An atom � 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

An atom 8 3 X is bombarded by shower of fundamental particles

Q. An atom ⁸₃X 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:

(A) 50

(B) 900

(D) 225%

Correct Answer: 225%

Explanation

Only protons and neutrons contribute to the number of nucleons. Electrons do not affect nuclear size.

Initial mass number:

A_i = 8

Number of nucleons absorbed:

10 protons + 9 neutrons = 19 nucleons

Final mass number:

A_f = 8 + 19 = 27

Radius of nucleus varies as:

R ∝ A^1/3

Surface area varies as:

S ∝ R² ∝ A^2/3

So,

S_i ∝ 8^2/3 = 4

S_f ∝ 27^2/3 = 9

Percentage growth recorded is taken as:

(S_f / S_i) × 100 = (9 / 4) × 100 = 225%

Hence, the recorded percentage growth in surface area is:

225%

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