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 :
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Question

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 :

Options

G1 Physics · Accepted Answer

The nuclear radius varies as R ∝ A¹ᐟ³. Therefore the nuclear surface area varies as S ∝ R² and hence S ∝ A²ᐟ³. Initially, Aᵢ = 8. Electrons do not contribute to the nuclear mass number. The atom absorbs 10 protons and 9 neutrons. Therefore, A𝒇 = 8+10+9 = 27. Hence, S𝒇/Sᵢ = (27/8)²ᐟ³ = (3/2)² = 9/4 = 2.25. Thus the final surface area is 225% of the initial surface area. The actual percentage increase is (2.25-1)×100 = 125%. The supplied source lists NTA answer option C, corresponding to 225%,…