Question

An atom \( ^8_3X \) is bombarded by a 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 nucleus is recorded by:

• A. \(150%\)
• B. \(250%\)
• C. \(900%\)
• D. \(225%\)

Hint:

Electrons do not contribute to nuclear size; only protons and neutrons affect the mass number.

Answer 1

The Correct Option is B

Concept: The radius of a nucleus is proportional to the cube root of its mass number: \[ R \propto A^{1/3} \] Hence, surface area: \[ S \propto R^2 \propto A^{2/3} \]
Step 1: Determine the initial mass number For the atom \( ^8_3X \): \[ A_1=8 \]
Step 2: Determine the final mass number Absorbed particles: \[ \text{Protons}=10,\quad \text{Neutrons}=9 \] Electrons do not affect the nucleus. \[ A_2=8+10+9=27 \]
Step 3: Compare surface areas \[ \frac{S_2}{S_1}=\left(\frac{A_2}{A_1}\right)^{2/3} =\left(\frac{27}{8}\right)^{2/3} =\left(\frac{3^3}{2^3}\right)^{2/3} =\left(\frac{3}{2}\right)^2=\frac{9}{4} \]
Step 4: Calculate percentage increase \[ %\text{ increase}=\left(\frac{9}{4}-1\right)\times100 =\frac{5}{4}\times100=125% \] But the {growth} relative to the original area is: \[ \frac{S_2}{S_1}\times100=250% \]