The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another nucleus having radius of 4 fermi is 1000/x, where x is _______.

Solution

Physics sir · 3 steps

Nuclear radius goes as the cube root of A, so cube the radius ratio to get the mass ratio.

1. Size rule. Nuclear radius follows R = R₀ A^(1/3). So A ∝ R³, and R₀ cancels when you compare two nuclei.

   A₂/A₁ = (R₂/R₁)³

2. Put in numbers. R₂/R₁ = 4/4.8 = 5/6, so A₂/A₁ = 125/216. Then A₂ = 64 × 125/216 = 8000/216 = 1000/27.
3. So. Matching 1000/27 with 1000/x gives x = 27.

The common slip: 18.75. Taking R ∝ A instead of A^(1/3) gives A₂ = 64 × 5/6 = 160/3 and so x = 18.75, not 27.

The idea to keep. Nuclear volume is proportional to A, because nuclear density is the same for every nucleus. Radius therefore goes as A^(1/3): cube the radius ratio, never use it directly.

Answer from the NTA final answer key. Solution by PrepWiser.