

A) \gamma $ - rays

B) \beta $ - rays

C) \alpha $ - rays

D) X$ - rays

299

MediumJEE Mains2003

The wavelengths involved in the spectrum of deuterium $\left( {{}_1^2\,D} \right)$ are slightly different from that of hydrogen spectrum, because

Options:

A) the size of the two nuclei are different

B) the nuclear forces are different in the two cases

C) the masses of the two nuclei are different

D) the attraction between the electron and the nucleus is different in the two cases

300

MediumJEE Mains2003

A nucleus with $Z=92 emits the following in a sequence: \alpha ,{\beta ^ - },{\beta ^ - },\alpha ,\alpha ,\alpha ,\alpha ,\alpha ,{\beta ^ - },{\beta ^ - },\alpha ,{\beta ^ + },{\beta ^ + },\alpha Then Z$ of the resulting nucleus is

Options:

A) 76

B) 78

C) 82

D) 74

301

MediumJEE Mains2003

When a ${U^{238}} nucleus originally at rest, decays by emitting an alpha particle having a speed 'u',$ the recoil speed of the residual nucleus is

Options:

A) {{4\mu } \over {238}}

B) - {{4\mu } \over {234}}

C) {{4\mu } \over {234}}

D) - {{4\mu } \over {238}}

302

MediumJEE Mains2002

At a specific instant emission of radioactive compound is deflected in a magnetic field. The compound can emit $\eqalign{ & \left( i \right)\,\,\,\,\,\,\,electrons\,\,\,\,\,\,\,\,\,\,\,\,\left( {ii} \right)\,\,\,\,\,\,\,protons \cr & \left( {iii} \right)\,\,\,H{e^{2 + }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {iv} \right)\,\,\,\,\,\,\,neutrons \cr} $ The emission at instant can be

Options:

A) i, ii, iii

B) i, ii, iii, iv

C) iv

D) ii, iii

303

MediumJEE Mains2002

If $13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n=2$ is

Options:

A) 10.2 eV

B) 0 eV

C) 3.4 eV

Options:

A) 4

B) 2

C) \frac{1}{2}

D) \frac{1}{4}

368

MediumMHT CET2025

The magnetic moment of electron due to orbital motion is proportional to ( \mathrm{n}= principal quantum number)

Options:

A) n

B) n^2

C) \frac{1}{n}

D) \frac{1}{\mathrm{n}^2}

369

MediumMHT CET2025

The frequencies for series limit of Balmer and Paschen series are ' \mathrm{V}_1 ' and ' \mathrm{V}_3 ' respectively. If frequency of first line of Balmer series ' \mathrm{V}_2 ' then the relation between V_1, V_2 and V_3 is

Options:

A) \mathrm{v}_1-\mathrm{v}_3=2 \mathrm{v}_1

B) v_1+v_2=v_3

C) \mathrm{v}_1-\mathrm{v}_2=\mathrm{v}_3

D) v_1+v_3=v_2

370

MediumMHT CET2025

A radio active element has rate of disintegration 8000 disintegrations per minute at a particular instant. After four minutes it becomes 2000 disintegrations per minute. The decay constant per minute is

Options:

A) 0.8 \log _{\mathrm{e}} 2

B) 0.6 \log _{\mathrm{e}} 2

C) 0.5 \log _{\mathrm{e}} 2

D) 0.2 \log _{\mathrm{e}} 2

371

MediumMHT CET2025

In Paschen series, wavelength of first line is ' \lambda_1 ' and for Brackett series, wavelength of first line is ' \lambda_2 ' then ratio \frac{\lambda_1}{\lambda_2} is

Options:

A) \frac{7}{400}

B) \frac{9}{144}

C) \frac{81}{175}

D) \frac{108}{509}

372

MediumMHT CET2025

The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) third to 2^{\text {nd }} energy level and (ii) highest energy level to 3^{\text {rd }} level is

Options:

A) 3: 2

B) 5: 4

C) 5: 3

D) 8: 3

373

MediumMHT CET2025

In hydrogen atom in its ground state, the first Bohr orbit has radius ' \mathrm{r}_1 '. When the atom is raised to one of its excited states, the electrons orbital velocity becomes one-third. The radius of that orbit is

Options:

A) 2 r_1

B) 3 r_1

C) 4 r_1

D) 9 r_1

374

MediumMHT CET2025

A radioactive element has rate of disintegration 9000 disintegration per minute at a particular instant. After two minutes it becomes 3000 disintegration per minute. The decay constant per minute is

Options:

A) 0.5 \log _{\mathrm{c}} 3

B) 0.2 \log _{\mathrm{e}} 3

C) 0.5 \log _{\mathrm{e}} 2

D) 0.2 \log _{\mathrm{e}} 2

375

MediumMHT CET2025

In hydrogen atom, transition from the state \mathrm{n}=6 to n=1 results in ultraviolet radiation. Infrared radiation will be obtained in the transition

Options:

A) \mathrm{n}=3 to \mathrm{n}=1

B) \mathrm{n}=4 to \mathrm{n}=2

C) n=6 to n=2

D) n=5 to n=3

376

MediumMHT CET2025

A radioactive element { }_{92}^{242} \mathrm{X} emits two \alpha particles, one electron and two positrons. The product nucleus is represented by { }_{\mathrm{p}}^{234} \mathrm{Y}. The value of P is

Options:

A) 87

B) 85

C) 92

D) 96

377

MediumMHT CET2025

The activity of radioactive sample is measured as \mathrm{N}_0 counts per minute at time \mathrm{t}=0, and \frac{\mathrm{N}_0}{\mathrm{e}} counts per minute at time \mathrm{t}=3 minute, The activity reduces to half its value in time (in minute)

Options:

A) \frac{1}{3} \log _{\mathrm{e}} 2

B) 3 \log _{\mathrm{e}} 2

C) 3 \log _{10} 2

D) \frac{3}{\log _{10} 2}

378

MediumMHT CET2025

In hydrogen atom, the energy of electron in first and third orbit is ' E_1 ' and' E_3 ' respectively. If E_3=x E_1 then the value of x will be

Options:

A) \frac{1}{9}

B) \frac{1}{64}

C) \frac{1}{27}

D) \frac{1}{8}

379

MediumMHT CET2025

A radioactive element A decays into radioactive element C by the following processes in succession. \mathrm{A} \rightarrow \mathrm{B}+{ }_2 \mathrm{H}_{\mathrm{e}}^4 ; \mathrm{B} \rightarrow \mathrm{C}+2 \mathrm{e}^{-}Then elements

Options:

A) A and B are isobars.

B) A and C are isobars.

C) A and C are isotopes.

D) A and B are isotopes.

380

MediumMHT CET2025

{ }_{88} \mathrm{R}_{\mathrm{a}}^{226} is converted into { }_{82} \mathrm{P}_{\mathrm{b}}^{206} by emission of alpha ( \alpha ) and beta ( \beta ) particles. The number of alpha and beta particles emitted are respectively

Options:

A) 5, 4

B) 4, 5

C) 6, 4

D) 4, 6

381

MediumMHT CET2025

Out of the following transitions in hydrogen atom, identify the transition which emits photons of highest frequency.

Options:

A) \mathrm{n}=1 to \mathrm{n}=2

B) \mathrm{n}=2 to \mathrm{n}=1

C) n=2 to n=6

D) n=6 to n=2

382

MediumMHT CET2025

Using Bohr's quantization condition, the rotational kinetic energy in the third orbit for a diatomic molecule is ( h= Planck's constant, \mathrm{I}= moment of inertia of diatomic molecule)

Options:

A) \frac{9 h^2}{8 \pi^2 I}

B) \frac{3 \mathrm{~h}^2}{8 \pi^2 \mathrm{I}}

C) \frac{6 h^2}{8 \pi I}

D) \frac{12 h^2}{7 \pi^2 I}

383

MediumMHT CET2025

Which of the following transitions in hydrogen atom emit photons of highest frequency? ( \mathrm{n}= principle quantum number)

Options:

A) \mathrm{n}=1 to \mathrm{n}=3

B) \mathrm{n}=2 to \mathrm{n}=4

C) \mathrm{n}=5 to \mathrm{n}=3

D) \mathrm{n}=2 to \mathrm{n}=1

384

MediumMHT CET2025

Two radioactive materials A and B having decay constant ' 7 \lambda ' and ' \lambda ' respectively, initially have same number of nuclei. The time taken to have the ratio of number of nuclei of material B to that of A as ' e ' is

Options:

A) \frac{1}{\lambda}

B) \frac{1}{6 \lambda}

C) \frac{1}{7 \lambda}

D) \frac{1}{8 \lambda}

385

MediumMHT CET2025

The ratio of angular momentum of an electron in \mathrm{n}^{\text {th }} orbit of hydrogen atom to the velocity of electron in \mathrm{n}^{\text {th }} orbit is proportional to

Options:

A) \mathrm{n}^2

B) \frac{1}{\mathrm{n}^2}

C) \mathrm{n}^3

D) \frac{1}{\mathrm{n}^3}

386

MediumMHT CET2025

In hydrogen atom spectrum, when an electron jumps from second excited state to the first excited state, the wavelength of radiation emitted is ' \lambda '. If the electron jumps from the third excited state to the second orbit, the wavelength of radiation emitted will be \frac{20 \lambda}{x}. The value of x is

Options:

A) 18

B) 27

C) 21

D) 36

387

MediumMHT CET2025

In hydrogen spectrum, the ratio of wavelengths of the last line of Lyman series and that of the last line of Balmer series is

Options:

A) 1

B) 0.5

C) 0.25

D) 0.2

388

MediumMHT CET2025

\begin{aligned} &\text { For the following reaction, the particle ' } \mathrm{x} \text { ' is }{ }_6 \mathrm{C}^{11}\longrightarrow{ }_5 \mathrm{~B}^{11}+\beta+\mathrm{X} \end{aligned}

Options:

A) proton

B) neutrino

C) anti neutrino

D) neutron

389

MediumMHT CET2025

The frequency of revolution of an electron in the \mathrm{n}^{\text {th }} orbit of hydrogen atom is

Options:

A) directly proportional to n^2

B) inversely proportional to \mathrm{n}^2

C) directly proportional to n^3

D) inversely proportional to \mathrm{n}^3

390

MediumMHT CET2025

If ' \lambda_1 ' and ' \lambda_2 ' are the wavelengths of the first member of the Balmer and Paschen series, in hydrogen atom respectively, then the ratio of respective frequencies, f_1 / f_2, is

Options:

A) 20: 7

B) 27: 5

C) 50: 9

D) 108: 7

391

MediumMHT CET2025

The ratio of the wavelength of the last line of Paschen series to that of Balmer series is

Options:

A) \frac{9}{4}

B) \frac{3}{2}

C) \frac{2}{3}

D) \frac{4}{9}

392

MediumMHT CET2024

In the second orbit of hydrogen atom, the energy of an electron is ' E '. In the third orbit of helium atom, the energy of the electron will be (atomic number of helium =2)

Options:

A) \frac{4 \mathrm{E}}{9}

B) \frac{4 \mathrm{E}}{3}

C) \frac{16 \mathrm{E}}{9}

D) \frac{16 \mathrm{E}}{3}

393

MediumMHT CET2024

Two radioactive substances A and B have decay constants ' 5 \lambda ' and ' \lambda ' respectively. At \mathrm{t}=0, they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be \left(\frac{1}{\mathrm{e}}\right)^2 after a time interval

Options:

A) \frac{1}{42}

B) 4 \lambda

C) 2 \lambda

D) \frac{1}{2 \lambda}

394

MediumMHT CET2024

In \mathrm{M}_{\mathrm{O}} is the mass of an oxygen isotope { }_8 \mathrm{O}^{17} and \mathrm{M}_{\mathrm{p}} and \mathrm{M}_{\mathrm{N}} are the mass of proton and mass of neutron respectively, then the nucleus binding energy of the isotope is

Options:

A) \mathrm{M}_{\mathrm{o}} \mathrm{C}^2

B) \left(\mathrm{M}_{\mathrm{o}}-8 \mathrm{M}_{\mathrm{P}}\right) \mathrm{C}^2

C) \mathrm{\left(M_o-17 M_N\right) C^2}

D) \left(\mathrm{M}_{\mathrm{o}}-8 \mathrm{M}_{\mathrm{P}}-9 \mathrm{M}_{\mathrm{N}}\right) \mathrm{C}^2

395

MediumMHT CET2024

When an electron orbiting in hydrogen atom in its ground state jumps to higher excited state, the de-Broglie wavelength associated with it

Options:

A) will become zero.

B) will remain same.

C) will decrease.

D) will increase.

396

MediumMHT CET2024

Frequency of the series limit of Balmer series of hydrogen atom of Rydberg's constant ' R ' and velocity of light ' C ' is

Options:

A) \frac{\mathrm{RC}}{4}

B) RC

C) \frac{4}{\mathrm{RC}}

D) 4 RC

397

MediumMHT CET2024

Acceleration of an electron in the first Bohr's orbit is proportional to \mathrm{m}= mass of electron, \mathrm{r}= radius of the orbit, \mathrm{h}= Planck's constant)

Options:

A) \frac{\mathrm{m}^3 \mathrm{r}^3}{\mathrm{~h}^2}

B) \frac{h^2}{m^2 r^3}

C) \frac{\mathrm{h}^2}{\mathrm{mr}^3}

D) \frac{\mathrm{mr}^3}{\mathrm{~h}^2}

398

MediumMHT CET2024

In the given reaction ${ }_z \mathrm{X}^A \rightarrow{ }_{z+1} \mathrm{Y}^A \rightarrow{ }_{z-1} \mathrm{~K}^{A-4} \rightarrow{ }_{z-1} \mathrm{~K}^{\mathrm{A}-4}$ radioactive radiations are emitted in the sequence

Options:

A) \alpha, \beta, \gamma

B) \beta, \alpha, \gamma

C) \gamma, \alpha, \beta

D) \beta, \gamma, \alpha

399

MediumMHT CET2024

A radioactive substance has half-life of 60 minute. During 3 hour, the amount of substance decayed would be

Options:

A) 8.5 \%

B) 25 \%

C) 12.5 \%

D) 87.5 \%

400

MediumMHT CET2024

The ratio of the areas of the electron orbits for the second excited state to the first excited state for the hydrogen atom is

Options:

A) 3: 2

B) 9: 4

C) 16: 81

D) 81: 16

401

MediumMHT CET2024

In a hydrogen atom in its ground state, the first Bohr orbit has radius r_1. The electron's orbital speed becomes one-third when the atom is raised to one of its excited states. The radius of the orbit in that excited state is

Options:

A) 3 r_1

B) 4 r_1

C) 9 \pi_1

D) 16 \mathrm{r}_1

402

MediumMHT CET2024

The angular momentum of the electron in the third Bohr orbit of hydrogen atom is ' l '. Its angular momentum in the fourth Bohr orbit is

Options:

A) 4 l

B) \frac{4}{3} l

C) \frac{5}{4} l

D) \frac{3}{2} l

403

MediumMHT CET2024

The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (a) second to first energy level and (b) highest energy level to second level is

Options:

A) 1: 3

B) 1: 2

C) 3: 1

D) 4: 1

404

MediumMHT CET2024

If 'T' is the half life of a radioactive substance then its instantaneous rate of change of activity is proportional to

Options:

A) T

B) T^{-2}

C) T^{+2}

D) T^{-1}

405

MediumMHT CET2024

Radius of first orbit in H -atom is ' a_0 ' Then, de-Broglie wavelength of electron in the third orbit is

Options:

A) 3 \pi \mathrm{a}_0

B) 6 \pi \mathrm{a}_0

C) 9 \pi \mathrm{a}_0

D) 12 \pi \mathrm{a}_0

406

MediumMHT CET2024

In the Bohr model of hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If ' r_0 ' is the radius of the ground state orbit, ' m ' is the mass, ' e ' is the charge on the electron and ' \varepsilon_0 ' is the permittivity of vacuum, the speed of the electron is

Options:

A) zero

B) \frac{\mathrm{e}}{\sqrt{\varepsilon_0 \mathrm{r}_0 \mathrm{~m}}}

C) \frac{\mathrm{e}}{\sqrt{4 \pi \varepsilon_0 \mathrm{r}_0 \mathrm{~m}}}

D) \frac{\sqrt{4 \pi \varepsilon_0 \mathrm{r}_0 \mathrm{~m}}}{\mathrm{e}}

407

MediumMHT CET2024

If the ionisation energy for the hydrogen atom is 13.6 eV , then the energy required to excite it from the ground state to the next higher state is nearly

Options:

A) 10.2 eV

B) 13.6 eV

C) -10.2 eV

D) -3.4 eV

408

MediumMHT CET2024

Using Bohr's model, the orbital period of electron in hydrogen atom in \mathrm{n}^{\text {th }} orbit is ( \mathrm{m}= mass of electron, \mathrm{h}= Planck's constant, \mathrm{e}= electronic charge, \varepsilon_0= permittivity of free space)

Options:

A) \frac{2 \varepsilon_0^2 n^2 h^2}{m e^4}

B) \frac{4 \varepsilon_0^2 \mathrm{n}^2 \mathrm{~h}^2}{\mathrm{me}^2}

C) \frac{4 \varepsilon_0^2 \mathrm{n}^3 \mathrm{~h}^3}{\mathrm{me}^4}

D) \frac{4 \varepsilon_0 \mathrm{n}^2 \mathrm{~h}^2}{\pi \mathrm{me}^2}

409

MediumMHT CET2024

The spectral series observed for hydrogen atom found in visible region is

Options:

A) Lyman

B) Balmer

C) Paschen

D) Brackett

410

MediumMHT CET2024

In hydrogen atom, if \mathrm{V}_{\mathrm{n}} and \mathrm{V}_{\mathrm{p}} are orbital velocities in \mathrm{n}^{\text {th }} and \mathrm{p}^{\text {th }} orbit respectively, then the ratio \mathrm{V}_{\mathrm{p}}: \mathrm{V}_{\mathrm{n}} is

Options:

A) \mathrm{p}: \mathrm{n}

B) \mathrm{n}: \mathrm{p}

C) \mathrm{p}^2: \mathrm{n}^2

D) \mathrm{n}^2: \mathrm{p}^2

411

MediumMHT CET2024

When a hydrogen atom is raised from the ground state to the excited state

Options:

A) potential energy increases and K.E. decreases.

B) potential energy decreases and K.E. increases.

C) both K.E. and potential energy will increase.

D) both K.E. and potential energy decreases.

412

MediumMHT CET2024

In hydrogen atom, ratio of the shortest wavelength in the Balmer series to that in the Paschen series is

Options:

A) 9: 4

B) 3: 1

C) 4: 9

D) 1: 3

413

MediumMHT CET2024

According to Bohr's theory of hydrogen atom, the ratio of the maximum and minimum wavelength of Lyman series will be

Options:

A) 3: 4

B) 4: 3

C) 2: 5

D) 5: 2

414

MediumMHT CET2024

The ratio of minimum wavelengths of Lyman and Balmer series will be

Options:

A) 1.25

B) 0.25

C) 5

D) 10

415

MediumMHT CET2024

Half-lives of two radioactive elements A and B are 30 minute and 60 minute respectively. Initially the samples have equal number of nuclei. After 120 minute the ratio of decayed numbers of nuclei of B to that of A will be

Options:

A) 1: 15

B) 1: 4

C) 4: 5

D) 5: 4

416

MediumMHT CET2024

For hydrogen atom, ' \lambda_1 ' and ' \lambda_2 ' are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of ' \lambda_1 ' and ' \lambda_2 ' is \frac{x}{32}. The value of ' x ' is

Options:

A) 3

B) 9

C) 27

D) 81

417

MediumMHT CET2024

The ratio of the radius of the first Bohr orbit to that of the second Bohr orbit of the orbital electron is

Options:

A) 4: 1

B) 2: 1

C) 1: 4

D) 1: 2

418

MediumMHT CET2024

A diatomic molecule has moment of inertia ' I ', By applying Bohr's quantization condition, its rotational energy in the \mathrm{n}^{\text {th }} level is [\mathrm{n} \geq 1] [h= Planck's constant]

Options:

A) \frac{1}{\mathrm{n}^2}\left(\frac{\mathrm{~h}^2}{8 \pi^2 \mathrm{I}}\right)

B) \frac{1}{\mathrm{n}}\left(\frac{\mathrm{h}^2}{8 \pi^2 \mathrm{I}}\right)

C) n\left(\frac{h^2}{8 \pi^2 \mathrm{I}}\right)

D) \mathrm{n}^2\left(\frac{\mathrm{~h}^2}{8 \pi^2 \mathrm{I}}\right)

419

MediumMHT CET2024

In the uranium radioactive series, the initial nucleus is { }_{92}^{238} \mathrm{U} and that the final nucleus is { }_{82}^{206} \mathrm{~Pb}. When uranium nucleus decays into lead, the number of \alpha-particles and \beta-particles emitted are

Options:

A) 4 \alpha, 5 \beta

B) 5 \alpha, 3 \beta

C) 6 \alpha, 7 \beta

D) 8 \alpha, 6 \beta

420

MediumMHT CET2024

If ' \lambda_1 ' and ' \lambda_2 ' are the wavelengths of the first line of the Lyman and Paschen series respectively, then \lambda_2: \lambda_1 is

Options:

A) 3: 1

B) 30: 1

C) 50: 7

D) 108: 7

421

MediumMHT CET2024

An electron of stationary Hydrogen atom passes from fifth energy level to ground level. The velocity that the atom acquired as a result of photo emission is ( \mathrm{m}= mass of electron, \mathrm{R}= Rydberg's constant) ( \mathrm{h}= Planck's constant)

Options:

A) \frac{24 \mathrm{Rh}}{25 \mathrm{~m}}

B) \frac{25 \mathrm{Rh}}{24 \mathrm{~m}}

C) \frac{25 \mathrm{~m}}{24 \mathrm{Rh}}

D) \frac{24 \mathrm{~m}}{25 \mathrm{Rh}}

422

MediumMHT CET2024

Which of the following statements about the Bohr model of the hydrogen atom is false?

Options:

A) Acceleration of electron in \mathrm{n}=2 orbit is less than that in n=1 orbit.

B) Angular momentum of electron in \mathrm{n}=2 orbit is more than that in n=1 orbit.

C) Kinetic energy of electron in \mathrm{n}=2 orbit is less than that in \mathrm{n}=1 orbit.

D) Potential energy of electron in \mathrm{n}=2 orbit is less than that in n=1 orbit.

423

MediumMHT CET2024

The radius of innermost orbit of hydrogen atom is 5.3 \times 10^{-11} \mathrm{~m}. The radius of fourth allowed orbit of hydrogen atom is

Options:

A) 8.48 $\mathop A\limits^o

B) 2.12 $\mathop A\limits^o

C) 4.77 $\mathop A\limits^o

D) 0.53 $\mathop A\limits^o

424

MediumMHT CET2024

In the third orbit of hydrogen atom the energy of an electron ' E '. In the fifth orbit of helium (Z=2) the energy of an electron will be

Options:

A) \frac{25 \mathrm{E}}{36}

B) \frac{36 \mathrm{E}}{25}

C) \frac{3 \mathrm{E}}{5}

D) \frac{5 \mathrm{E}}{3}

425

MediumMHT CET2023

Ratio of longest wavelength corresponding to Lyman and Balmer series in hydrogen spectrum is

Options:

A) \frac{7}{29}

B) \frac{9}{31}

C) \frac{5}{27}

D) \frac{3}{23}

426

MediumMHT CET2023

Half life of radio-active element is 1600 years. The fraction of sample remains undecayed after 6400 years will be

Options:

A) \frac{1}{16}

B) \frac{1}{4}

C) \frac{1}{8}

D) \frac{1}{24}

427

MediumMHT CET2023

Frequency of the series limit of Balmer series of hydrogen atom in terms of Rydberg's constant (R) and velocity of light (c) is

Options:

A) 4 \mathrm{Rc}

B) \frac{4}{\mathrm{Rc}}

C) \mathrm{Rc}

D) \frac{\mathrm{Rc}}{4}

428

MediumMHT CET2023

If the radius of the first Bohr orbit is '$r' then the de-Broglie wavelength of the electron in the 4^{\text {th }}$ orbit will be

Options:

A) 4 \pi \mathrm{r}

B) 6 \pi \mathrm{r}

C) 8 \pi \mathrm{r}

D) \frac{\pi r}{4}

429

MediumMHT CET2023

Magnetic field at the centre of the hydrogen atom due to motion of electron in $\mathrm{n}^{\text {th }}$ orbit is proportional to

Options:

A) \mathrm{n}^4

B) \mathrm{n}^{-3}

C) n^3

D) \mathrm{n}^{-5}

430

MediumMHT CET2023

An excited hydrogen atom emits a photon of wavelength $\lambda in returning to ground state. The quantum number n of the excited state is (R=$ Rydberg's constant)

Options:

A) \sqrt{\lambda R(\lambda R-1)}

B) \sqrt{\frac{\lambda R}{(\lambda R-1)}}

C) \sqrt{\frac{(\lambda R-1)}{\lambda R}}

D) \sqrt{\frac{1}{\lambda R(\lambda R-1)}}

431

MediumMHT CET2023

When an electron is excited from its 4 th orbit to 5 th stationary orbit, the change in the angular momentum of electron is approximately. (Planck's constant $=h=6.63 \times 10^{-34} \mathrm{~J}-\mathrm{s}$ )

Options:

A) 2 \times 10^{-34} \mathrm{~J}-\mathrm{s}

B) 6.63 \times 10^{-34} \mathrm{~J}-\mathrm{s}

C) 1 \times 10^{-34} \mathrm{~J}-\mathrm{s}

D) 3.14 \times 10^{-34} \mathrm{~J}-\mathrm{s}

432

MediumMHT CET2023

A radioactive sample has half-life of 5 years. The percentage of fraction decayed in 10 years will be

Options:

A) 25%

B) 50%

C) 75%

D) 100%

433

MediumMHT CET2023

An isotope of the original nucleus can be formed in a radioactive decay, with the emission of following particles.

Options:

A) one $\alpha and one \beta

B) one $\alpha and two \beta

C) one $\alpha and four \beta

D) four $\alpha and one \beta

434

MediumMHT CET2023

Two different radioactive elements with half lives '$\mathrm{T}_1' and '\mathrm{T}_2' have undecayed atoms '\mathrm{N}_1' and '\mathrm{N}_2$' respectively present at a given instant. The ratio of their activities at that instant is

Options:

A) \frac{\mathrm{N}_1 \mathrm{~T}_1}{\mathrm{~N}_2 \mathrm{~T}_2}

B) \frac{\mathrm{N}_2 \mathrm{~T}_2}{\mathrm{~N}_1 \mathrm{~T}_1}

C) \frac{\mathrm{N}_1 \mathrm{~T}_2}{\mathrm{~N}_2 \mathrm{~T}_1}

D) \frac{\mathrm{N}_1 \mathrm{~N}_2}{\mathrm{~T}_1 \mathrm{~T}_2}

435

MediumMHT CET2023

In Balmer series, wavelength of the $2^{\text {nd }} line is '\lambda_1' and for Paschen series, wavelength of the 1^{\text {st }} line is '\lambda_2', then the ratio '\lambda_1' to '\lambda_2$' is

Options:

A) 5: 128

B) 5: 81

C) 7: 27

D) 9: 132

436

MediumMHT CET2023

In Lyman series, series limit of wavelength is $\lambda_1. The wavelength of first line of Lyman series is \lambda_2 and in Balmer series, the series limit of wavelength is \lambda_3. Then the relation between \lambda_1, \lambda_2 and \lambda_3$ is

Options:

A) \lambda_1=\lambda_2+\lambda_3

B) \lambda_2=\lambda_1+\lambda_3

C) \frac{1}{\lambda_1}=\frac{1}{\lambda_2}-\frac{1}{\lambda_3}

D) \frac{1}{\lambda_1}-\frac{1}{\lambda_2}=\frac{1}{\lambda_3}

437

MediumMHT CET2023

The wavelength of radiation emitted is '$\lambda_0' when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be \frac{20}{x} \lambda_0. The value of x$ is

Options:

A) 3

B) 9

C) 13

D) 27

438

MediumMHT CET2023

According to Bohr's theory of hydrogen atom, the total energy of the electron in the $\mathrm{n}^{\text {th }}$ stationary orbit is

Options:

A) directly proportional to $n

B) inversely proportional to $n

C) directly proportional to $\mathrm{n}^2

D) inversely proportional to $\mathrm{n}^2

439

MediumMHT CET2023

Bohr model is applied to a particle of mass '$\mathrm{m}' and charge '\mathrm{q}' moving in a plane under the influence of a transverse magnetic field 'B'. The energy of the charged particle in the \mathrm{n}^{\text {th }} leve will be [\mathrm{h}= Planck's constant ]

Options:

A) \frac{n h q B}{4 \pi \mathrm{m}}

B) \frac{n h q B}{2 \pi m}

C) \frac{\text { nhqB }}{\pi \mathrm{m}}

D) \frac{2 \mathrm{nhqB}}{\pi \mathrm{m}}

440

MediumMHT CET2023

The orbital magnetic moment associated with orbiting electron of charge '$e$' is

Options:

A) inversely proportional to angular momentum

B) directly proportional to mass of electron

C) directly proportional to angular momentum

D) inversely proportional to charge on electron

441

MediumMHT CET2023

An electron in the hydrogen atom jumps from the first excited state to the ground state. What will be the percentage change in the speed of electron?

Options:

A) 25%

B) 50%

C) 75%

D) 100%

442

MediumMHT CET2023

In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at time $t=\frac{1}{2 \lambda} is [\lambda=$ decay constant]

Options:

A) \frac{1}{\mathrm{e}}

B) \sqrt{\mathrm{e}}

C) e

D) 2e

443

MediumMHT CET2023

The ratio of the velocity of the electron in the first Bohr orbit to that in the second Bohr orbit of hydrogen atom is

Options:

A) 8: 1

B) 2: 1

C) 4: 1

D) 1: 4

444

MediumMHT CET2023

The shortest wavelength in the Balmer series of hydrogen atom is equal to the shortest wavelength in the Brackett series of a hydrogen like atom of atomic number $\mathrm{z}. The value of \mathrm{z}$ is

Options:

A) 2

B) 3

C) 4

D) 6

445

MediumMHT CET2023

The ratio of longest to shortest wavelength emitted in Paschen series of hydrogen atom is

Options:

A) \frac{144}{63}

B) \frac{25}{9}

C) \frac{9}{25}

D) \frac{63}{144}

446

MediumMHT CET2023

The force acting on the electron in hydrogen atom (Bohr' theory) is related to the principle quantum number '$n$' as

Options:

A) \mathrm{n}^4

B) \mathrm{n}^{-4}

C) \mathrm{n}^2

D) \mathrm{n}^{-2}

447

MediumMHT CET2023

The wavelength of light for the least energetic photons emitted in the Lyman series of the hydrogen spectrum is nearly [Take $\mathrm{hc}=1240 ~\mathrm{eV} - \mathrm{nm}, change in energy of the levels =10.2 ~\mathrm{eV}$ ]

Options:

A) 150 \mathrm{~nm}

B) 122 \mathrm{~nm}

C) 102 \mathrm{~nm}

D) 82 \mathrm{~nm}

448

MediumMHT CET2023

The ratio of wavelengths for transition of electrons from $2^{\text {nd }} orbit to 1^{\text {st }} orbit of Helium \left(\mathrm{He}^{++}\right) and Lithium \left(\mathrm{Li}^{++1}\right) is (Atomic number of Helium =2, Atomic number of Lithium =3$ )

Options:

A) 9: 4

B) 9: 36

C) 4: 9

D) 2: 3

449

MediumMHT CET2023

For an electron moving in the $\mathrm{n}^{\text {th }}$ Bohr orbit the deBroglie wavelength of an electron is

Options:

A) \mathrm{n} \pi \mathrm{r}

B) \frac{\pi r}{\mathrm{n}}

C) \frac{\mathrm{nr}}{2 \pi}

D) \frac{2 \pi r}{\mathrm{n}}

450

MediumMHT CET2023

If an electron in a hydrogen atom jumps from an orbit of level $n=3 to orbit of level n=2$, then the emitted radiation frequency is (where R = Rydberg's constant, C = Velocity of light)

Options:

A) \frac{3 \mathrm{RC}}{27}

B) \frac{\mathrm{RC}}{25}

C) \frac{8 \mathrm{RC}}{9}

D) \frac{5 \mathrm{RC}}{36}

451

MediumMHT CET2022

Using Bohr's model, the orbital period of electron in hydrogen atom in the $\mathrm{n}^{\text {th }} orbit is \left(\varepsilon_0=\right. permittivity of vacuum, \mathrm{h}= Planck's constant, \mathrm{m}= mass of electron, \mathrm{e}=$ electronic charge)

Options:

A) \frac{4 \varepsilon_0 \mathrm{nh}^3}{\mathrm{me}^2}

B) \frac{4 \varepsilon_0 \mathrm{n}^2 \mathrm{~h}^2}{\mathrm{me}^2}

C) \frac{4 \varepsilon_0^2 n^3 h^3}{m e^4}

D) \frac{4 \varepsilon_0^2 \mathrm{n}^2 \mathrm{~h}^3}{m \mathrm{e}^3}

452

MediumMHT CET2022

The wave number of the last line of the Balmer series in hydrogen spectrum will be (Rydberg's constant $=10^7 \mathrm{~m}^{-1}$ )

Options:

A) 250 \mathrm{~m}^{-1}

B) 2.5 \times 10^6 \mathrm{~m}^{-1}

C) 0.25 \times 10^9 \mathrm{~m}^{-1}

D) 2.5 \times 10^5 \mathrm{~m}^{-1}

453

MediumMHT CET2021

The half life of a radioactive substance is 30 minute. The time taken between 40% decay and 85% decay of the same radioactive substance is

Options:

A) 15 minute

B) 90 minute

C) 60 minute

D) 30 minute

454

MediumMHT CET2021

The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) second to first energy level and (ii) highest energy level to second energy level is

Options:

A) 6:1

B) 3: 1

C) 12: 1

D) 8: 1

455

MediumMHT CET2021

An electron makes a transition from an excited state to the ground state of a hydrogen like atom. Out of the following statements which one is correct?

Options:

A) Kinetic energy, potential energy and total energy decreases

B) Kinetic energy and total energy decreased but potential energy increases

C) Kinetic energy increases but potential energy and total energy decreases

D) Kinetic energy decreases, potential energy increases but total energy remains the same.

456

MediumMHT CET2021

The ratio of maximum to minimum wavelength in Balmer series of hydrogen atom is

Options:

A) 36 : 5

B) 3 : 4

C) 9 : 5

D) 5 : 9

457

MediumMHT CET2021

Energy of electron in the second orbit of hydrogen atom is $\mathrm{E}. The energy of electron '\mathrm{E}_3' in the third orbit of helium (\mathrm{He})$ atom will be

Options:

A) \mathrm{E}_3=\frac{4 \mathrm{E}}{9}

B) \mathrm{E}_3=\frac{16 \mathrm{E}}{3}

C) \mathrm{E}_3=\frac{16 \mathrm{E}}{9}

D) \mathrm{E}_3=\frac{4 \mathrm{E}}{3}

458

MediumMHT CET2021

The shortest wavelength for Lyman series is 912 $\mathop A\limits^o $. The longest wavelength in Paschen series is

Options:

A) 1216 $\mathop A\limits^o

B) 3646 $\mathop A\limits^o

C) 18760 $\mathop A\limits^o

D) 8208 $\mathop A\limits^o

459

MediumMHT CET2021

In the Bohr model, an electron moves in a circular orbit around the nucleus. Considering an orbiting electron to be a circular current loop, the magnetic moment of the hydrogen atom, when the electron is in nth excited state, is (e = electronic charge, m$_e$ = mass of the electron, h = Planck's constant)

Options:

A) \left(\frac{\mathrm{e}}{\mathrm{m}_{\mathrm{e}}}\right) \frac{\mathrm{nh}}{2 \pi}

B) \mathrm{\left(\frac{e}{m_e}\right) \frac{n^2 h}{2 \pi}}

C) \mathrm{\left(\frac{e}{2 m_e}\right) \frac{n^2 h}{2 \pi}}

D) \left(\frac{\mathrm{e}}{2 \mathrm{~m}_{\mathrm{e}}}\right) \frac{\mathrm{nh}}{2 \pi}

460

MediumMHT CET2021

The energy of an electron in the excited hydrogen atom is $-3.4 \mathrm{~eV}. Then according to Bohr's theory, the angular momentum of the electron in that excited state is (\mathrm{h}=$ Plank's constant)

Options:

A) \frac{2 \pi}{h}

B) \frac{\mathrm{nh}}{2 \pi}

C) \frac{\mathrm{h}}{\pi}

D) \frac{3 \mathrm{~h}}{2 \pi}

461

MediumMHT CET2021

In $n^{\text {th }}$ Bohr orbit, the ratio of the kinetic energy of an electron to the total energy of it, is

Options:

A) 2: 1

B) 1:-1

C) +1: 1

D) -1: 2

462

MediumMHT CET2021

If '$E' and 'L' denote the magnitude of total energy and angular momentum of revolving electron in \mathrm{n}^{\text {th }}$ Bohr orbit, then

Options:

A) \mathrm{E} \propto \mathrm{L}^{-1}

B) \mathrm{E} \propto \mathrm{L}

C) \mathrm{E} \propto \mathrm{L}^{-2}

D) \mathrm{E} \propto \mathrm{L}^2

463

MediumMHT CET2021

Two radioactive materials $X_1 and X_2 have decay constants '5 \lambda' and '\lambda' respectively. Initially, they have the same number of nuclei. After time 't', the ratio of number of nuclei of X_1 to that of \mathrm{X}_2 is \frac{1}{\mathrm{e}}. Then \mathrm{t}$ is equal to

Options:

A) \frac{\lambda}{2}

B) \frac{\mathrm{e}}{\lambda}

C) \lambda

D) \frac{1}{4 \lambda}

464

MediumMHT CET2021

A nucleus breaks into two nuclear parts, which have their velocity ratio $2: 1$. The ratio of their nuclear radii will be

Options:

A) \sqrt{2}

B) \frac{1}{2}

C) \frac{1}{2^{1 / 3}}

D) \frac{1}{\sqrt{2}}

465

MediumMHT CET2021

Ratio centripetal acceleration for an electron revolving in 3 rd and 5 th Bohr orbit of hydrogen atom is

Options:

A) 425 : 18

B) 625 : 81

C) 125 : 27

D) 221 : 36

466

MediumMHT CET2021

When an electron in hydrogen atom jumps from third excited state to the ground state, the de-Broglie wavelength associated with the electron becomes

Options:

A) \left(\frac{1}{2}\right)^{\text {th }}

B) \left(\frac{1}{4}\right)^{\text {th }}

C) \left(\frac{1}{8}\right)^{\text {th }}

D) \left(\frac{1}{6}\right)^{\text {th }}

467

MediumMHT CET2021

'$\lambda_1' is the wavelength of series limit of Lyman series, '\lambda_2' is the wavelength of the first line line of Lyman series and '\lambda_3' is the series limit of the Balmer series. Then the relation between \lambda_1, \lambda_2 and \lambda_3$ is

Options:

A) \frac{1}{\lambda_1}-\frac{1}{\lambda_2}=\frac{1}{\lambda_3}

B) \frac{1}{\lambda_1}=\frac{1}{\lambda_2}-\frac{1}{\lambda_3}

C) \lambda_2=\lambda_1+\lambda_3

D) \lambda_1=\lambda_2+\lambda_3

468

MediumMHT CET2021

A sample of radioactive element contains $8 \times 10^{16}$ active nuclei. The halt-life of the element is 15 days. The number of nuclei decayed after 60 days is

Options:

A) 7.5 \times 10^{16}

B) 2.0 \times 10^{16}

C) 0.5 \times 10^{16}

D) 4.0 \times 10^{16}

469

MediumMHT CET2021

The P.E. 'U' of a moving particle of mass 'm' varies with 'x'-axis as shown in figure. The deBroglie wavelength or the particle in the regions $0 \leq x \leq 1 and x > 1 are \lambda_1 and \lambda_2 respectively. II the total energy of the particle is '\mathrm{nE}', then the ratio \lambda_1 / \lambda_2$ is

Options:

A) \sqrt{\frac{n^2}{n-1}}

B) \sqrt{\frac{n-1}{n}}

C) \sqrt{\frac{\mathrm{n}}{\mathrm{n}-1}}

D) \sqrt{\frac{\mathrm{n}(\mathrm{n}-1)}{\mathrm{n}}}

470

MediumMHT CET2021

The gyromagnetic ratio of an electron in an hydrogen atom, according to Bohr model is

Options:

A) decreases with the quantum number 'n'.

B) independent of which orbit it is in.

C) negative

D) positive

471

MediumMHT CET2021

The electron in hydrogen atom is initially in the third excited state. When it finally moves to ground state, the maximum number of spectral lines emitted are

Options:

A) 3

B) 4

C) 5

D) 6

472

MediumMHT CET2021

If the electron in a hydrogen atom moves from ground state orbit to 5 th orbit, then the potential energy of the electron

Options:

A) is increased

B) is zero

C) is decreased

D) remains unchanged

473

MediumMHT CET2020

The energy levels with transitions for the atom are shown. The transitions corresponding to emission of radiation of maximum and minimum wavelength are respectively

Options:

A) B, C

B) A, C

C) C, D

D) A, D

474

MediumMHT CET2020

Using Bohr's model, the orbital period of electron in hydrogen atom in nth orbit is ( \varepsilon_0= permittivity of free space, h= Planck's constant, m= mass of electron and \theta= electronic charge)

Options:

A) \frac{2 \varepsilon_0^2 n^3 h^3}{m e^4}

B) \frac{8 \varepsilon_0^2 n^3 h^3}{m e^4}

C) \frac{2 \varepsilon_0 n^2 h^2}{m e^4}

D) \frac{4 \varepsilon_0^2 n^3 h^3}{m e^4}

475

MediumMHT CET2020

A radioactive nucleus emits $4 \alpha-particles and 7 \beta-particles in succession. The ratio of number of neutrons of that of protons, is [A= mass number, Z=$ atomic number]

Options:

A) \frac{A-Z-13}{Z-2}

B) \frac{A-Z-15}{Z-1}

C) \frac{A-Z-13}{Z-1}

D) \frac{A-Z-11}{Z-2}

476

MediumMHT CET2020

The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) second to first energy level and (ii) highest energy level to second level is respectively

Options:

A) 2.5: 1

B) 3: 1

C) 2: 1

D) 4: 1

477

MediumMHT CET2020

Using Bohr's quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule? ($I= moment of inertia of diatomic molecule and, h=$ Planck's constant)

Options:

A) \frac{h}{2 I \pi^2}

B) \frac{h^2}{2 I \pi^2}

C) \frac{h^2}{2 I^2 \pi^2}

D) \frac{h}{2 I^2 \pi}

478

MediumMHT CET2020

The ratio of speed of an electron in the ground state in the Bohr's first orbit of hydrogen atom to velocity of light $(c) is ( h= Planck's constant, \varepsilon_0= permittivity of free space, e=$ charge on electron)

Options:

A) \frac{2 \theta^2 \varepsilon_0}{h c}

B) \frac{e^3}{2 \varepsilon_0 h c}

C) \frac{e^2}{2 \varepsilon_0 h c}

D) \frac{2 \varepsilon_0 h c}{e^2}

479

MediumMHT CET2020

The force acting on the electrons in hydrogen atom (Bohr's theory) is related to the principle quantum number $n$ as

Options:

A) n^{-4}

B) n^4

C) n^{-2}

D) n^2

480

MediumMHT CET2019

If the speed of an electron of hydrogen atom in the ground state is 2.2 \times 10^6 \mathrm{~m} / \mathrm{s}, then its speed in the third excited state will be

Options:

A) 5.5 \times 10^6 \mathrm{~m} / \mathrm{s}

B) 5.5 \times 10^5 \mathrm{~m} / \mathrm{s}

C) 8.8 \times 10^5 \mathrm{~m} / \mathrm{s}

D) 6.8 \times 10^6 \mathrm{~m} / \mathrm{s}

481

MediumMHT CET2019

In hydrogen emission spectrum, for any series, the principal quantum number is n. Corresponding maximum wavelength \lambda is ( R= Rydberg's constant)

Options:

A) \frac{R(2 n+1)}{n^2(n+1)}

B) \frac{n^2(n+1)^2}{R(2 n+1)}

C) \frac{n^2(n+1)}{R(2 n+1)}

D) \frac{R(2 n+1)}{n^2(n+1)^2}

482

MediumMHT CET2019

When the electron in hydrogen atom jumps from fourth Bohr orbit to second Bohr orbit, one gets the

Options:

A) second line of Balmer series

B) first line of Balmer series

C) first line of Pfund series

D) second line of Paschen series

483

MediumMHT CET2019

In Balmer series, wavelength of first line is ' \lambda_1 ' and in Brackett series wavelength of first line is ' \lambda_2 ' then \frac{\lambda_1}{\lambda_2} is

Options:

A) 0.162

B) 0.124

C) 0.138

D) 0.188

484

MediumMHT CET2019

Bohr model is applied to a particle of mass ' m ' and charge ' q ' is moving in a plane under the influence of a transverse magnetic field ' B '. The energy of the charged particle in the nth level will be ( h= Planck's constant)

Options:

A) 2 n h q B / \pi \mathrm{m}

B) n h q B / 2 \pi \mathrm{~m}

C) n h q B / 4 \pi \mathrm{~m}

D) n h q B / \pi \mathrm{m}

485

MediumMHT CET2019

The angle made by orbital angular momentum of electron with the direction of the orbital magnetic moment is

Options:

A) 120^{\circ}

B) 60^{\circ}

C) 180^{\circ}

D) 90^{\circ}

486

MediumMHT CET2019

The wavelength of the first line in Balmer series in the hydrogen spectrum is ' \lambda '. What is the wavelength of the second line in the same series?

Options:

A) \frac{20}{27} \lambda

B) \frac{3}{16} \lambda

C) \frac{5}{36} \lambda

D) \frac{3}{4} \lambda

487

HardNEET2025

A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If Bohr model is used to describe its motion, the radius of the n^{\text {th }} orbit and the particle's speed v in the orbit depend on n as

Options:

A) r \propto n^{2 / 3} ; v \propto n^{1 / 3}

B) r \propto n^{4 / 3} ; v \propto n^{-1 / 3}

C) r \propto n^{1 / 3} ; v \propto n^{1 / 3}

D) r \propto n^{1 / 3} ; v \propto n^{2 / 3}

488

MediumNEET2024

The spectral series which corresponds to the electronic transition from the levels $n_2=5,6, \ldots to the level n_1=4$ is

Options:

A) Pfund series

B) Brackett series

C) Lyman series

D) Balmer series

489

MediumNEET2024

Water is used as a coolant in a nuclear reactor because of its

Options:

A) high thermal expansion coefficient

B) high specific heat capacity

C) low density

D) low boiling point

490

MediumNEET2024

Some energy levels of a molecule are shown in the figure with their wavelengths of transitions. Then :

Options:

A) \lambda_3>\lambda_2, \lambda_1=2 \lambda_2

B) \lambda_3>\lambda_2, \lambda_1=4 \lambda_2

C) \lambda_1>\lambda_2, \lambda_2=2 \lambda_3

D) \lambda_2>\lambda_1, \lambda_2=2 \lambda_3

491

MediumNEET2024

Select the correct statements among the following : A. Slow neutrons can cause fission in ${ }_{92}^{235} \mathrm{U} than fast neutrons. B. \alpha-rays are Helium nuclei. C. \beta-rays are fast moving electrons or positrons. D. \gamma-rays are electromagnetic radiations of wavelengths larger than \mathrm{X}$-rays. Choose the most appropriate answer from the options given below :

Options:

A) A, B and C only

B) A, B and D only

C) A and B only

D) C and D only

492

MediumNEET2024

Given below are two statements: Statement I: Atoms are electrically neutral as they contain equal number of positive and negative charges. Statement II: Atoms of each element are stable and emit their characteristic spectrum. In the light of the above statements, choose the most appropriate answer from the options given below.

Options:

A) Both Statement I and Statement II are correct

B) Both Statement I and Statement II are incorrect

C) Statement I is correct but Statement II is incorrect

D) Statement I is incorrect but Statement II is correct

493

MediumNEET2024

Match List I with List II: List I (Spectral Lines of Hydrogen for transitions from) List II (Wavelengths (nm)) A. $ n_2=3 \text { to } n_1=2 I. 410.2 B. n_2=4 \text { to } n_1=2 II. 434.1 C. n_2=5 \text { to } n_1=2 III. 656.3 D. n_2=6 \text { to } n_1=2 $ IV. 486.1 Choose the correct answer from the options given below:

Options:

A) A-II, B-I, C-IV, D-III

B) A-III, B-IV, C-II, D-I

C) A-IV, B-III, C-I, D-II

D) A-I, B-II, C-III, D-IV

494

MediumNEET2024

{ }_{82}^{290} X \xrightarrow{\alpha} Y \xrightarrow{e^{+}} Z \xrightarrow{\beta^{-}} P \xrightarrow{e^{-}} Q In the nuclear emission stated above, the mass number and atomic number of the product Q$ respectively, are

Options:

A) 280, 81

B) 286, 80

C) 288, 82

D) 286, 81

495

MediumNEET2023

The ground state energy of hydrogen atom is $-13.6 ~\mathrm{eV}$. The energy needed to ionize hydrogen atom from its second excited state will be :

Options:

A) 13.6 ~\mathrm{eV}

B) 6.8 ~\mathrm{eV}

C) 1.51 ~\mathrm{eV}

D) 3.4 ~\mathrm{eV}

496

MediumNEET2023

The wavelength of Lyman series of hydrogen atom appears in:

Options:

A) visible region

B) far infrared region

C) ultraviolet region

D) infrared region

497

MediumNEET2023

The angular momentum of an electron moving in an orbit of hydrogen atom is $\mathrm{1.5\left(\frac{h}{\pi}\right)}$. The energy in the same orbit is nearly.

Options:

A) -1.5$ eV

B) -1.6$ eV

C) -1.3$ eV

D) -1.4$ eV

498

MediumNEET2023

The half life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to $\left(\frac{1}{16}\right)^{\text {th }}$ of its initial value?

Options:

A) 40 minutes

B) 60 minutes

C) 80 minutes

D) 20 minutes

499

MediumNEET2023

In hydrogen spectrum, the shortest wavelength in the Balmer series is $\lambda$. The shortest wavelength in the Bracket series is :

Options:

A) 4 \lambda

B) 9 \lambda

C) 16 \lambda

D) 2 \lambda

500

MediumNEET2023

The radius of inner most orbit of hydrogen atom is $5.3 \times 10^{-11} \mathrm{~m}$. What is the radius of third allowed orbit of hydrogen atom?

Options:

A) 1.06 $\mathop A\limits^o

B) 1.59 $\mathop A\limits^o

C) 4.77 $\mathop A\limits^o

D) 0.53 $\mathop A\limits^o

501

MediumNEET2022

Let R 1 be the radius of the second stationary orbit and R 2 be the radius of the fourth stationary orbit of an electron in Bohr's model. The ratio ${{{R_1}} \over {{R_2}}}$ is :

Options:

A) 4

B) 0.25

C) 0.5

D) 2

502

MediumNEET2022

Given below are two statements Statement I : The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is inversely proportional to the total number of nuclei in the sample. Statement II : The half of a radionuclide is the sum of the life time of all nuclei, divided by the initial concentration of the nuclei at time t = 0. In the light of the above statements, choose the most appropriate answer from the options given below :

Options:

A) Statement I is incorrect but statement II is correct

B) Both statement I and statement II are correct

C) Both statement I and statement II are incorrect

D) Statement I is correct but statement II is incorrect

503

MediumNEET2022

At any instant, two elements X 1 and X 2 have same number of radioactive atoms. If the decay constant of X 1 and X 2 are 10 $\lambda and \lambda respectively, then the time when the ratio of their atoms becomes {1 \over e}$ respectively will be :

Options:

A) {1 \over {5\lambda }}

B) {1 \over {11\lambda }}

C) {1 \over {9\lambda }}

D) {1 \over {6\lambda }}

504

MediumNEET2022

The ratio of Coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is 2.4 $\times 10 39 . The ratio of the proportionality constant, K = {1 \over {4\pi {\varepsilon _0}}} to the gravitational constant G is nearly (Given that the charge of the proton and electron each = 1.6 \times 10 -19 C, the mass of the electron = 9.11 \times 10 -31 kg, the mass of the proton = 1.67 \times 10 -$27 kg) :

Options:

A) 10

B) 10 20

C) 10 30

D) 10 40

505

MediumNEET2022

The graph which shows the variation of the de Broglie wavelength ($\lambda$) of a particle and its associated momentum (p) is

Options:

506

MediumNEET2022

In the given nuclear reaction, the element X is ${}_{11}^{22}Na \to X + {e^ + } + v

Options:

A) {}_{11}^{23}Na

B) {}_{10}^{23}Ne

C) {}_{10}^{22}Ne

D) {}_{12}^{22}Mg

507

MediumNEET2022

Let T 1 and T 2 be the energy of an electron in the first and second excited states of hydrogen atoms, respectively. According to the Bohr's model of an atom, the ratio T 1 : T 2 is

Options:

A) 1 : 4

B) 4 : 1

C) 4 : 9

D) 9 : 4

508

MediumNEET2022

A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is

Options:

A) 1 : 1

B) 4 : 5

C) 5 : 4

D) 25 : 16

509

MediumNEET2021

A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding per nucleon of unfragmented nuclei is 7.6MeV while that of fragments is 8.5MeV. The total gain in the Binding Energy in the process is :

Options:

A) 216MeV

B) 0.9MeV

C) 9.4MeV

D) 804MeV

510

MediumNEET2021

The half life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be :

Options:

A) {2 \over {3\sqrt 2 }}

B) {1 \over 2}

C) {1 \over {2\sqrt 2 }}

D) {2 \over 3}

511

MediumNEET2021

A radioactive nucleus $_Z^AX \to {}_{Z - 1}B \to {}_{Z - 3}C \to {}_{Z - 2}D$, where Z is the atomic number of element X. The possible decay particles in the sequence are :

Options:

A) \beta - , \alpha, \beta$ +

B) \alpha, \beta - , \beta$ +

C) \alpha, \beta + , \beta -

D) \beta + , \alpha, \beta -

512

MediumNEET2020

When a uranium isotope $_{92}^{235}U is bombarded with a neutron, it generates _{36}^{89}Kr$ three neutrons and :

Options:

A) {}_{40}^{91}Zr

B) {}_{36}^{101}Kr

C) {}_{36}^{103}Kr

D) {}_{56}^{144}Ba

513

MediumNEET2020

For which one of the following, Bohr model is not valid?

Options:

A) Singly ionised helium atom (He + )

B) Deuteron atom

C) Singly ionised neon atom (Ne + )

D) Hydrogen atom

514

MediumNEET2020

The energy equivalent of 0.5 g of a substance is :

Options:

A) 4.5 \times {10^{13}}J

B) 1.5 \times {10^{13}}J

C) 0.5 \times {10^{13}}J

D) 4.5 \times {10^{16}}J

515

MediumNEET2019

\alpha $-particale consists of :

Options:

A) 2 electrons, 2 protons and 2 neutrons

B) 2 electrons and 4 protons only

C) 2 protons only

D) 2 protons and 2 neutrons only

516

MediumNEET2019

The total energy of an electron in an atom in an orbit is –3.4 eV. Its kinetic and potential energies are, respectively.

Options:

A) 3.4 eV, – 6.8 eV

B) 3.4 eV, 3.4 eV

C) – 3.4 eV, – 3.4 eV

D) – 3.4 eV, – 6.8 eV

517

MediumNEET2018

For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is

Options:

A) 20

B) 10

C) 30

D) 15

518

MediumNEET2018

The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom, is

Options:

A) 1 : 1

B) 1 : -1

C) 2 : -1

D) 1 : -2

519

MediumNEET2017

Radioactive material 'A' has decay constant '8 $\lambda ' and material 'B' has decay constant '\lambda $'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be e ?

Options:

A) {1 \over {7\lambda }}

B) {1 \over {8\lambda }}

C) {1 \over {9\lambda }}

D) {1 \over {\lambda }}

520

MediumNEET2017

The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is

Options:

A) 1

B) 4

C) 0.5

D) 2

521

MediumNEET2016

If an electron in a hydrogen atom jumps from the 3 rd orbit to the 2 nd orbit, it emits a photon of wavelength $\lambda $. When it jumps from the 4 th orbit to the 3 rd orbit, the corresponding wavelength of the photon will be

Options:

A) {{16} \over {25}}\lambda

B) {9 \over {16}}\lambda

C) {{20} \over 7}\lambda

D) {{20} \over {13}}\lambda

522

MediumNEET2016

The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is

Options:

A) 15

B) 30

C) 45

D) 60

523

MediumNEET2016

When an $\alpha $-particle of mass m moving with velocity v bombards on a heavy nucleus of charge Ze, its distance of closest approach from the nucleus depends on m as

Options:

A) {1 \over {{m^2}}}

B) m

C) {1 \over m}

D) {1 \over {\sqrt m }}

524

MediumNEET2016

Given the value of Rydberg constant is 10 7 m $-$1 , the wave number of the last line of the Balmer series in hydrogen spectrum will be

Options:

A) 0.25 $ \times 10 7 m -$1

B) 2.5 $ \times 10 7 m -$1

C) 0.025 $ \times 10 4 m -$1

D) 0.5 $ \times 10 7 m -$1

525

MediumNEET2015

In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is

Options:

A) {{27} \over 5}

B) {5 \over {27}}

C) {4 \over 9}

D) {9 \over 4}

526

MediumNEET2015

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then

Options:

A) The helium nucleus has more momentum than the thorium nucleus.

B) The helium nucleus has less kinetic energy than the thorium nucleus.

C) The helium nucleus has more kinetic energy than the thorium nucleus.

D) The helium nucleus has less momentum than the thorium nucleus.

527

MediumNEET2015

Consider 3 rd orbit of He + (Helium), using non-relativistic approach, the speed of electron in this orbit will be [given K = 9 $ \times 10 9 constant, Z = 2 and h (Planck's Constant) = 6.6 \times 10 -$34 J s]

Options:

A) 0.73 $ \times $ 10 6 m/s

B) 3.0 $ \times $ 10 8 m/s

C) 2.92 $ \times $ 10 6 m/s

D) 1.46 $ \times $ 10 6 m/s

528

MediumNEET2015

If radius of the ${}_{13}^{27} Al nucleus is taken to be R Al , then the radius of {}_{53}^{125}$Te nucleus is nearly

Options:

A) {3 \over 5}{R_{Al}}

B) {\left( {{{13} \over {53}}} \right)^{1/3}}{R_{Al}}

C) {\left( {{{53} \over {13}}} \right)^{1/3}}{R_{Al}}

D) {5 \over 3}{R_{Al}}

529

MediumNEET2014

The binding energy per nucleon of and nuclei are 5.60 MeV and 7.06 MeV respectively. In the nuclear reaction ${}_3^7Li + {}_1^1H \to {}_2^4He + _2^4He + Q$ the value of energy Q released is

Options:

A) 19.6 MeV

B) -$ 2.4 MeV

C) 8.4 MeV

D) 17.3 MeV

530

MediumNEET2014

A radioactive X with a half life 1.4 $ \times $ 10 9 years decays to Y which is stable. A sample of the rock from a cave was found to contain X and Y in the ratio 1 : 7. The age of the rock is

Options:

A) 1.96 $ \times $ 10 9 years

B) 3.92 $ \times $ 10 9 years

C) 4.20 $ \times $ 10 9 years

D) 8.40 $ \times $ 10 9 years

531

MediumNEET2014

Hydrogen atom in ground state is excited by a monochromatic radiation of $\lambda = 975 \mathop A\limits^ \circ $. Number of spectral lines in the resulting spectrum emitted will be

Options:

A) 3

B) 2

C) 6

D) 0 10

532

MediumNEET2013

\alpha -particles, \beta -particles and \gamma $-rays are all having same energy. Their penetrating power in a given medium in increasing order will be

Options:

A) \gamma , \alpha , \beta

B) \alpha , \beta , \gamma

C) \beta , \alpha , \gamma

D) \beta , \gamma , \alpha

533

MediumNEET2013

How does the Binding Energy per nucleon vary with the increase in the number of nucleons ?

Options:

A) Decrease continuously with mass number.

B) First decreases and then increases with increase in mass number.

C) First increases and then decreases with increase in mass number.

D) increases continuously with mass number.

534

MediumNEET2013

An electron in hydrogen atom makes a transition n 1 $ \to $ n 2 where n 1 and n 2 are principal quantum numbers of the two states . Assuming Bohr's model to be valid, the time period of the electron in the initial state is eight times that in the final state. The possible values of n 1 and n 2 are

Options:

A) n 1 = 6 and n 2 = 2

B) n 1 = 8 and n 2 = 1

C) n 1 = 8 and n 2 = 2

D) n 1 = 4 and n 2 = 2

535

MediumNEET2013

A certain mass of Hydrogen is changed to Helium by the process of fusion. The mass defect in fusion reaction is 0.02866 u. The energy liberated per u is (given 1 u = 931 MeV)

Options:

A) 6.675 MeV

B) 13.35 MeV

C) 2.67 MeV

D) 26.7 MeV

536

MediumNEET2013

Ratio of longest wave lengths corresponding to Lyman and Balmer series in hydrogen spectrum is

Options:

A) {7 \over {29}}

B) {9 \over {31}}

C) {5 \over {27}}

D) {3 \over {23}}

537

MediumNEET2013

The half life of a radioactive isotope 'X' is 20 years. It decays to another element 'Y' which is stable. The two elements 'X' and 'Y' were found to be in the ratio 1 : 7 in a sample of a given rock. The age of the rock is estimated to be

Options:

A) 80 years

B) 100 years

C) 40 years

D) 60 years

538

MediumNEET2012

The half life of a radioactive nucleus is 50 days. The time invertal (t 2 $- t 1 ) between the time t 2 when {2 \over 3} of it has decayed and the time t 1 when {1 \over 3}$ of it had decayed is

Options:

A) 30 days

B) 50 days

C) 60 days

D) 15 days

539

MediumNEET2012

The transition from the state n = 3 to n = 1 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from

Options:

A) 2 $ \to $ 1

B) 3 $ \to $ 2

C) 4 $ \to $ 2

D) 4 $ \to $ 3

540

MediumNEET2012

Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelengths $\lambda 1 : \lambda $ 2 emitted in the two cases is

Options:

A) {7 \over 5}

B) {27 \over 20}

C) {27 \over 5}

D) {20 \over 7}

541

MediumNEET2012

If the nuclear radius of 27 Al is 3.6 fermi, the approximate nuclear radius of 64 Cu in fermi is

Options:

A) 2.4

B) 1.2

C) 4.8

D) 3.6

542

MediumNEET2012

An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquired as a result of photon emission will be

Options:

A) {{24hR} \over {25m}}

B) {{25hR} \over {24m}}

C) {{25m} \over {24hR}}

D) {{24m} \over {25hR}}

543

MediumNEET2012

A mixture consists of two radioactive materials A 1 and A 2 with half lives of 20 s and 10 s respectively. Initially the mixture has 40 g of A 1 and 160 g of A 2 . The amount of the two in the mixture will become equal after

Options:

A) 60 s

B) 80 s

C) 20 s

D) 40 s

544

MediumNEET2011

Two radioactive nuclei P and Q, in a given sample decay into a stable nucleus R. At time t = 0. number of P species are 4 N 0 and that of Q are N 0 . Half -life of P (for conversion to R) is 1 minute where as that of Q is 2 minutes. Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be

Options:

A) 2 N 0

B) 3 N 0

C) {{9{N_0}} \over 2}

D) {{5{N_0}} \over 2}

545

MediumNEET2011

Out of the following which one is not a possible energy for a photon to be emitted by hydrogen atom according to Bohr's atomic model?

Options:

A) 0.65 eV

B) 1.9 eV

C) 11.1 eV

D) 13.6 eV

546

MediumNEET2011

An electron in the hydrogen atom jumps from excited state n to the ground state. The wavelength so emitted illuminates a photosensitive material having work function 2.75 eV. If the stopping potential of the photoelectron is 10 V, then the value of n is

Options:

A) 2

B) 3

C) 4

D) 5

547

MediumNEET2011

Fusion reaction takes place at high temperature because

Options:

A) nuclei break up at high temperature

B) atoms get ionised at high temperature

C) kinetic energy is high enough to overcome the coulomb repulsion between nuclei

D) molecules break up at high temperature

548

MediumNEET2011

The half life of a radioactive isotope X is 50 years. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio of 1 : 15 in a sample of a given rock. The age of the rock was estimated to be

Options:

A) 150 years

B) 200 years

C) 250 years

D) 100 years

549

MediumNEET2011

The power obtained in a reactor using U 235 disintegration is 1000 kW. The mass decay of U 235 per hour is

Options:

A) 10 microgram

B) 20 microgram

C) 40 microgram

D) 1 microgram

550

MediumNEET2011

A nucleus ${}_n^mX emits one \alpha particle and two \beta $ particles. The resulting nucleus is

Options:

A) {}_{n - 4}^{m - 6}Z

B) {}_n^{m - 6}Z

C) {}_n^{m - 4}X

D) {}_{n - 2}^{m - 4}Y

551

MediumNEET2011

A radioactive nucleus of mass M emits a photon of frequency $v$ and the nucleus recoils. The recoil energy will be

Options:

A) Mc 2 $- hv

B) h 2 $\upsilon $ 2 /2Mc 2

C) zero

D) h$v

552

MediumNEET2011

The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen like ion. The atomic number Z of hydrogen like ion is

Options:

A) 3

B) 4

C) 1

D) 2

553

MediumNEET2010

The binding energy per nucleon in deuterium and helium nuclei are 1.1 MeV and 7.0 MeV, respectively. When two deuterium nuclei fuse to form a helium nucleus the energy released in the fusion is

Options:

A) 23.6 MeV

B) 2.2 MeV

C) 28.0 MeV

D) 30.2 MeV

554

MediumNEET2010

The decay constant of a radio isotope is $\lambda . If A 1 and A 2 are its activities at times t 1 and t 2 respectively, the number of nuclei which have decayed during the time (t 1 -$ t 2 )

Options:

A) A 1 t 1 $-$ A 2 t 2

B) A 1 $-$ A 2

C) (A 1 $- A 2 )/\lambda

D) \lambda ({A_1} - {A_2})

555

MediumNEET2010

An alpha nucleus of energy ${1 \over 2}$ mv 2 bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to

Options:

A) {1 \over {Ze}}

B) v 2

C) {1 \over m}

D) {1 \over {{v_4}}}

556

MediumNEET2010

The activity of a radioactive sample is measured as N 0 counts per minute at t = 0 and N 0 /e counts per minute at t = 5 minutes. The time (in minutes) at which the activity reduces to half its value is

Options:

A) {\log _e}{2 \over 5}

B) {5 \over {{{\log }_e}2}}

C) 5log 10 2

D) 5log e 2

557

MediumNEET2010

The energy of a hydrogen atom in the ground state is $-$ 13.6 eV. The energy of a He + ion in the first excited state will be

Options:

A) -$ 13.6 eV

B) -$ 27.2 eV

C) -$ 54.4 eV

D) -$ 6.8 eV

558

MediumNEET2010

The energy of a hydrogen atom in the ground state is $-$ 13.6 eV. The energy of a He + ion in the first excited state will be

Options:

A) -$ 13.6 eV

B) -$ 27.2 eV

C) -$ 54.4 eV

D) -$ 6.8 eV

559

MediumNEET2010

The mass of a ${}_3^7Li Li nucleus is 0.042 u less than the sum of the masses of all its nucleons. The binding energy per nucleon of {}_3^7Li$ nucleus is nearly

Options:

A) 46 MeV

B) 5.6 MeV

C) 3.9 MeV

D) 23 MeV

560

MediumNEET2009

The ionization energy of the electron in the hydrogen atom in its ground state is 13.6 eV. The atoms are excited to higher energy levels to emit radiations of 6 wavelengths, Maximum wavelength of emitted radiation corresponds to the transition between

Options:

A) n = 3 to n = 1 states

B) n = 2 to n = 1 states

C) n = 4 to n = 3 states

D) n = 3 to n = 2 states

561

MediumNEET2009

The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an

Options:

A) isomer of parent

B) isotone of parent

C) isotope of parent

D) isobar of parent

562

MediumNEET2009

In the nuclear decay given below ${}_Z^AX \to {}_{Z + 1}^AY \to {}_{Z - 1}^{A - 4}B{}^ * \to {}_{Z - 1}^{A - 4}B,$ the particles emitted in the sequence are

Options:

A) \gamma , \beta , \alpha

B) \beta , \gamma , \alpha

C) \alpha , \beta , \gamma

D) \beta , \alpha , \gamma

563

MediumNEET2009

In a Rutherford scattering experiment when a projectile of charge z 1 and mass M 1 approaches a target nucleus of charge z 2 and mass M 2 , the distance of closest approach is r 0 . The energy of the projectile is

Options:

A) directly proportional to z 1 z 2

B) inversely proportional to z 1

C) directly proportional to mass M 1

D) directly proportional to M 1 $ \times $ M 2

564

MediumNEET2008

The ground state energy of hydrogen atom is $-$ 13.6 eV. When its electron is in the first excited state, its excitation energy is

Options:

A) 10.2 eV

B) 0

C) 3.4 eV

D) 6.8 eV

565

MediumNEET2008

If M(A; Z), M p and M n denote the masses of the nucleus ${}_Z^AX,$ proton and neutron respectively in units of u (1 u = 931.5 MeV/c 2 ) and BE represents its bonding energy in MeV, then

Options:

A) M(A, Z) = ZM p + (A $- Z)M n -$ BE

B) M(A, Z) = ZM p + (A $-$ Z)M n + BE/c 2

C) M(A, Z) = ZM p + (A $- Z)M n -$ BE/c 2

D) M(A, Z) = ZM p + (A $-$ Z)M n + BE

566

MediumNEET2008

Two radioactive materials X 1 and X 2 have decay constants $5\lambda and \lambda $ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X 1 to that X 2 will be 1/e after a time

Options:

A) 1/4$\lambda

B) e/$\lambda

C) \lambda

D) {1 \over 2}\lambda

567

MediumNEET2008

Two nuclei have their mass numbers in the ratio of 1 : 3. The ratio of their nuclear densities would be

Options:

A) {\left( 3 \right)^{1/3}}:1

B) 1 : 1

C) 1 : 3

D) 3 : 1

568

MediumNEET2007

A nucleus ${}_Z^AX$ has mass represented by M(A, Z). If M p and M n denote the mass of proton and neutron respectively and B.E. the binding energy in MeV, then

Options:

A) B.E. = [ZM p + (A $- Z)M n -$ M(A, Z)]c 2

B) B.E. = [ZM p + AM p $-$ M(A, Z)]c 2

C) B.E. = M(A, Z) $- ZM p - (A -$ Z)M n

D) B.E. = [M(A, Z) $- ZM p - (A -$ Z)M n ]c 2

569

MediumNEET2007

In a radioactive decay process, the negatively charged emitted $\beta $-particles are

Options:

A) the electrons produced as a result of the decay of neutrons inside the nucleus

B) the electrons produced as a result of collisions between atoms

C) the electrons orbitting around the nucleus

D) the electrons present inside the nucleus

570

MediumNEET2007

Two radioactive substances A and B have decay constants 5$\lambda and \lambda $ respectively. At t = 0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be (1/e) 2 after a time interval

Options:

A) 4\lambda

B) 2\lambda

C) 1/$2\lambda

D) 1/$4\lambda

571

MediumNEET2007

If the nucleus ${}_{13}^{27}Al has a nuclear radius of about 3.6 fm, them {}_{32}^{125}Te$ would have its radius approximately as

Options:

A) 9.6 fm

B) 12.0 fm

C) 4.8 fm

D) 6.0 fm

572

MediumNEET2007

In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential $V and then made to describe semicircular paths of radius R using a magnetic field B. If V and B are kept constant, the ratio \left( {{{ch\arg e\,\,on\,\,\,the\,\,ion\,\,} \over {mass\,\,of\,\,the\,\,ion}}} \right)$ will be proportional to

Options:

A) 1/R 2

B) R 2

C) R

D) 1/R

573

MediumNEET2007

The total energy of electron in the ground state of hydrogen atom is $-$ 13.6 eV. The kinetic energy of an electron in the first excited state is

Options:

A) 6.8 eV

B) 13.6 eV

C) 1.7 eV

D) 3.4 eV.

574

MediumNEET2006

The radius of germanium (Ge) nuclide is measured to be twice the radius of ${}_4^9$Be. The number of nucleons in Ge are

Options:

A) 72

B) 73

C) 74

D) 75

575

MediumNEET2006

The binding energy of deuteron is 2.2 MeV and that of ${}_2^4He is 28 MeV. If two deuterons are fused to form one {}_2^4$He then the energy released is

Options:

A) 30.2 MeV

B) 25.8 MeV

C) 23.6 MeV

D) 19.2 MeV

576

MediumNEET2006

Ionization potential of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. According to Bohr's theory, the spectral lines emited by hydrogen will be

Options:

A) one

B) two

C) three

D) four

577

MediumNEET2006

In a radioactive material the activity at time t 1 is R 1 and at a later time t 2 , it is R 2 . If the decay constant of the material is $\lambda $, then

Options:

A) R 1 = R 2

B) R 1 = R 2 e $-\lambda (t 1 -$t 2 )

C) R 1 = R 2 e $\lambda (t 1 -$t 2 )

D) R 1 = R 2 (t 2 /t 1 ).

578

MediumNEET2005

In the reaction ${}_1^2H + {}_1^3H \to {}_2^4He + {}_0^1n, if the binding energies of {}_1^2 H, {}_1^3H and {}_2^4$He are respectively a, b and c (in MeV), then the energy (in MeV) released in this reaction is

Options:

A) a + b + c

B) a + b $-$ c

C) c $- a -$ b

D) c + a $-$ b

579

MediumNEET2005

Energy levels A, B and C of a certain atom corresponding to increasing values of energy i.e. E A < E B < E C . If $\lambda 1 , \lambda 2 and \lambda $ 3 are wavelengths of radioations corresponding to transitions C to B, B to A and C to A respectively, which of the following relations is correct?

Options:

A) {\lambda _3} = {\lambda _1} + {\lambda _2}

B) {\lambda _3} = {{{\lambda _1}{\lambda _2}} \over {{\lambda _1} + {\lambda _2}}}

C) {\lambda _1} + {\lambda _2} + {\lambda _3} = 0

D) {\lambda _3}^2 = {\lambda _1}^2 + {\lambda _2}^2

580

MediumNEET2005

Fission of nuclei is possible because the binding energy per nucleon in them

Options:

A) increases with mass number at low mass numbers

B) decreases with mass number at low mass numbers

C) increases with mass number at high mass numbers

D) decreases with mass number at high mass numbers.

581

MediumNEET2005

In any fission process the ratio mass of fission products mass of parent nucleus is

Options:

A) equal to 1

B) greater than 1

C) less than 1

D) depends on the mass of the parent nucleus.

582

MediumNEET2005

Which one of the following pairs of nuclei are isotones ?

Options:

A) 34 Se 74 , 31 Ga 71

B) 38 Sr 84 , 38 Sr 86

C) 42 Mo 92 , 40 Zr 92

D) 20 Ca 40 , 16 S 32

583

MediumNEET2005

The total energy of an electron in the first excited state of hydrogen atom is about $-$ 3.4 eV. Its kinetic energy in this state is

Options:

A) 3.4 eV

B) 6.8 eV

C) -$ 3.4 eV

D) -$ 6.8 eV

584

MediumNEET2004

If in a nuclear fusion process the masses of the fusing nuclei be m 1 and m 2 and the mass of the resultant nucleus be m 3 , then

Options:

A) m 3 = m 1 + m 2

B) m 3 = $\left| {{m_1} - {m_2}} \right|

C) m 3 < (m 1 + m 2 )

D) m 3 > (m 1 + m 2 )

585

MediumNEET2004

A nucleus represented by the symbol ${}_Z^AX$ has

Options:

A) Z neutrons and A $-$ Z protons

B) Z protons and A $-$ Z neutrons

C) Z protons and A neutrons

D) A protons and Z $-$ A neutrons

586

MediumNEET2004

The Bohr model of atoms

Options:

A) Assumes that the angular momentum of electrons is quantized.

B) Uses Einstein's photoelectric equation.

C) Predicts continuous emission spectra fror atoms.

D) Predicts the same emission spectra for all types of atoms.

587

MediumNEET2004

If M(A; Z), M p and M n denote the masses of the nucleus ${}_Z^AX,$ proton and neutron respectively in units of u (1 u = 931.5 MeV/c 2 ) and BE represents its bonding energy in MeV, then

Options:

A) M(A, Z) = ZM p + (A $- Z)M n -$ BE

B) M(A, Z) = ZM p + (A $-$ Z)M n + BE/c 2

C) M(A, Z) = ZM p + (A $- Z)M n -$ BE/c 2

D) M(A, Z) = ZM p + (A $-$ Z)M n + BE

588

MediumNEET2004

The half life of radian is about 1600 years. Of 100 g of radium existing now, 25 g will remain unchanged after

Options:

A) 4800 years

B) 6400 years

C) 2400 years

D) 3200 years

589

MediumNEET2003

Solar energy is mainly caused due to

Options:

A) burning of hydrogen in the oxygen

B) fission of uranium present in the Sun

C) fusion of protons during synthesis of heavier elements

D) gravitational contraction

590

MediumNEET2003

A nuclear reaction given by Z X A $ \to z+1 Y A + -1 e 0 + \overline v $ represents

Options:

A) \beta $-decay

B) \gamma $-decay

C) fusion

D) fission

591

MediumNEET2003

An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius r. The Coulomb force $\overrightarrow F $ between the two is

Options:

A) K{{{e^2}} \over {{r^2}}}\widehat r

B) - K{{{e^2}} \over {{r^3}}}\widehat r

C) K{{{e^2}} \over {{r^3}}}\widehat r

D) - K{{{e^2}} \over {{r^2}}}\widehat r

592

MediumNEET2003

A sample of radioactive element has a mass of 10 g at an instant t = 0. The approximate mass of this element in the sample after two mean lives is

Options:

A) 1.35 g

B) 2.50 g

C) 3.70 g

D) 6.30 g

593

MediumNEET2003

The mass number of a nucleus is

Options:

A) always less than its atomic number

B) always more than its atomic number

C) sometimes equal to its atomic number

D) sometimes less than and sometimes more than its atomic number

594

MediumNEET2003

In which of the following systems will the radius of the first orbit (n = 1) be minimum ?

Options:

A) doubly ionized lithium

B) singly ionized helium

C) deuterium atom

D) hydrogen atom

595

MediumNEET2003

The volume occupied by an atom is greater than the volume of the nucleus by a factor of about

Options:

A) 10 1

B) 10 5

C) 10 10

D) 10 15

596

MediumNEET2003

The mass of proton is 1.0073 u and that of neutron is 1.0087 u (u = atomic mass unit). The binding energy of ${}_2^4 He is (Given helium nucleus mass \approx $ 4.0015 u.)

Options:

A) 0.0305 J

B) 0.0305 erg

C) 28.4 MeV

D) 0.061 u

597

MediumNEET2002

Which of the following are suitable for the fusion process ?

Options:

A) light nuclei

B) heavy nuclei

C) element lying in the middle of the periodic table

D) middle elements, which are lying on binding energy curve.

598

MediumNEET2002

A deutron is bombarded on 8 O 16 nucleus then $\alpha $-particle is emitted. The product nucleus is

Options:

A) 7 N 13

B) 5 B 10

C) 4 Be 9

D) 7 N 14

599

MediumNEET2002

A sample of radioactive element containing 4 $ \times $ 10 16 active nuclei. Half life of element is 10 days, then number of decayed nuclei after 30 days

Options:

A) 0.5 $ \times $ 10 16

B) 2 $ \times $ 10 16

C) 3.5 $ \times $ 10 16

D) 1 $ \times $ 10 16

600

MediumNEET2001

Half life of a radioactive element is 12.5 hour and its quantity is 256 g. After how much time its quantity will remain 1 g?

Options:

A) 50 hrs

B) 100 hrs

C) 150 hrs

D) 200 hrs

601

MediumNEET2001

The energy of hydrogen atom in n th orbit is E n then the energy in n th orbit of singly ionised helium atom will be

Options:

A) 4E n

B) E n /4

C) 2E n

D) E n /2

602

MediumNEET2001

X(n, $\alpha ) {}_3^7$Li, then X will be

Options:

A) {}_5^{10}$ B

B) {}_5^9$ B

C) {}_5^{11}$ Be

D) {}_2^4$ He.

603

MediumNEET2001

M n and M p represent the mass of neutron and proton respectively. An element having mass M has N neutrons and Z protons, then the correct relation will be

Options:

A) M < {N $ \cdot M n + Z \cdot $ M p }

B) M > {N $ \cdot M n + Z \cdot $ M p }

C) M = {N $ \cdot M n + Z \cdot $ M p }

D) M = N {M n + M p }

604

MediumNEET2001

Which rays contain (positive) charged particles ?

Options:

A) \alpha $-rays

B) \beta $-rays

C) \gamma $-rays

D) X-rays

605

MediumNEET2001

The interplanar distance in a crystal is 2.8 $ \times 10 -$8 m. The value of maximum wavelength which can be diffracted

Options:

A) 2.8 $ \times 10 -$8 m

B) 5.6 $ \times 10 -$8 m

C) 1.4 $ \times 10 -$8 m

D) 7.6 $ \times 10 -$8 m

606

MediumNEET2001

Energy released in nuclear fission is due to

Options:

A) some mass is converted into energy

B) total binding energy of fragments is more than the binding energy of parantal element

C) total binding energy of fragments is less than the binding energy of parental element

D) total binding energy of fragments is equal to the binding energy of parental element.

607

MediumNEET2000

The life span of atomic hydrogen is

Options:

A) fraction of one second

B) one year

C) one hour

D) one day

608

MediumNEET2000

Nuclear fission is best explained by

Options:

A) liquid droplet theory

B) Yukawa $\pi $-meson theory

C) independent particle model of the nucleus

D) proton-proton cycle.

609

MediumNEET2000

For the given reaction, the particle X is $_6{C^{11}} \to {}_5{B^{11}} + {\beta ^ + } + X

Options:

A) neutron

B) anti neutrino

C) neutrino

D) proton

610

MediumNEET2000

Maximum frequency of emission is obtained for the transition

Options:

A) n = 2 to n = 1

B) n = 6 to n = 2

C) n = 1 to n = 2

D) n = 2 to n = 6.

611

MediumNEET2000

When an electron does transition from n = 4 to n = 2, then emitted line spectrum will be

Options:

A) first line of Lyman series

B) second line of Balmer series

C) first line of Balmer series

D) second line of Paschen series.

612

MediumNEET2000

The relation between $\lambda and T 1/2 as (T 1/2 \to $ half life)

Options:

A) T 1/2 = ${{\ln 2} \over \lambda }

B) T 1/2 ln2 = $\lambda

C) T 1/2 = ${1 \over \lambda }

D) ($\lambda $ + T 1/2 ) = ln2

613

MediumVITEEE2025

In the fusion reaction, $ { }_1^2 \mathrm{H}+{ }_1^2 \mathrm{H} \longrightarrow{ }_2^3 \mathrm{He}+{ }_0^1 \mathrm{n} the masses of deuteron, helium and neutron expressed in amu are 2.015, 3.017 and 1.009, respectively. If 1 kg of deuterium undergoes complete fusion, then find the amount of total energy released. ( 1 \mathrm{amu}=9315 \mathrm{MeV}$ )

Options:

A) 9 \times 10^{13} \mathrm{~J}

B) 20 \times 10^5 \mathrm{~J}

C) 4 \times 10^{22} \mathrm{~J}

D) 5 \times 10^{15} \mathrm{~J}

614

MediumVITEEE2025

The radius of the orbit of an electron in a Hydrogen-like atom is 45 a_0, where a_0 is the Bohr radius. Its orbital angular momentum is \frac{3 h}{2 \pi}. It is given that h is Planck constant and R is Rydberg constant. The possible wavelength(s), when the atom de-excites, is (are)

Options:

A) \frac{9}{32 R}

B) \frac{9}{16 R}

C) \frac{9}{15 R}

D) \frac{4}{3 R}

615

MediumVITEEE2024

The ratio of minimum wavelengths of Balmer and Paschen series of hydrogen atom will be

Options:

A) 1: 4

B) 4: 9

C) 9: 4

D) 4: 1

616

MediumVITEEE2023

The activity of a radioactive sample is measured as No counts per minute at $t=0 and \mathrm{N}_0 / \mathrm{e} counts per minute at t=6 \mathrm{~min}$. The time (in minutes) at which the activity reduces to half its value is.

Options:

A) \left(\log _e 2\right) / 6

B) 6 / \log _e 2

C) 6 \log _0 2

D) 6 \log _e 2

617

MediumVITEEE2023

The wavelength of $k_\alpha-line characteristic X-rays emitted by an element is 0.32 \mathop A\limits^o. The wavelength of the k_\beta$-line emitted by the same element will be

Options:

A) 0.32 $\mathop A\limits^o

B) 0.39 $\mathop A\limits^o

C) 0.49 $\mathop A\limits^o

D) 0.27 $\mathop A\limits^o

618

MediumVITEEE2023

A radioactive element $X convents into another stable element Y. Half-life of X is 2 hrs. Initially only X is present. After time t, the ratio of atoms of X and Y is found to be 1: 4, then t$ in hours is

Options:

A) 2

B) 4

C) between 4 and 6

D) 6

619

MediumVITEEE2022

A nuclide at rest emits an \alpha-particle. In this process

Options:

A) \alpha$-particle moves with large velocity and the nucleus remains at rest.

B) Both $\alpha$-particle and nucleus move with equal speed in opposite directions.

C) Both move in opposite directions except $\alpha$-particle with greater speed.

D) Both move in opposite direction with greater velocity of $\alpha$-particle.

620

MediumVITEEE2022

The half-life period of a radioactive element $x is same as the mean life time of another radioactive element y$. Initially, both of them have the same number of atoms. Then,

Options:

A) x and y$ have the same decay rate initially

B) x and y$ decay at the same rate always

C) y will decay at a faster rate than x

D) x will decay at a faster rate than y

621

MediumVITEEE2021

Polonium has a half-life of 140 days. If we take $20 \mathrm{~g}$ of polonium initially then the amount of it that remains after 280 days is

Options:

A) 2.5 g

B) 5 g

C) 10 g

D) 15 g

622

MediumVITEEE2021

According to Bohr model of hydrogen atom, only those orbits are permissible which satisfy the condition

Options:

A) m v=n h

B) \frac{m v^2}{r}=n\left(\frac{h}{2 \pi}\right)

C) m v r=n\left(\frac{h}{2 \pi}\right)

D) m v r^2=n\left(\frac{h}{2 \pi}\right)

623

MediumVITEEE2021

The Rutherford scattering experiment proves that an atom consists of

Options:

A) a sphere of positive charge in which electrons are embedded like seeds of water-melon

B) a sphere of negative charge in which protons are embedded like seeds of water-melon

C) a sphere of electron cloud in which the positive charge in placed at the centre of the sphere

D) a sphere of neutral charge

624

HardJEE Advanced2025

List-I shows various functional dependencies of energy (E) on the atomic number (Z). Energies associated with certain phenomena are given in List-II. Choose the option that describes the correct match between the entries in List-I to those in List-II. List–I List–II (P) E \propto Z^2 (1) energy of characteristic x-rays (Q) E \propto (Z - 1)^2 (2) electrostatic part of the nuclear binding energy for stable nuclei with mass numbers in the range 30 to 170 (R) E \propto Z(Z - 1) (3) energy of continuous x-rays (S) E is practically independent of Z (4) average nuclear binding energy per nucleon for stable nuclei with mass number in the range 30 to 170 (5) energy of radiation due to electronic transitions from hydrogen-like atoms

Options:

A) P→4, Q→3, R→1, S→2

B) P→5, Q→2, R→1, S→4

C) P→5, Q→1, R→2, S→4

D) P→3, Q→2, R→1, S→5

625

MediumJEE Advanced2023

List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option. List - I List - II (P) { }_{92}^{238} U \rightarrow{ }_{91}^{234} \mathrm{~Pa} (1) one \alpha particle and one \beta^{+}particle (Q) { }_{82}^{214} \mathrm{~Pb} \rightarrow{ }_{82}^{210} \mathrm{~Pb} (2) three \beta^{-}particles and one \alpha particle (R) { }_{81}^{210} \mathrm{Tl} \rightarrow{ }_{82}^{206} \mathrm{~Pb} (3) two \beta^{-}particles and one \alpha particle (S) { }_{91}^{228} \mathrm{~Pa} \rightarrow{ }_{88}^{224} \mathrm{Ra} (4) one \alpha particle and one \beta^{-}particle (5) one \alpha particle and two \beta^{+}particles

Options:

A) P \rightarrow 4, Q \rightarrow 3, R \rightarrow 2, S \rightarrow 1

B) P \rightarrow 4, Q \rightarrow 1, R \rightarrow 2, S \rightarrow 5

C) P \rightarrow 5, Q \rightarrow 3, R \rightarrow 1, S \rightarrow 4

D) P \rightarrow 5, Q \rightarrow 1, R \rightarrow 3, S \rightarrow 2

626

EasyJEE Advanced2021

A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is

Options:

A) 50

B) 75

C) 350

D) 525

627

MediumJEE Advanced2019

In a radioactive sample, ${}_{19}^{40}K nuclei either decay into stable {}_{20}^{40}Ca nuclei with decay constant 4.5 \times 10 -10 per year or into stable {}_{18}^{40}Ar nuclei with decay constant 0.5 \times 10 -10 per year. Given that in this sample all the stable {}_{20}^{40}Ca and {}_{18}^{40}Ar nuclei are produced by the {}_{19}^{40}K nuclei only. In time t \times 10 9 years, if the ratio of the sum of stable {}_{20}^{40}Ca and {}_{18}^{40}Ar nuclei to the radioactive {}_{19}^{40}K$ nuclei is 99, the value of t will be [Given : In 10 = 2.3]

Options:

A) 9.2

B) 1.15

C) 4.6

D) 2.3

628

EasyJEE Advanced2016

An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?

Options:

A) 64

B) 90

C) 108

D) 120

629

HardJEE Advanced2016

The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by $E = {3 \over 5}{{Z(Z - 1){e^2}} \over {4\pi {\varepsilon _0}R}} The measured masses of the neutron, _1^1H, _7^{15}N and _8^{15}O are 1.008665u, 1.007825u, 15.000109u and 15.003065u, respectively. Given that the radii of both the _7^{15}N and _8^{15}O nuclei are same, 1 u = 931.5 MeV/c 2 (c is the speed of light) and e 2 /(4\pi{{\varepsilon _0}}) = 1.44 MeV fm. Assuming that the difference between the binding energies of _7^{15}N and _8^{15}O is purely due to the electrostatic energy, the radius of either of the nuclei is (1 fm = 10 -$15 m)

Options:

A) 2.85 fm

B) 3.03 fm

C) 3.42 fm

D) 3.80 fm

630

MediumJEE Advanced2015

Match the nuclear processes given in Column I with the appropriate option(s) in Column II:

Options:

A) (A)→(R) or (RT), (T); (B)→(P), (S); (C)→(Q), (T); (D)→(R)

B) (A)→(R), (T); (B)→(Q), (S); (C)→(Q), (T); (D)→(R)

C) (A)→(R) or (RT), (T); (B)→(P), (S); (C)→(S), (T); (D)→(R)

D) (A)→(P), (T); (B)→(P), (S); (C)→(Q), (T); (D)→(R)

631

MediumJEE Advanced2014

If $\lambda Cu is the wavelength of K \alpha X-ray line of copper (atomic number 29) and \lambda Mo is the wavelength of the K \alpha X-ray line of molybdenum (atomic number 42), then the ratio \lambda Cu /\lambda$ Mo is close to

Options:

A) 1.99

B) 2.14

C) 0.50

D) 0.48

632

EasyJEE Advanced2013

The mass of a nucleus $_Z^AX is less than the sum of the masses of (A-Z) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of masses m 1 and m 2 only if (m 1 + m 2 ) < M. Also two light nuclei of masses m 3 and m 4 can undergo complete fusion and form a heavy nucleus of mass M' only if (m 3 + m 4 ) > M'. The masses of some neutral atoms are given in the table below : _1^1H 1.007825 u _1^2H 2.014102 u _3^6Li 6.015123 u _3^7Li 7.016004 u _{64}^{152}Gd 151.919803 u _{82}^{206}Pb 205.974455 u _1^3H 3.016050 u _2^4He 4.002603 u _{30}^{70}Zn 69.925325 u _{34}^{82}Se 81.916709 u _{83}^{209}Bi 208.980388 u _{84}^{210}Po$ 209.982876 u (1 u = 932 MeV/c 2 )

Options:

A) the nucleus $_3^6Li$ can emit an alpha particle.

B) the nucleus $_{84}^{210}Po$ can emit a proton.

C) deuteron and alpha particle can undergo complete fusion.

D) the nuclei $_{30}^{70}Zn and _{34}^{82}Se$ can undergo complete fusion.

633

MediumJEE Advanced2013

The mass of a nucleus $_Z^AX is less than the sum of the masses of (A-Z) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of masses m 1 and m 2 only if (m 1 + m 2 ) < M. Also two light nuclei of masses m 3 and m 4 can undergo complete fusion and form a heavy nucleus of mass M' only if (m 3 + m 4 ) > M'. The masses of some neutral atoms are given in the table below : _1^1H 1.007825 u _1^2H 2.014102 u _3^6Li 6.015123 u _3^7Li 7.016004 u _{64}^{152}Gd 151.919803 u _{82}^{206}Pb 205.974455 u _1^3H 3.016050 u _2^4He 4.002603 u _{30}^{70}Zn 69.925325 u _{34}^{82}Se 81.916709 u _{83}^{209}Bi 208.980388 u _{84}^{210}Po$ 209.982876 u (1 u = 932 MeV/c 2 )

Options:

A) 5319

B) 5422

C) 5707

D) 5818

634

MediumJEE Advanced2013

Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists : List I List II P. Alpha decay 1. $_8^{15}O \to _7^{15}N + ... Q. {\beta ^ + } decay 2. _{91}^{238}U \to _{90}^{234}Th + ... R. Fission 3. _{83}^{185}Bi \to _{82}^{184}Pb + ... S. Proton emission 4. _{94}^{239}Pu \to _{57}^{140}La + ...

Options:

A) P-4, Q-2, R-1, S-3

B) P-1, Q-3, R-2, S-4

C) P-2, Q-1, R-4, S-3

D) P-4, Q-3, R-2, S-1

635

MediumJEE Advanced2012

The $\beta-decay process, discovered in around 1900, is basically the decay of a neutron (n). In the laboratory, a proton (p) and an electron (e - ) are observed as the decay products of the neutron. Therefore, considering the decay of a neutron as a two-body decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic energy has continuous spectrum. Considering a three-body decay process, that is, n \to p + e - + {\overline v _e}, around 1930, Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino ({\overline v _e}) to be massless and possessing negligible energy, and the neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron is 0.8 \times$ 10 6 eV. The kinetic energy carried by the proton is only the recoil energy.

Options:

A) Zero.

B) Much less than 0.8 $\times$ 10 6 eV.

C) Nearly 0.8 $\times$ 10 6 eV.

D) much larger than 0.8 $\times$ 10 6 eV.

636

MediumJEE Advanced2012

The $\beta-decay process, discovered in around 1900, is basically the decay of a neutron (n). In the laboratory, a proton (p) and an electron (e - ) are observed as the decay products of the neutron. Therefore, considering the decay of a neutron as a two-body decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic energy has continuous spectrum. Considering a three-body decay process, that is, n \to p + e - + {\overline v _e}, around 1930, Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino ({\overline v _e}) to be massless and possessing negligible energy, and the neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron is 0.8 \times$ 10 6 eV. The kinetic energy carried by the proton is only the recoil energy.

Options:

A) 0 $\le K \le 0.8 \times$ 10 6 eV

B) 3.0 eV $\le K \le 0.8 \times$ 10 6 eV

C) 3.0 eV $\le K < 0.8 \times$ 10 6 eV

D) 0 $\le K < 0.8 \times$ 10 6 eV

637

MediumJEE Advanced2011

The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 $\mathop A\limits^o $. The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is

Options:

A) 1215 $\mathop A\limits^o

B) 1640 $\mathop A\limits^o

C) 2430 $\mathop A\limits^o

D) 4687 $\mathop A\limits^o

638

EasyJEE Advanced2010

The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.

Options:

A) {1 \over {{n^2}}}\left( {{{{h^2}} \over {8{\pi ^2}I}}} \right)

B) {1 \over n}\left( {{{{h^2}} \over {8{\pi ^2}I}}} \right)

C) n\left( {{{{h^2}} \over {8{\pi ^2}I}}} \right)

D) {n^2}\left( {{{{h^2}} \over {8{\pi ^2}I}}} \right)

639

MediumJEE Advanced2010

The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.

Options:

A) 2.76 $\times 10 -$46 kg m 2

B) 1.87 $\times 10 -$46 kg m 2

C) 4.67 $\times 10 -$47 kg m 2

D) 1.17 $\times 10 -$47 kg m 2

640

MediumJEE Advanced2010

The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.

Options:

A) 2.4 $\times 10 -$10 m

B) 1.9 $\times 10 -$10 m

C) 1.3 $\times 10 -$10 m

D) 4.4 $\times 10 -$11 m

641

EasyJEE Advanced2009

When a particle is restricted to move along x-axis between x = 0 and x = a, where a is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends x = 0 and x = a. The wavelength of this standing wave is related to the linear momentum p of the particle according to the de Broglie relation. The energy of the particle of mass m is related to its linear momentum as $E = {{{p^2}} \over {2m}}. Thus, the energy of the particle can be denoted by a quantum number 'n' taking values 1, 2, 3, ... (n = 1, called the ground state) corresponding to the number of loops in the standing wave. Use the model described above to answer the following three questions for a particle moving in the line x = 0 to x = a. Take h = 6.6 \times {10^{ - 34}} J-s and e = 1.6 \times {10^{ - 19}}$ C.

Options:

A) {n^{ - 3/2}}

B) {n^{ - 1}}

C) {n^{1/2}}

D) n

642

EasyJEE Advanced2009

Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, $_1^2H, known as deuteron and denoted by D, can be thought of as a candidate for fusion reactor. The D-D reaction is _1^2H + _1^2H \to _2^3He + n + energy. In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of _1^2H nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time t_0 before the particles fly away from the core. If n is the density (number/volume) of deuterons, the product nt_0 is called Lawson number. In one of the criteria, a reactor is termed successful if Lawson number is greater than 5 \times 10^{14} s/cm^3. It may be helpful to use the following : Boltzmann constant k = 8.6 \times {10^{ - 5}} eV/K; {{{e^2}} \over {4\pi {\varepsilon _0}}} = 1.44 \times {10^9}$ eVm.

Options:

A) strong nuclear force acting between the deuterons.

B) Coulomb force acting between the deuterons.

C) Coulomb force acting between deuteron-electrons pairs.

D) the high temperature maintained inside the reactor core.

643

MediumJEE Advanced2009

Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, $_1^2H, known as deuteron and denoted by D, can be thought of as a candidate for fusion reactor. The D-D reaction is _1^2H + _1^2H \to _2^3He + n + energy. In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of _1^2H nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time t_0 before the particles fly away from the core. If n is the density (number/volume) of deuterons, the product nt_0 is called Lawson number. In one of the criteria, a reactor is termed successful if Lawson number is greater than 5 \times 10^{14} s/cm^3. It may be helpful to use the following : Boltzmann constant k = 8.6 \times {10^{ - 5}} eV/K; {{{e^2}} \over {4\pi {\varepsilon _0}}} = 1.44 \times {10^9}$ eVm.

Options:

A) 1.0 \times {10^9}K < T < 2.0 < {10^9}K

B) 2.0 \times {10^9}K < T < 3.0 < {10^9}K

C) 3.0 \times {10^9}K < T < 4.0 < {10^9}K

D) 4.0 \times {10^9}K < T < 5.0 < {10^9}K

644

EasyJEE Advanced2009

Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, $_1^2H, known as deuteron and denoted by D, can be thought of as a candidate for fusion reactor. The D-D reaction is _1^2H + _1^2H \to _2^3He + n + energy. In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of _1^2H nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time t_0 before the particles fly away from the core. If n is the density (number/volume) of deuterons, the product nt_0 is called Lawson number. In one of the criteria, a reactor is termed successful if Lawson number is greater than 5 \times 10^{14} s/cm^3. It may be helpful to use the following : Boltzmann constant k = 8.6 \times {10^{ - 5}} eV/K; {{{e^2}} \over {4\pi {\varepsilon _0}}} = 1.44 \times {10^9}$ eVm.

Options:

A) Deuteron density = $2.0\times10^{12}~\mathrm{cm^{-3}}; Confinement time = 5.0\times10^{-3}~\mathrm{s}$.

B) Deuteron density = $8.0\times10^{14}~\mathrm{cm^{-3}}; Confinement time = 9.0\times10^{-1}~\mathrm{s}$.

C) Deuteron density = $4.0\times10^{23}~\mathrm{cm^{-3}}; Confinement time = 1.0\times10^{-11}~\mathrm{s}$.

D) Deuteron density = $1.0\times10^{24}~\mathrm{cm^{-3}}; Confinement time = 4.0\times10^{-12}~\mathrm{s}$.

645

EasyJEE Advanced2008

A radioactive sample S 1 having activity of 5 $\muCi has twice the number of nuclei as another sample S 2 which has an activity of 10 \mu$Ci. The half lives of S 1 and S 2 can be :

Options:

A) 20 years and 5 years, respectively

B) 20 years and 10 years, respectively

C) 10 years each

D) 5 years each

646

MediumJEE Advanced2008

In a mixture of H - He$^+ gas (He^+ is singly ionized He atom), H atoms and He^+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He^+$ ions (by collisions). Assume that the Bohr model of atom is exactly valid.

Options:

A) 2

B) 3

C) 4

D) 5

647

MediumJEE Advanced2008

In a mixture of H - He$^+ gas (He^+ is singly ionized He atom), H atoms and He^+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He^+$ ions (by collisions). Assume that the Bohr model of atom is exactly valid.

Options:

A) 6.5\times10^{-7}$ m

B) 5.6\times10^{-7}$ m

C) 4.8\times10^{-7}$ m

D) 4.0\times10^{-7}$ m

648

EasyJEE Advanced2008

In a mixture of H - He$^+ gas (He^+ is singly ionized He atom), H atoms and He^+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He^+$ ions (by collisions). Assume that the Bohr model of atom is exactly valid.

Options:

A) \frac{1}{4}

B) \frac{1}{2}

C) 1

D) 2

649

MediumJEE Advanced2007

In the option given below, let E denote the rest mass energy of a nucleus and n a neutron. The correct option is

Options:

A) E\left( {_{92}^{236}U} \right) > E\left( {_{53}^{137}I} \right) + E\left( {_{39}^{97}Y} \right) + 2E(n)

B) E\left( {_{92}^{236}U} \right) < E\left( {_{53}^{137}I} \right) + E\left( {_{39}^{97}Y} \right) + 2E(n)

C) E\left( {_{92}^{236}U} \right) < E\left( {_{56}^{140}Ba} \right) + E\left( {_{36}^{94}Kr} \right) + 2E(n)

D) E\left( {_{92}^{236}U} \right) = E\left( {_{56}^{140}Ba} \right) + E\left( {_{36}^{94}Kr} \right) + 2E(n)

650

MediumJEE Advanced2007

The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is

Options:

A) 802 nm

B) 823 nm

C) 1882 nm

D) 1648 nm

651

MediumJEE Advanced2006

\text { Match the following Columns. } Column I Column II (A) Nuclear fusion. (P) Converts some matter into energy. (B) Nuclear fission. (Q) Generally possible for nuclei with low atomic number. (C) \beta$-decay. (R) Generally possible for nuclei with higher atomic number. (D) Exothermic nuclear reaction. (S) Essentially proceeds by weak nuclear forces.

Options:

A) [\mathrm{A} \rightarrow( \mathrm{Q}) ; \mathrm{B} \rightarrow(\mathrm{P}, \mathrm{R}) ; \mathrm{C} \rightarrow(\mathbf{P}, \mathbf{S}) ; \mathbf{D} \rightarrow( \mathbf{R})]

B) [\mathrm{A} \rightarrow(\mathrm{P}) ; \mathrm{B} \rightarrow(\mathrm{P}, \mathrm{R}) ; \mathrm{C} \rightarrow(\mathbf{P}) ; \mathbf{D} \rightarrow(\mathbf{P}, \mathbf{Q}, \mathbf{R})] .

C) [\mathrm{A} \rightarrow(\mathrm{P}, \mathrm{Q}) ; \mathrm{B} \rightarrow(\mathrm{P}, \mathrm{R}) ; \mathrm{C} \rightarrow(\mathbf{P}, \mathbf{S}) ; \mathbf{D} \rightarrow(\mathbf{P}, \mathbf{Q}, \mathbf{R})] .

D) [\mathrm{A} \rightarrow(\mathrm{P}, \mathrm{Q}) ; \mathrm{B} \rightarrow(\mathrm{P}, \mathrm{R}) ; \mathrm{C} \rightarrow( \mathbf{S}) ; \mathbf{D} \rightarrow(\mathbf{P}, \mathbf{Q})] .

652

MediumJEE Advanced2006

\text { Match the following Columns. } Column I Column II (A) Dielectric ring uniformly charged. (P) Time independent electrostatic field out of system. (B) Dielectric ring uniformly charged rotating with angular velocity \omega. (Q) Magnetic field. (C) Constant current in ring io (R) Induced electric field. (D) i=i_o \cos \omega \mathrm{t} $ (S) Magnetic moment.

Options:

A) [\mathbf{A} \rightarrow(\mathbf{P}) ; \mathbf{B} \rightarrow(\mathbf{Q}, \mathbf{S}) ; \mathbf{C} \rightarrow (\mathrm{Q}) ; \mathrm{D} \rightarrow(\mathrm{Q})]

B) [\mathbf{A} \rightarrow(\mathbf{P}) ; \mathbf{B} \rightarrow( \mathbf{S}) ; \mathbf{C} \rightarrow (\mathrm{Q}) ; \mathrm{D} \rightarrow(\mathrm{Q}, \mathrm{R})]

C) [\mathbf{A} \rightarrow(\mathbf{P}) ; \mathbf{B} \rightarrow( \mathbf{S}) ; \mathbf{C} \rightarrow (\mathrm{Q}, \mathrm{~S}) ; \mathrm{D} \rightarrow(\mathrm{Q}, \mathrm{R})]

D) [\mathbf{A} \rightarrow(\mathbf{P}) ; \mathbf{B} \rightarrow(\mathbf{Q}, \mathbf{S}) ; \mathbf{C} \rightarrow (\mathrm{Q}, \mathrm{~S}) ; \mathrm{D} \rightarrow(\mathrm{Q}, \mathrm{R}, \mathrm{~S})]

653

MediumJEE Advanced2005

Highly energetic electrons are bombarded on a target of an element containing 30 neutrons. The ratio of radii of nucleus to that of Helium nucleus is $(14)^{\frac{1}{3}}. Find (A) Atomic number of the nucleus; (B) the frequency of \mathrm{K}_{\alpha} line of the X-ray produced. \left(\mathrm{R}=1.1 \times 10^{7} \mathrm{~m}^{-1}\right. and \left.c=3 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)

Options:

A) (A) 26 ; (B) $2.55 \times 10^{18} \mathrm{~Hz}

B) (A) 26 ; (B) $1.55 \times 10^{18} \mathrm{~Hz}

C) (A) 36 ; (B) $1.55 \times 10^{18} \mathrm{~Hz}

D) (A) 46 ; (B) $2.55 \times 10^{18} \mathrm{~Hz}

654

MediumJEE Advanced2024

A particle of mass m is moving in a circular orbit under the influence of the central force F(r)=-k r, corresponding to the potential energy V(r)=k r^2 / 2, where k is a positive force constant and r is the radial distance from the origin. According to the Bohr's quantization rule, the angular momentum of the particle is given by L=n \hbar, where \hbar=h /(2 \pi), h is the Planck's constant, and n a positive integer. If v and E are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?

Options:

A) r^2=n \hbar \sqrt{\frac{1}{m k}}

B) v^2=n \hbar \sqrt{\frac{k}{m^3}}

C) \frac{L}{m r^2}=\sqrt{\frac{k}{m}}

D) E=\frac{n \hbar}{2} \sqrt{\frac{k}{m}}

655

HardJEE Advanced2022

The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be E_{b}^{p} and the binding energy of a neutron be E_{b}^{n} in the nucleus. Which of the following statement(s) is(are) correct?

Options:

A) E_{b}^{p}-E_{b}^{n} is proportional to Z(Z-1) where Z is the atomic number of the nucleus.

B) E_{b}^{p}-E_{b}^{n} is proportional to A^{-\frac{1}{3}} where A is the mass number of the nucleus.

C) E_{b}^{p}-E_{b}^{n} is positive.

D) E_{b}^{p} increases if the nucleus undergoes a beta decay emitting a positron.

656

MediumJEE Advanced2021

Which of the following statement(s) is(are) correct about the spectrum of the hydrogen atom?

Options:

A) The ratio of the longest wavelength to the shortest wavelength in Balmer series is 9/5

B) There is an overlap between the wavelength ranges of Balmer and Paschen series

C) The wavelengths of Lyman series are given by $\left( {1 + {1 \over {{m^2}}}} \right){\lambda _0}, where {\lambda _0}$ is the shortest wavelength of Lyman series and m is an integer

D) The wavelength ranges of Lyman and Balmer series do not overlap

657

MediumJEE Advanced2021

A heavy nucleus N, at rest, undergoes fission N $\to P + Q, where P and Q are two lighter nuclei. Let \delta = M N - M P -$ M Q , where M P , M Q and M N are the masses of P, Q and N, respectively. E P and E Q are the kinetic energies of P and Q, respectively. The speeds of P and Q are v P and v Q , respectively. If c is the speed of light, which of the following statement(s) is(are) correct?

Options:

A) {E_P} + {E_Q} = {c^2}\delta

B) {E_P} = \left( {{{{M_P}} \over {{M_P} + {M_Q}}}} \right){c^2}\delta

C) {{{v_P}} \over {{v_Q}}} = {{{M_Q}} \over {{M_P}}}

D) The magnitude of momentum for P as well Q is $c\sqrt {2\mu \delta } , where \mu = {{{M_P}{M_Q}} \over {({M_P} + {M_Q})}}

658

MediumJEE Advanced2020

A particle of mass m moves in circular orbits with potential energy V(r) = Fr, where F is a positive constant and r is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle’s orbit is denoted by R and its speed and energy are denoted by v and E, respectively, then for the n th orbit (here h is the Planck’s constant)

Options:

A) R \propto {n^{{1 \over 3}}} and v \propto {n^{{2 \over 3}}}

B) R \propto {n^{{2 \over 3}}} and v \propto {n^{{1 \over 3}}}

C) E = {3 \over 2}{\left( {{{{n^2}{h^2}{F^2}} \over {4{\pi ^2}m}}} \right)^{{1 \over 3}}}

D) E = 2{\left( {{{{n^2}{h^2}{F^2}} \over {4{\pi ^2}m}}} \right)^{{1 \over 3}}}

659

MediumJEE Advanced2020

In an X-ray tube, electrons emitted from a filament (cathode) carrying current I hit a target (anode) at a distance d from the cathode. The target is kept at a potential V higher than the cathode resulting in emission of continuous and characteristic X-rays. If the filament current I is decreased to ${1 \over 2}, the potential difference V is increased to 2V, and the separation distance d is reduced to {d \over 2}$, then

Options:

A) the cut-off wavelength will reduce to half, and the wavelengths of the characteristic X-rays will remain the same

B) the cut-off wavelength as well as the wavelengths of the characteristic X-rays will remain the same

C) the cut-off wavelength will reduce to half, and the intensities of all the X-rays will decrease

D) the cut-off wavelength will become two times larger, and the intensity of all the X-rays will decrease

660

MediumJEE Advanced2019

A free hydrogen atom after absorbing a photon of wavelength $\lambda a gets excited from the state n = 1 to the state n = 4. Immediately after that the electron jumps to n = m state by emitting a photon of wavelength \lambda e . Let the change in momentum of atom due to the absorption and the emission be \Delta {p_a} and \Delta {p_e}, respectively. If {{{\lambda _a}} \over {{\lambda _e}}} = {1 \over 5}$, which of the option(s) is/are correct? [Use hc = 1242 eVnm; 1 nm = 10 -9 m, h and c are Planck's constant and speed of light in vacuum, respectively]

Options:

A) The ratio of kinetic energy of the electron in the state n = m to the state, n = 1 is ${1 \over 4}

B) m = 2

C) {{\Delta {p_a}} \over {\Delta {p_e}}} = {1 \over 2}

D) \lambda $ e = 418 nm

661

MediumJEE Advanced2018

In a radioactive decay chain, ${}_{90}^{232}Th nucleus decays to {}_{82}^{212}Pb nucleus. Let {N_\alpha } and {N_\beta } be the number of \alpha and {\beta ^ - }$ particles, respectively, emitted in this decay process. Which of the following statements is (are) true?

Options:

A) {N_\alpha } = 5

B) {N_\alpha } = 6

C) {N_\beta } = 2

D) {N_\beta } = 4

662

MediumJEE Advanced2016

Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principle quantum number n, where n >> 1. Which of the following statement(s) is(are) true?

Options:

A) Relative change in the radii of two consecutive orbitals does not depend on Z.

B) Relative change in the radii of two consecutive orbitals varies as 1/n

C) Relative change in the energy of two consecutive orbitals varies as 1/n 3

D) Relative change in the angular momenta of two consecutive orbitals varies as 1/n

663

HardJEE Advanced2015

A fission reaction is given by $_{92}^{236}U \to _{54}^{140}Xe + _{38}^{94}Sr + x + y, where x and y are two particles. Considering _{92}^{236}U to be at rest, the kinetic energies of the products are denoted by {K_{Xe}},{K_{Sr}},{K_x}(2MeV) \text { and } \mathrm{K}_{\mathrm{y}}(2 \mathrm{MeV}) , respectively. Let the binding energies per nucleon of _{92}^{236}U, _{54}^{140}Xe and _{38}^{94}Sr$ be 7.5 MeV, 8.5 MeV and 8.5 MeV, respectively. Considering different conservation laws, the correct options is/are

Options:

A) x = n, y = n, K sr = 129 MeV, K Xe = 86 MeV

B) x = p, y = e $-$ , K sr = 129 MeV, K Xe = 86 MeV

C) x = p, y = n, K sr = 129 MeV, K Xe = 86 MeV

D) x = n, y = n, K sr = 86 MeV, K Xe = 129 MeV

664

MediumJEE Advanced2013

The radius of the orbit of an electron in a hydrogen-like atom is 4.5a 0 , where a 0 is the Bohr radius. Its orbital angular momentum is ${{3h} \over {2\pi }}$. It is given that h is Planck constant and R is Rydberg constant. The possible wavelength(s), when the atom de-excites, is(are)

Options:

A) {9 \over {32R}}

B) {9 \over {16R}}

C) {9 \over {5R}}

Answer: Enter a numeric value

679

MediumInteger TypeJEE Advanced2010

To determine the half-life of a radioactive element, a student plots a graph of $\ln \left| {{{dN(t)} \over {dt}}} \right| versus t. Here, {{dN(t)} \over {dt}}$ is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is __________.

Answer: Enter a numeric value

680

MediumInteger TypeJEE Advanced2006

In hydrogen-like atom (z=11), nth line of Lyman series has wavelength A equal to the de Broglie's wavelength of electron in the level from which it originated. What is the value of n ?

Answer: Enter a numeric value

680

Total Questions

129

Easy

542

Medium

Hard

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