Class 12 • Physics

Dual Nature of Matter and Radiation

Chapter-11

384 Questions

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77 Easy304 Medium3 Hard

Practice Questions

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C) 2.24

D) 1.58

MediumJee Advance2022

When light of a given wavelength is incident on a metallic surface, the minimum potential needed to stop the emitted photoelectrons is 6.0 \mathrm{~V}. This potential drops to 0.6 \mathrm{~V} if another source with wavelength four times that of the first one and intensity half of the first one is used. What are the wavelength of the first source and the work function of the metal, respectively? [Take \frac{h c}{e}=1.24 \times 10^{-6} \mathrm{JmC}^{-1}.]

Options:

A) 1.72 \times 10^{-7} \mathrm{~m}, 1.20 \mathrm{eV}

B) 1.72 \times 10^{-7} \mathrm{~m}, 5.60 \mathrm{eV}

C) 3.78 \times 10^{-7} \mathrm{~m}, 5.60 \mathrm{eV}

D) 3.78 \times 10^{-7} \mathrm{~m}, 1.20 \mathrm{eV}

MediumJee Advance2017

A photoelectric material having work-function ${\phi _0} is illuminated with light of wavelength \lambda \left( {\lambda < {{he} \over {{\phi _0}}}} \right). The fastest photoelectron has a de-Broglic wavelength {\lambda _d}. A change in wavelength of the incident light by \Delta \lambda result in a change \Delta {\lambda _d} in {\lambda _d}. Then the ratio \Delta {\lambda _d}/\Delta \lambda $ is proportional to

Options:

A) {\lambda _d}/\lambda

B) \lambda _d^2/{\lambda ^2}

C) \lambda _d^3/\lambda

D) \lambda _d^3/{\lambda ^2}

MediumJee Advance2016

In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength ($\lambda ) of incident light and the corresponding stopping potential (V0) are given below: \lambda \left( {\mu m} \right) V0(Volt) 0.3 2.0 0.4 1.0 0.5 0.4 Given that c = 3 \times 108 ms-1 and e = 1.6 \times $ 10-19 C, Planck's constant (in units of J-s) found from such an experiment is) :

Options:

A) 6.0 $ \times $ 10-34

B) 6.6 $ \times $ 10-34

C) 6.4 $ \times $ 10-34

D) 6.8 $ \times $ 10-34

MediumJee Advance2014

A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are u1 and u2, respectively. If the ratio u1 : u2 = 2 : 1 and hc = 1240 eV nm, the work function of the metal is nearly

Options:

A) 3.7 eV

B) 3.2 eV

Options:

A) Planck's constant

B) Work function of the metal

C) Charge of electron

D) Ratio of Planck's constant to electric charge

100

EasyJEE Mains2024

If the total energy transferred to a surface in time $\mathrm{t} is 6.48 \times 10^5 \mathrm{~J}$, then the magnitude of the total momentum delivered to this surface for complete absorption will be:

Options:

A) 2.16 \times 10^{-3} \mathrm{~kg} \mathrm{~m} / \mathrm{s}

B) 2.46 \times 10^{-3} \mathrm{~kg} \mathrm{~m} / \mathrm{s}

C) 1.58 \times 10^{-3} \mathrm{~kg} \mathrm{~m} / \mathrm{s}

D) 4.32 \times 10^{-3} \mathrm{~kg} \mathrm{~m} / \mathrm{s}

101

EasyJEE Mains2024

The work function of a substance is $3.0 \mathrm{~eV}$. The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately;

Options:

A) 215 nm

B) 400 nm

C) 414 nm

D) 200 nm

102

EasyJEE Mains2024

Two sources of light emit with a power of $200 \mathrm{~W}. The ratio of number of photons of visible light emitted by each source having wavelengths 300 \mathrm{~nm} and 500 \mathrm{~nm}$ respectively, will be :

Options:

A) 5: 3

B) 3: 5

C) 1: 5

D) 1: 3

103

MediumJEE Mains2024

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is $25 \%$ of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be:

Options:

A) \frac{1}{4}

B) \frac{8}{1}

C) \frac{1}{8}

D) \frac{1}{1}

104

EasyJEE Mains2024

The threshold frequency of a metal with work function $6.63 \mathrm{~eV}$ is :

Options:

A) 16 \times 10^{15} \mathrm{~Hz}

B) 16 \times 10^{12} \mathrm{~Hz}

C) 1.6 \times 10^{15} \mathrm{~Hz}

D) 1.6 \times 10^{12} \mathrm{~Hz}

105

EasyJEE Mains2023

The de Broglie wavelength of an electron having kinetic energy \mathrm{E} is \lambda. If the kinetic energy of electron becomes \frac{E}{4}, then its de-Broglie wavelength will be :

Options:

A) \sqrt{2} \lambda

B) 2 \lambda

C) \frac{\lambda}{2}

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

106

EasyJEE Mains2023

Given below are two statements: Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface. Statement II : Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light. In the light of above statements, choose the correct answer form 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

107

EasyJEE Mains2023

The difference between threshold wavelengths for two metal surfaces $\mathrm{A} and \mathrm{B} having work function \phi_{A}=9 ~\mathrm{eV} and \phi_{B}=4 \cdot 5 ~\mathrm{eV} in \mathrm{nm} is: \{ Given, hc =1242 ~\mathrm{eV} \mathrm{nm}\}

Options:

A) 264

B) 138

C) 540

D) 276

108

EasyJEE Mains2023

A proton and an $\alpha-particle are accelerated from rest by 2 \mathrm{~V} and 4 \mathrm{~V}$ potentials, respectively. The ratio of their de-Broglie wavelength is :

Options:

A) 4 : 1

B) 2 : 1

C) 8 : 1

D) 16 : 1

109

EasyJEE Mains2023

The ratio of the de-Broglie wavelengths of proton and electron having same Kinetic energy : (Assume $m_{p}=m_{e} \times 1849$ )

Options:

A) 1:43

B) 1:62

C) 2:43

D) 1:30

110

MediumJEE Mains2023

A metallic surface is illuminated with radiation of wavelength $\lambda, the stopping potential is V_{0}. If the same surface is illuminated with radiation of wavelength 2 \lambda. the stopping potential becomes \frac{V_{o}}{4}$. The threshold wavelength for this metallic surface will be

Options:

A) 3 \lambda

B) 4 \lambda

C) \frac{3}{2} \lambda

D) \frac{\lambda}{4}

111

EasyJEE Mains2023

The variation of stopping potential $\left(\mathrm{V}_{0}\right) as a function of the frequency (v)$ of the incident light for a metal is shown in figure. The work function of the surface is

Options:

A) 1.36 eV

B) 18.6 eV

C) 2.98 eV

D) 2.07 eV

112

EasyJEE Mains2023

The de Broglie wavelength of a molecule in a gas at room temperature (300 K) is $\lambda_1$. If the temperature of the gas is increased to 600 K, then the de Broglie wavelength of the same gas molecule becomes

Options:

A) 2 $\lambda_1

B) \frac{1}{2}\lambda_1

C) \frac{1}{\sqrt2}\lambda_1

D) \sqrt2~\lambda_1

113

EasyJEE Mains2023

In photo electric effect A. The photocurrent is proportional to the intensity of the incident radiation B. Maximum Kinetic energy with which photoelectrons are emitted depends on the intensity of incident light. C. Max. K.E with which photoelectrons are emitted depends on the frequency of incident light. D. The emission of photoelectrons require a minimum threshold intensity of incident radiation. E. Max. K.E of the photoelectrons is independent of the frequency of the incident light. Choose the correct answer from the options given below:

Options:

A) A and E only

B) A and B only

C) B and C only

D) A and C only

114

MediumJEE Mains2023

Proton $(\mathrm{P}) and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, \mathrm{m}_{\mathrm{p}}=1849 \mathrm{~m}_{\mathrm{e}}$ ):

Options:

A) 1 : 1

B) 1 : 43

C) 1 : 1849

D) 43 : 1

115

MediumJEE Mains2023

The work functions of Aluminium and Gold are $4.1 ~\mathrm{eV} and and 5.1 ~\mathrm{eV}$ respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is

Options:

A) 1.5

B) 1.24

C) 1

D) 2

116

MediumJEE Mains2023

The kinetic energy of an electron, $\alpha-particle and a proton are given as 4 \mathrm{~K}, 2 \mathrm{~K} and \mathrm{K} respectively. The de-Broglie wavelength associated with electron (\lambda \mathrm{e}), \alpha-particle ((\lambda \alpha) and the proton (\lambda p)$ are as follows:

Options:

A) \lambda \alpha<\lambda p<\lambda e

B) \lambda \alpha>\lambda p>\lambda e

C) \lambda \alpha=\lambda p<\lambda e

D) \lambda \alpha=\lambda p>\lambda e

117

EasyJEE Mains2023

The threshold frequency of a metal is $f_{0}. When the light of frequency 2 f_{0} is incident on the metal plate, the maximum velocity of photoelectrons is v_{1}. When the frequency of incident radiation is increased to 5 \mathrm{f}_{0}, the maximum velocity of photoelectrons emitted is v_{2}. The ratio of v_{1} to v_{2}$ is :

Options:

A) \frac{v_{1}}{v_{2}}=\frac{1}{2}

B) \frac{v_{1}}{v_{2}}=\frac{1}{16}

C) \frac{v_{1}}{v_{2}}=\frac{1}{4}

D) \frac{v_{1}}{v_{2}}=\frac{1}{8}

118

MediumJEE Mains2023

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $\lambda. An alpha particle having certain kinetic energy has the same de-Brogle wavelength \lambda$. The ratio of kinetic energy of proton and that of alpha particle is:

Options:

A) 1 : 4

B) 2 : 1

C) 4 : 1

D) 1 : 2

119

EasyJEE Mains2023

If the two metals \mathrm{A} and \mathrm{B} are exposed to radiation of wavelength 350 \mathrm{~nm}. The work functions of metals \mathrm{A} and \mathrm{B} are 4.8 \mathrm{eV} and 2.2 \mathrm{eV}. Then choose the correct option.

Options:

A) Metal B will not emit photo-electrons

B) Both metals \mathrm{A} and \mathrm{B} will not emit photo-electrons

C) Metal A will not emit photo-electrons

D) Both metals A and B will emit photo-electrons

120

EasyJEE Mains2023

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R Assertion A : The beam of electrons show wave nature and exhibit interference and diffraction. Reason R : Davisson Germer Experimentally verified the wave nature of electrons. In the light of the above statements, choose the most appropriate answer from the options given below :

Options:

A) A is not correct but R is correct.

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

C) Both A and R are correct but R is Not the correct explanation of A

D) A is correct but R is not correct

121

MediumJEE Mains2023

If a source of electromagnetic radiation having power $15 \mathrm{~kW} produces 10^{16} photons per second, the radiation belongs to a part of spectrum is. (Take Planck constant h=6 \times 10^{-34} \mathrm{Js}$ )

Options:

A) Gamma rays

B) Radio waves

C) Micro waves

D) Ultraviolet rays

122

MediumJEE Mains2023

An electron accelerated through a potential difference V_{1} has a de-Broglie wavelength of \lambda. When the potential is changed to V_{2}, its de-Broglie wavelength increases by 50 \%. The value of \left(\frac{V_{1}}{V_{2}}\right) is equal to

Options:

A) \frac{3}{2}

B) 4

C) 3

D) \frac{9}{4}

123

MediumJEE Mains2023

A small object at rest, absorbs a light pulse of power $20 \mathrm{~mW} and duration 300 \mathrm{~ns}. Assuming speed of light as 3 \times 10^{8} \mathrm{~m} / \mathrm{s}$, the momentum of the object becomes equal to :

Options:

A) 1 \times 10^{-17} \mathrm{~kg} \mathrm{~m} / \mathrm{s}

B) 0.5 \times 10^{-17} \mathrm{~kg} \mathrm{~m} / \mathrm{s}

C) 3 \times 10^{-17} \mathrm{~kg} \mathrm{~m} / \mathrm{s}

D) 2 \times 10^{-17} \mathrm{~kg} \mathrm{~m} / \mathrm{s}

124

MediumJEE Mains2023

The ratio of de-Broglie wavelength of an $\alpha particle and a proton accelerated from rest by the same potential is \frac{1}{\sqrt m}$, the value of m is -

Options:

A) 2

B) 16

C) 8

D) 4

125

EasyJEE Mains2023

The threshold wavelength for photoelectric emission from a material is 5500 $\mathop A\limits^o $. Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a A. 75 W infra-red lamp B. 10 W infra-red lamp C. 75 W ultra-violet lamp D. 10 W ultra-violet lamp Choose the correct answer from the options given below :

Options:

A) C only

B) A and D only

C) C and D only

D) B and C only

126

EasyJEE Mains2023

Given below are two statements : Statement I : Stopping potential in photoelectric effect does not depend on the power of the light source. Statement II : For a given metal, the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light. In the light of above statements, choose the most appropriate answer from the options given below

Options:

A) Both Statement I and Statement II are incorrect

B) Statement I is correct but Statement II is incorrect

C) Both Statement I and Statement II are correct

D) Statement I is incorrect but Statement II is correct

127

EasyJEE Mains2023

Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of $\lambda_0$. IF the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be :

Options:

A) 3 $\lambda_0

B) 9 $\lambda_0

C) \frac{\lambda_0}{\sqrt2}

D) \frac{\lambda_0}{2}

128

EasyJEE Mains2023

An $\alpha$-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength:

Options:

A) {\lambda _\alpha } > {\lambda _p} < {\lambda _e}

B) {\lambda _\alpha } > {\lambda _p} > {\lambda _e}

C) {\lambda _\alpha } = {\lambda _p} = {\lambda _e}

D) {\lambda _\alpha } < {\lambda _p} < {\lambda _e}

129

MediumJEE Mains2023

From the photoelectric effect experiment, following observations are made. Identify which of these are correct. A. The stopping potential depends only on the work function of the metal. B. The saturation current increases as the intensity of incident light increases. C. The maximum kinetic energy of a photo electron depends on the intensity of the incident light. D. Photoelectric effect can be explained using wave theory of light. Choose the correct answer from the options given below :

Options:

A) A, B, D only

B) A, C, D only

C) B, C only

D) B only

130

EasyJEE Mains2022

An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:

Options:

A) \sqrt2$ : 1

B) 2$\sqrt2$ : 1

C) 4$\sqrt2$ : 1

D) 8 : 1

131

MediumJEE Mains2022

The kinetic energy of emitted electron is E when the light incident on the metal has wavelength $\lambda$. To double the kinetic energy, the incident light must have wavelength:

Options:

A) \frac{\mathrm{hc}}{\mathrm{E} \lambda-\mathrm{hc}}

B) \frac{\mathrm{hc} \lambda}{\mathrm{E} \lambda+\mathrm{hc}}

C) \frac{\mathrm{h} \lambda}{\mathrm{E} \lambda+\mathrm{hc}}

D) \frac{\text { hc } \lambda}{\mathrm{E} \lambda-\mathrm{hc}}

132

EasyJEE Mains2022

Two streams of photons, possessing energies equal to five and ten times the work function of metal are incident on the metal surface successively. The ratio of maximum velocities of the photoelectron emitted, in the two cases respectively, will be

Options:

A) 1 : 2

B) 1 : 3

C) 2 : 3

D) 3 : 2

133

EasyJEE Mains2022

The equation $\lambda=\frac{1.227}{x} \mathrm{~nm} can be used to find the de-Brogli wavelength of an electron. In this equation x stands for : Where \mathrm{m}= mass of electron \mathrm{P}= momentum of electron \mathrm{K}= Kinetic energy of electron \mathrm{V}=$ Accelerating potential in volts for electron

Options:

A) \sqrt{\mathrm{mK}}

B) \sqrt{\mathrm{P}}

C) \sqrt{\mathrm{K}}

D) \sqrt{\mathrm{V}}

134

MediumJEE Mains2022

With reference to the observations in photo-electric effect, identify the correct statements from below : (A) The square of maximum velocity of photoelectrons varies linearly with frequency of incident light. (B) The value of saturation current increases on moving the source of light away from the metal surface. (C) The maximum kinetic energy of photo-electrons decreases on decreasing the power of LED (light emitting diode) source of light. (D) The immediate emission of photo-electrons out of metal surface can not be explained by particle nature of light/electromagnetic waves. (E) Existence of threshold wavelength can not be explained by wave nature of light/ electromagnetic waves. Choose the correct answer from the options given below :

Options:

A) (A) and (B) only

B) (A) and (E) only

C) (C) and (E) only

D) (D) and (E) only

135

MediumJEE Mains2022

An electron (mass $\mathrm{m}) with an initial velocity \vec{v}=v_{0} \hat{i}\left(v_{0}>0\right) is moving in an electric field \vec{E}=-E_{0} \hat{i}\left(E_{0}>0\right) where E_{0} is constant. If at \mathrm{t}=0 de Broglie wavelength is \lambda_{0}=\frac{h}{m v_{0}}$, then its de Broglie wavelength after time t is given by

Options:

A) \lambda_{0}

B) \lambda_{0}\left(1+\frac{e E_{0} t}{m v_{0}}\right)

C) \lambda_{0} t

D) \frac{\lambda_{0}}{\left(1+\frac{e E_{0} t}{m v_{0}}\right)}

136

EasyJEE Mains2022

A parallel beam of light of wavelength $900 \mathrm{~nm} and intensity 100 \,\mathrm{Wm}^{-2} is incident on a surface perpendicular to the beam. The number of photons crossing 1 \mathrm{~cm}^{2}$ area perpendicular to the beam in one second is :

Options:

A) 3 \times 10^{16}

B) 4.5 \times 10^{16}

C) 4.5 \times 10^{17}

D) 4.5 \times 10^{20}

137

MediumJEE Mains2022

The ratio of wavelengths of proton and deuteron accelerated by potential Vp and Vd is 1 : $\sqrt2$. Then the ratio of Vp to Vd will be :

Options:

A) 1 : 1

B) \sqrt2$ : 1

C) 2 : 1

D) 4 : 1

138

EasyJEE Mains2022

A metal exposed to light of wavelength $800 \mathrm{~nm} and and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength 500 \mathrm{~nm} is used. The workfunction of the metal is : (Take hc =1230 \,\mathrm{eV}-\mathrm{nm}$ ).

Options:

A) 1.537 eV

B) 2.46 eV

C) 0.615 eV

D) 1.23 eV

139

EasyJEE Mains2022

A source of monochromatic light liberates 9 $\times$ 1020 photon per second with wavelength 600 nm when operated at 400 W. The number of photons emitted per second with wavelength of 800 nm by the source of monochromatic light operating at same power will be :

Options:

A) 12 $\times$ 1020

B) 6 $\times$ 1020

C) 9 $\times$ 1020

D) 24 $\times$ 1020

140

MediumJEE Mains2022

The electric field at a point associated with a light wave is given by E = 200 [sin (6 $\times 1015)t + sin (9 \times 1015)t] Vm-1 Given : h = 4.14 \times 10-$15 eVs If this light falls on a metal surface having a work function of 2.50 eV, the maximum kinetic energy of the photoelectrons will be

Options:

A) 1.90 eV

B) 3.27 eV

C) 3.60 eV

D) 3.42 eV

141

EasyJEE Mains2022

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R : Assertion A : The photoelectric effect does not takes place, if the energy of the incident radiation is less than the work function of a metal. Reason R : Kinetic energy of the photoelectrons is zero, if the energy of the incident radiation is equal to the work function of a metal. In the light of the above statements, choose the most appropriate answer from the options given below.

Options:

A) Both A and R are correct and R is the correct explanation of A.

B) Both A and R are correct but R is not the correct explanation of A.

C) A is correct but R is not correct.

D) A is not correct but R is correct.

142

MediumJEE Mains2022

Let K1 and K2 be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength $\lambda1 and \lambda2, respectively are incident on a metallic surface. If \lambda1 = 3\lambda$2 then :

Options:

A) {K_1} > {{{K_2}} \over 3}

B) {K_1} < {{{K_2}} \over 3}

C) {K_1} = {{{K_2}} \over 3}

D) {K_2} = {{{K_1}} \over 3}

143

EasyJEE Mains2022

The de Broglie wavelengths for an electron and a photon are $\lambdae and \lambda$p respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two ?

Options:

A) {\lambda _p} \propto \lambda _e^2

B) {\lambda _p} \propto {\lambda _e}

C) {\lambda _p} \propto \sqrt {{\lambda _e}}

D) {\lambda _p} \propto \sqrt {{1 \over {{\lambda _e}}}}

144

EasyJEE Mains2022

An $\alpha particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelengths ({\lambda _\alpha }:{\lambda _{C12}})$ is :

Options:

A) 1:\sqrt 3

B) \sqrt 3 :1

C) 3:1

D) 2:\sqrt 3

145

MediumJEE Mains2022

A metal surface is illuminated by a radiation of wavelength 4500 $\mathop A\limits^o . The ejected photo-electron enters a constant magnetic field of 2 mT making an angle of 90^\circ$ with the magnetic field. If it starts revolving in a circular path of radius 2 mm, the work function of the metal is approximately :

Options:

A) 1.36 eV

B) 1.69 eV

C) 2.78 eV

D) 2.23 eV

146

MediumJEE Mains2022

An electron with speed v and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are Ee and pe and that of photon are Eph and pph respectively. Which of the following is correct?

Options:

A) {{{E_e}} \over {{E_{ph}}}} = {{2c} \over v}

B) {{{E_e}} \over {{E_{ph}}}} = {v \over {2c}}

C) {{{p_e}} \over {{p_{ph}}}} = {{2c} \over v}

D) {{{p_e}} \over {{p_{ph}}}} = {v \over {2c}}

147

EasyJEE Mains2022

A proton, a neutron, an electron and an $\alpha particle have same energy. If \lambdap, \lambdan, \lambdae and \lambdaa are the de Broglie's wavelengths of proton, neutron, electron and \alpha$ particle respectively, then choose the correct relation from the following :

Options:

A) \lambdap = \lambdan > \lambdae > \lambda$a

B) \lambdaa < \lambdan < \lambdap < \lambda$e

C) \lambdae < \lambdap = \lambdan > \lambda$a

D) \lambdae = \lambdap = \lambdan = \lambda$a

148

EasyJEE Mains2022

Given below are two statements : Statement I : Davisson-Germer experiment establishes the wave nature of electrons. Statement II : If electrons have wave nature, they can interfere and show diffraction. In the light of the above statements choose the correct answer from the option 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 true but Statement II is false.

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

149

EasyJEE Mains2022

The light of two different frequencies whose photons have energies 3.8 eV and 1.4 eV respectively, illuminate a metallic surface whose work function is 0.6 eV successively. The ratio of maximum speeds of emitted electrons for the two frequencies respectively will be :

Options:

A) 1 : 1

B) 2 : 1

C) 4 : 1

D) 1 : 4

150

MediumJEE Mains2021

The temperature of an ideal gas in 3-dimensions is 300 K. The corresponding de-Broglie wavelength of the electron approximately at 300 K, is :[me = mass of electron = 9 $\times 10-31 kg, h = Planck constant = 6.6 \times 6.6 \times 10-34 Js, kB = Boltzmann constant = 1.38 \times 10-23 JK-$1]

Options:

A) 6.26 nm

B) 8.46 nm

C) 2.26 nm

D) 3.25 nm

151

MediumJEE Mains2021

A free electron of 2.6 eV energy collides with a H+ ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. (h = 6.6 $\times 10-$34 Js)

Options:

A) 1.45 $\times$ 1016 MHz

B) 0.19 $\times$ 1015 MHz

C) 1.45 $\times$ 109 MHz

D) 9.0 $\times$ 1027 MHz

152

MediumJEE Mains2021

Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to :-

Options:

A) {\left( {{{{m_p}} \over {{m_e}}}} \right)^{3/2}}

B) \sqrt {{{{m_e}} \over {{m_p}}}}

C) \sqrt {{{{m_p}} \over {{m_e}}}}

D) {{{m_p}} \over {{m_e}}}

153

EasyJEE Mains2021

A moving proton and electron have the same de-Broglie wavelength. If K and P denote the K.E. and momentum respectively. Then choose the correct option :

Options:

A) Kp < Ke and Pp = Pe

B) Kp = Ke and Pp = Pe

C) Kp < Ke an Pp < Pe

D) Kp > Ke and Pp = Pe

154

MediumJEE Mains2021

A monochromatic neon lamp with wavelength of 670.5 nm illuminates a photo-sensitive material which has a stopping voltage of 0.48 V. What will be the stopping voltage if the source light is changed with another source of wavelength of 474.6 nm?

Options:

A) 0.96 V

B) 1.25 V

C) 0.24 V

D) 1.5 V

155

EasyJEE Mains2021

In a photoelectric experiment, increasing the intensity of incident light :

Options:

A) increases the number of photons incident and also increases the K.E. of the ejected electrons

B) increases the frequency of photons incident and increases the K.E. of the ejected electrons

C) increases the frequency of photons incident and the K.E. of the ejected electrons remains unchanged

D) increases the number of photons incident and the K.E. of the ejected electrons remains unchanged

156

MediumJEE Mains2021

The de-Broglie wavelength of a particle having kinetic energy E is $\lambda$. How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to 75% of the initial value?

Options:

A) {1 \over 9}$E

B) {7 \over 9}$E

C) E

D) {16 \over 9}$E

157

MediumJEE Mains2021

In a photoelectric experiment ultraviolet light of wavelength 280 nm is used with lithium cathode having work function $\phi = 2.5 eV. If the wavelength of incident light is switched to 400 nm, find out the change in the stopping potential. (h = 6.63 \times 10-34 Js, c = 3 \times 108 ms-$1)

Options:

A) 1.3 V

B) 1.1 V

C) 1.9 V

D) 0.6 V

158

MediumJEE Mains2021

An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electron and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength 4000$\mathop A\limits^o $. What is the maximum kinetic energy of the emitted photoelectron?

Options:

A) 7.61 eV

B) 1.41 eV

C) 3.3 eV

D) No photoelectron would be emitted

159

MediumJEE Mains2021

An electron moving with speed v and a photon moving with speed c, have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is :

Options:

A) {{3c} \over v}

B) {v \over {3c}}

C) {v \over {2c}}

D) {{2c} \over v}

160

MediumJEE Mains2021

When radiation of wavelength $\lambda$ is incident on a metallic surface, the stopping potential of ejected photoelectrons is 4.8 V. If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes 1.6 V. The threshold wavelength of the metal is :

Options:

A) 2$\lambda

B) 4$\lambda

C) 8$\lambda

D) 6$\lambda

161

EasyJEE Mains2021

What should be the order of arrangement of de-Broglie wavelength of electron ($\lambdae), an \alpha-particle (\lambdaa) and proton (\lambda$p) given that all have the same kinetic energy?

Options:

A) \lambdae = \lambdap = \lambda\alpha

B) \lambdae < \lambdap < \lambda\alpha

C) \lambdae > \lambdap > \lambda\alpha

D) \lambdae = \lambdap > \lambda\alpha

162

EasyJEE Mains2021

A particle of mass 4M at rest disintegrates into two particles of mass M and 3M respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass M to that of mass 3M will be :

Options:

A) 1 : 3

B) 3 : 1

C) 1 : $\sqrt 3

D) 1 : 1

163

EasyJEE Mains2021

An electron of mass me and a proton of mass mp are accelerated through the same potential difference. The ratio of the de-Broglie wavelength associated with the electron to that with the proton is

Options:

A) {{{m_e}} \over {{m_p}}}

B) 1

C) {{{m_p}} \over {{m_e}}}

D) \sqrt {{{{m_p}} \over {{m_e}}}}

164

MediumJEE Mains2021

An electron having de-Broglie wavelength $\lambda$ is incident on a target in a X-ray tube. Cut-off wavelength of emitted X-ray is :

Options:

A) 0

B) {{2{m^2}{c^2}{\lambda ^2}} \over {{h^2}}}

C) {{2mc{\lambda ^2}} \over h}

D) {{hc} \over {mc}}

165

MediumJEE Mains2021

The radiation corresponding to 3 $\to 2 transition of a hydrogen atom falls on a gold surface to generate photoelectrons. The electrons are passed through a magnetic field of 5 \times 10-4 T. Assume that the radius of the largest circular path followed by these electrons is 7 mm, the work function of the metal is : (Mass of electron = 9.1 \times 10-$31 kg)

Options:

A) 1.36 eV

B) 1.88 eV

C) 0.82 eV

D) 0.16 eV

166

MediumJEE Mains2021

The speed of electrons in a scanning electron microscope is 1 $\times$ 107 ms-1. If the protons having the same speed are used instead of electrons, then the resolving power of scanning proton microscope will be changed by a factor of :

Options:

A) {1 \over {1837}}

B) 1837

C) {\sqrt {1837} }

D) {1 \over {\sqrt {1837} }}

167

MediumJEE Mains2021

A particle is travelling 4 time as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is 2 : 1, the mass of the particle is :

Options:

A) {1 \over {16}} times the mass of e-

B) 8 times the mass of e$-

C) 16 times the mass of e$-

D) {1 \over {8}} times the mass of e-

168

EasyJEE Mains2021

Two identical photocathodes receive the light of frequencies f1 and f2 respectively. If the velocities of the photo-electrons coming out are v1 and v2 respectively, then

Options:

A) {v_1} - {v_2} = {\left[ {{{2h} \over m}({f_1} - {f_2})} \right]^{{1 \over 2}}}

B) v_1^2 + v_2^2 = {{2h} \over m}[{f_1} + {f_2}]

C) {v_1} + {v_2} = {\left[ {{{2h} \over m}({f_1} + {f_2})} \right]^{{1 \over 2}}}

D) v_1^2 - v_2^2 = {{2h} \over m}[{f_1} - {f_2}]

169

MediumJEE Mains2021

An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to that of photon is : (c being the velocity of light)

Options:

A) {1 \over c}{\left( {{{2m} \over E}} \right)^{1/2}}

B) {1 \over c}{\left( {{E \over {2m}}} \right)^{1/2}}

C) {\left( {{E \over {2m}}} \right)^{1/2}}

D) c{(2mE)^{1/2}}

170

EasyJEE Mains2021

The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100 V. What should nearly be the ratio of their wavelengths? (mp = 1.00727u me = 0.00055u)

Options:

A) 41.4 : 1

B) (1860)2 : 1

C) 1860 : 1

D) 43 : 1

171

EasyJEE Mains2021

The stopping potential in the context of photoelectric effect depends on the following property of incident electromagnetic radiation :

Options:

A) Phase

B) Frequency

C) Amnplitude

D) Intensity

172

MediumJEE Mains2021

The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state will be :

Options:

A) 4.34 m/s

B) 2.19 m/s

C) 3.25 m/s

D) 4.17 m/s

173

EasyJEE Mains2021

Given below are two statements : one is labeled as Assertion A and the other is labelled as Reason R.Assertion A : An electron microscope can achieve better resolving power than an optical microscope.Reason R : The de Broglie's wavelength of the electrons emitted from an electron gun is much less than wavelength of visible light.In the light of the above statements, choose the correct answer from the options given below :

Options:

A) A is false but R is true.

B) Both A and R are true but R is NOT the correct explanation of A.

C) Both A and R are true and R is the correct explanation of A.

D) A is true but R is false.

174

EasyJEE Mains2021

An electron of mass me and a proton of mass mp = 1836 me are moving with the same speed. The ratio of their de Broglie wavelength ${{{}^\lambda electron} \over {{}^\lambda proton}}$ will be :

Options:

A) 1

B) 1836

C) {1 \over {1836}}

D) 918

175

MediumJEE Mains2021

The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength 491 nm is 0.710 V. When the incident wavelength is changed to a new value, the stopping potential is 1.43 V. The new wavelength is :

Options:

A) 400 nm

B) 329 nm

C) 309 nm

D) 382 nm

176

MediumJEE Mains2021

An $\alpha particle and a proton are accelerated from rest by a potential difference of 200V. After this, their de Broglie wavelengths are \lambda\alpha and \lambdap respectively. The ratio {{{{\lambda _p}} \over {{\lambda _\alpha }}}}$ is :

Options:

A) 8

B) 2.8

C) 7.8

D) 3.8

177

MediumJEE Mains2021

An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be :

Options:

A) 10$-$2 nm

B) 10$-$1 nm

C) 10$-$3 nm

D) 10$-$4 nm

178

EasyJEE Mains2021

The de-Broglie wavelength of a proton and $\alpha$-particle are equal. The ratio of their velocities is :

Options:

A) 4 : 2

B) 4 : 3

C) 4 : 1

D) 1 : 4

179

EasyJEE Mains2021

Given below are two statements : Statement I : Two photons having equal linear momenta have equal wavelengths.Statement II : If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease.In the light of the above statements, choose the correct answer from the options given below.

Options:

A) Statement I is false but Statement II is true

B) Both Statement I and Statement II are false

C) Both Statement I and Statement II are true

D) Statement I is true but Statement II is false

180

MediumJEE Mains2020

Assuming the nitrogen molecule is moving with r.m.s. velocity at 400 K, the de-Broglie wavelength of nitrogen molecule is close to : (Given : nitrogen molecule weight : 4.64 $ \times 10–26 kg, Boltzman constant: 1.38 \times 10–23 J/K, Planck constant : 6.63 \times $ 10–34 J.s)

Options:

A) 0.44 $\mathop A\limits^o

B) 0.34 $\mathop A\limits^o

C) 0.20 $\mathop A\limits^o

D) 0.24 $\mathop A\limits^o

181

MediumJEE Mains2020

An electron, a doubly ionized helium ion (He++) and a proton are having the same kinetic energy. The relation between their respective de-Broglie wavelengths $\lambda e, \lambda He++ and \lambda $p is :

Options:

A) \lambda e > \lambda He++ > \lambda $p

B) \lambda e < \lambda p < \lambda $He++

C) \lambda e > \lambda p > \lambda $He++

D) \lambda e < \lambda He++ = \lambda $p

182

MediumJEE Mains2020

In a photoelectric effect experiment, the graph of stopping potential V versus reciprocal of wavelength obtained is shown in the figure. As the intensity of incident radiation is increased :

Options:

A) Slope of the straight line get more steep

B) Graph does not change

C) Straight line shifts to left

D) Straight line shifts to right

183

MediumJEE Mains2020

Given figure shows few data points in a phot electric effect experiment for a certain metal. The minimum energy for ejection of electron from its surface is: (Plancks constant h = 6.62 × 10–34 J.s)

Options:

A) 2.10 eV

B) 2.27 eV

C) 2.59 eV

D) 1.93 eV

184

MediumJEE Mains2020

Particle A of mass mA = ${m \over 2} moving along the x-axis with velocity v0 collides elastically with another particle B at rest having mass mB = {m \over 3}. If both particles move along the x-axis after the collision, the change \Delta \lambda in de-Broglie wavlength of particle A, in terms of its de-Broglie wavelength (\lambda $0) before collision is :

Options:

A) \Delta \lambda = {5 \over 2}{\lambda _0}

B) \Delta \lambda = {3 \over 2}{\lambda _0}

C) \Delta \lambda = 2\lambda $0

D) \Delta \lambda = 4\lambda $0

185

MediumJEE Mains2020

Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respectively. Both the sources emit light of the same power 200 W. The ratio of the number density of photons of X-rays to the number density of photons of the visible light of the given wavelengths is :

Options:

A) {1 \over {500}}

B) 500

C) 250

D) {1 \over {250}}

186

MediumJEE Mains2020

When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to :

Options:

A) 1.02 eV

B) 0.81 eV

C) 0.61 eV

D) 0.52 eV

187

MediumJEE Mains2020

A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is 1.878 $ \times $ 10–4. The mass of the particle is close to

Options:

A) 1.2 $ \times $ 10–28 kg

B) 9.1 $ \times $ 10–31 kg

C) 4.8 $ \times $ 10–27 kg

D) 9.7 $ \times $ 10–28 kg

188

MediumJEE Mains2020

An electron of mass m and magnitude of charge |e| initially at rest gets accelerated by a constant electric field E. The rate of change of de-Broglie wavelength of this electron at time t ignoring relativistic effects is :

Options:

A) {{ - h} \over {\left| e \right|Et}}

B) {{ - h} \over {\left| e \right|E\sqrt t }}

C) {{ - h} \over {\left| e \right|E{t^2}}}

D) {{\left| e \right|Et} \over h}

189

MediumJEE Mains2020

A particle moving with kinetic energy E has de Broglie wavelength $\lambda . If energy \Delta E is added to its energy, the wavelength become \lambda /2. Value of \Delta $E, is :

Options:

A) E

B) 3E

C) 2E

D) 4E

190

MediumJEE Mains2020

Radiation, with wavelength 6561 $\mathop A\limits^o $ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of 3 × 10–4 T. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :

Options:

A) 1.8eV

B) 0.8eV

C) 1.1eV

D) 1.6eV

191

MediumJEE Mains2020

An electron (mass m) with initial velocity $\overrightarrow v = {v_0}\widehat i + {v_0}\widehat j is in an electric field \overrightarrow E = - {E_0}\widehat k. If \lambda _0$ is initial de-Broglie wavelength of electron, its de-Broglie wave length at time t is given by :

Options:

A) {{{\lambda _0} } \over {\sqrt {1 + {{{e^2}{E^2}{t^2}} \over {{m^2}v_0^2}}} }}

B) {{{\lambda _0}\sqrt 2 } \over {\sqrt {1 + {{{e^2}{E^2}{t^2}} \over {{m^2}v_0^2}}} }}

C) {{{\lambda _0} } \over {\sqrt {1 + {{{e^2}{E^2}{t^2}} \over {2{m^2}v_0^2}}} }}

D) {{{\lambda _0}} \over {\sqrt {2 + {{{e^2}{E^2}{t^2}} \over {{m^2}v_0^2}}} }}

192

MediumJEE Mains2020

When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy TA eV end de-Broglie wavelength $\lambda _A. The maximum kinetic energy of photoelectrons liberated from another metal B by photon of energy 4.50 eV is TB = (TA – 1.5) eV. If the de-Broglie wavelength of these photoelectrons \lambda _B = 2\lambda _A$, then the work function of metal B is :

Options:

A) 1.5eV

B) 4eV

C) 2eV

D) 3eV

193

MediumJEE Mains2020

An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (c = speed of light in vaccuum)

Options:

A) {1 \over c}{\left( {{{2E} \over m}} \right)^{{1 \over 2}}}

B) {1 \over c}{\left( {{E \over {2m}}} \right)^{{1 \over 2}}}

C) {\left( {{E \over {2m}}} \right)^{{1 \over 2}}}

D) c{\left( {2mE} \right)^{{1 \over 2}}}

194

MediumJEE Mains2019

The stopping potential V0 (in volt) as a function of frequency ($\upsilon $) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be: (Given: Planck’s constant (h) = 6.63 × 10–34 Js, electron charges e = 1.6 × 10–19 C)

Options:

A) 1.95 eV

B) 2.12 eV

C) 1.82 eV

D) 1.66 eV

195

MediumJEE Mains2019

A 2 mW laser operates at wavelength of 500 nm. The number of photons that will be emitted per second is : [Given Planck's constant h = 6.6 × 10–34 Js, speed of light c = 3.0 × 108 m/s]

Options:

A) 5 × 1015

B) 1.5 × 1016

C) 1 × 1016

D) 2 × 1016

196

MediumJEE Mains2019

In a photoelectric effect experiment the threshold wavelength of the light is 380 nm. If the wavelentgh of incident light is 260 nm, the maximum kinetic energy of emitted electrons will be: Given E (in eV) = 1237/$\lambda $ (in nm)

Options:

A) 4.5 eV

B) 15.1 eV

C) 3.0 eV

D) 1.5 eV

197

MediumJEE Mains2019

A particle 'P' is formed due to a completely inelastic collision of particles 'x' and 'y' having de-Broglie wavelengths '$\lambda x' and '\lambda $y' respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of 'P' is :-

Options:

A) {\lambda _x} - {\lambda _y}

B) {{{\lambda _x}{\lambda _y}} \over {\left| {{\lambda _x} - {\lambda _y}} \right|}}

C) {\lambda _x} + {\lambda _y}

D) {{{\lambda _x}{\lambda _y}} \over {{\lambda _x} + {\lambda _y}}}

198

MediumJEE Mains2019

The electric field of light wave is given as $$\overrightarrow E = {10^{ - 3}}\cos \left( {{{2\pi x} \over {5 \times {{10}^{ - 7}}}} - 2\pi \times 6 \times {{10}^{14}}t} \right)\mathop x\limits^ \wedge {{\rm N} \over C} This light falls on a metal plate of work function 2eV. The stopping potential of the photoelectrons is : Given, E (in eV) = 12375/\lambda $(inÅ)

Options:

A) 2.48 V

B) 0.48 V

C) 0.72 V

D) 2.0 V

199

MediumJEE Mains2019

A nucleus A, with a finite de-broglie wavelength $\lambda A, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of B. The de-Broglie wavelengths \lambda B and \lambda $C of B and C are respectively :

Options:

A) \lambda A, 2\lambda $A

B) 2$\lambda A, \lambda $A

C) \lambda A, \lambda $A/2

D) \lambda A/2, \lambda $A

200

MediumJEE Mains2019

Two particles move at right angle to each other. Their de-Broglie wavelengths are $\lambda _1 and \lambda _2 respectively. The particles suffer perfectly inelastic collision. The de-Broglie wavelength \lambda _2$ of the final particle, is given by :

Options:

A) \lambda = {{{\lambda _1} + {\lambda _2}} \over 2}

B) {1 \over {{\lambda ^2}}} = {1 \over {\lambda _1^2}} + {1 \over {\lambda _2^2}}

C) \lambda = \sqrt {{\lambda _1}{\lambda _2}}

D) {2 \over \lambda } = {1 \over {{\lambda _1}}} + {1 \over {{\lambda _2}}}

201

MediumJEE Mains2019

When a certain photosensitive surface is illuminated with monochromatic light of frequency v, the stopping potential for the current is –V0/2. When the surface is illuminated by monochromatic light of frequency v/2, the stopping potential is – V0. The threshold frequency for photoelectric emission is :

Options:

A) 2$v

B) {4 \over 3}v

C) {{3v} \over 2}

D) {{5v} \over 3}

202

MediumJEE Mains2019

In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to :

Options:

A) 2020 nm

B) 250 nm

C) 1700 nm

D) 220 nm

203

MediumJEE Mains2019

A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another particle B of mass ' 4 m' and charge 'q' is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths ${{{\lambda _A}} \over {{\lambda _B}}}$ is close to :

Options:

A) 4.47

B) 10.00

C) 14.14

D) 0.07

204

MediumJEE Mains2019

In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to: (${{{hc} \over e}}$ = 1240 nm eV)

Options:

A) 0.5 V

B) 1.0 V

C) 2.0 V

D) 1.5 V

205

MediumJEE Mains2019

If the de Broglie wavelength of an electron is equal to the 10–3 times the wavelength of a photon of frequency 6 $ \times 1014 Hz, then the speed of electron is equal to : (Speed of light = 3 \times 108 m/s, Planck's constant = 6.63 \times 10–34 J.s, Mass of electron = 9.1 \times $ 10–31 kg)

Options:

A) 1.7 $ \times $ 106 m/s

B) 1.45 $ \times $ 106 m/s

C) 1.1 $ \times $ 106 m/s

D) 1.8 $ \times $ 106 m/s

206

MediumJEE Mains2019

A metal plate of area 1 $ \times $ 10–4 m2 is illuminated by a radiation of intensity 16 mW/m2. The work function of the metal is 5 eV. The energy of the incident photons is 10 eV and only 10% of it produces photo electrons. The number of emitted photoelectrons per second and their maximum energy, respectively, will be

Options:

A) 1014 and 10 eV

B) 1012 and 5 eV

C) 1011 and 5 eV

D) 1010 and 5 eV

207

MediumJEE Mains2019

In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 × 10–12 m, the minimum electron energy required is close to -

Options:

A) 25 keV

B) 500 keV

C) 100 keV

D) 1 keV

208

MediumJEE Mains2019

The magnetic field associated with a light wave is given, at the origin, by B = B0 [sin(3.14 $ \times 107)ct + sin(6.28 \times 107)ct]. If this light falls on a silver plate having a work function of 4.7 eV, what will be the maximum kinetic energy of the photo electrons ? (Take c = 3 \times 108 ms-1, h = 6.6 \times 10-$34J-s)

Options:

A) 6.82 eV

B) 12.5 eV

C) 8.52 eV

D) 7.72 eV

209

MediumJEE Mains2019

Surface of certain metal is first illuminated with light of wavelength $\lambda 1 = 350 nm and then, by light of wavelength \lambda 2 = 540 nm. It is found that the maximum speed of the photo electrons in the two cases differ by a factor of 2. The work function of the metal (in eV) is close to : (Energy of photon n = {{1240} \over {\lambda (in\,mm)}}$eV)

Options:

A) 1.8

B) 2.5

C) 5.6

D) 1.4

210

MediumJEE Mains2018

The de-Broglie wavelength ($\lambda B) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state (\lambda $G) by :

Options:

A) \lambda B = 2\lambda $G

B) \lambda B = 3\lambda $G

C) \lambda B = \lambda $G/2

D) \lambda B = \lambda $G/3

211

MediumJEE Mains2018

Both the nucleus and the atom of some element arein their respective first excited states. They get de-excted by emitting photons of wavelengths $\lambda N, \lambda A respectively. The ratio {{{}^\lambda N} \over {{}^\lambda A}}$is closest to :

Options:

A) 10$-$6

B) 10

C) 10$-$10

D) 10$-$1

212

MediumJEE Mains2018

If the de Broglie wavelengths associated with a proton and an $\alpha -particle are equal, then the ratio of velocities of the proton and the \alpha $-particle will be :

Options:

A) 4 : 1

B) 2 : 1

C) 1 : 2

D) 1 : 4

213

MediumJEE Mains2018

Two electrons are moving with non-relativistic speed perpendicular to each other. If corresponding de Broglie wavelength are ${\lambda _1} and {\lambda _2},$ their de Broglie wavelength in the frame of reference attached to their center of masses :

Options:

A) {\lambda _{CM}} = {\lambda _1} = {\lambda _2}

B) {\lambda _{CM}} = {{2{\lambda _1}{\lambda _2}} \over {\sqrt {\lambda _1^2 + \lambda _2^2} }}

C) {1 \over {{\lambda _{CM}}}} = {1 \over {{\lambda _1}}} + {1 \over {{\lambda _2}}}

D) {\lambda _{CM}} = \left( {{{{\lambda _1} + {\lambda _2}} \over 2}} \right)

214

MediumJEE Mains2017

A Laser light of wavelength 660 nm is used to weld Retina detachment. If a Laser pulse of width 60 ms and power 0.5 kW is used the approximate number of photons in the pulse are : [Take Planck's constant h $= 6.62 \times 10-$34 Js]

Options:

A) 1020

B) 1018

C) 1022

D) 1019

215

MediumJEE Mains2017

The maximum velocity of the photoelectrons emitted from the surface is v when light of frequency n falls on a metal surface. If the incident frequency is increased to 3n, the maximum velocity of the ejected photoelectrons will be :

Options:

A) less than $\sqrt 3 $ v

B) v

C) more than $\sqrt 3 \,v

D) equal to $\sqrt 3 \,v

216

MediumJEE Mains2017

A particle A of mass m and initial velocity v collides with a particle B of mass m/2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths ${\lambda _A} to {\lambda _B}$ after the collision is:

Options:

A) {{{\lambda _A}} \over {{\lambda _B}}} = {1 \over 3}

B) {{{\lambda _A}} \over {{\lambda _B}}} = 2

C) {{{\lambda _A}} \over {{\lambda _B}}} = {2 \over 3}

Options:

A) E_{\max }=h v-\phi

B) E=m c^2

C) E^2=p^2 c^2+m_0^2 c^4

D) E=\left(\frac{1}{2}\right) m v^2

384

Total Questions

Easy

304

Medium

Hard

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