The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is :

Solution

Physics sir · 3 steps

Radius goes as the cube root of A, so halving the radius divides A by 2³ = 8.

1. Size of a nucleus. Nuclear radius depends on mass number as R = R₀ A^(1/3), where R₀ is the same constant for every nucleus.

   R₂/R₁ = (A₂/A₁)^(1/3)

2. Put in numbers. Here R₂/R₁ = 1/2 and A₁ = 192. Cube both sides: A₂/192 = (1/2)³ = 1/8.
3. So. A₂ = 192/8 = 24, which is option (b).

The idea to keep. Since R ∝ A^(1/3), mass number goes as the cube of the radius. Scale the radius by k and the mass number scales by k³.

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