Question 79: Atoms & Nuclei

Question

An atom ${ }_3^8 X$ is bombarded by shower of fundamental particles and in 10 s this atom absorbed 10 electrons, 10 protons and 9 neutrons. The percentage growth in the surface area of the nucleons is recorded by :

Accepted Answer

The mass number of initial nucleus is $\mathrm{A}_1=8$
The radius of a nucleus is proportional to $A^{1 / 3}\left(R=R_0 A^{1 / 3}ight)$.
So, the nuclear radius of initial nucleus is $R_1=R_0(8)^{1 / 3}=2 R_0$
Hence, initial surface area
$$ \mathrm{S}_1=4 \pi \mathrm{R}_1^2 $$
$$\Rightarrow $$ $$ S_1=4 \pi\left(2 R_0ight)^2=16 \pi R_0^2 $$
The atom absorbs 10 protons and 9 neutrons.
Total nucleons in final state of nucleus is 10 protons +9 neutrons $=19$ nucleons.
So, new mass number is $\mathrm{A}_2=\mathrm{A}_1+19=8+19=27$
The final radius,
$$ \mathrm{R}_2=\mathrm{R}_0(27)^{1 / 3}=3 \mathrm{R}_0 $$
So, final surface area is
$$ S_2=4 \pi\left(3 R_0ight)^2=36 \pi R_0^2 $$
The question has asked about the percentage growth recorded, that means final surface area is what percentage
So, the percentage growth is,
So, the percentage growth is,
$$ \frac{\Delta S}{\mathrm{~S}_1} 	imes 100 \%=\frac{36 \pi \mathrm{R}_0^2-16 \pi \mathrm{R}_0^2}{16 \pi \mathrm{R}_0^2} 	imes 100 \%=125 \% $$

Answer

$150 \%$

Answer

$900\%$

Answer

$125 \%$

Answer

$225 \%$

Atoms & Nuclei

An atom { }_3^8 X is bombarded by shower of fundamental particles and in 10 s this atom absorbed 10 electrons, 10 protons and 9 neutrons. The percentage growth in the surface area of the nucleons is recorded by :

Choose the correct answer: