A nucleus splits into two parts whose nuclear radii are in the ratio 1 : 2 1 3 2^{\frac13} 2 3 1 . Their speeds are in the ratio n : 1. Find n.

Question

A nucleus splits into two parts whose nuclear radii are in the ratio 1 : 2 1 3 2^{\frac13} 2 3 1 ​ . Their speeds are in the ratio n : 1. Find n.

G1 Physics · Accepted Answer

Nuclear radius R ∝ A ( 1 / 3 ) , A^(1/3), A ( 1/3 ) , so mass is proportional to R³. Thus m₁:m₂ = 1³:[2^(1/3)]³ = 1:2. Initial nucleus is at rest, so momentum conservation gives m₁v₁ = m₂v₂. v₁/v₂ = m₂/m₁ = 2. Therefore n = 2.

A nucleus splits into two parts whose nuclear radii are in the ratio 1 : 2 1 3 2^{\frac13} 2 3 1 ​ . Their speeds are in the ratio n : 1. Find n.

A nucleus splits into two parts whose nuclear radii are in the ratio 1 : 2 1 3 2^{\frac13} 2 3 1 . Their speeds are in the ratio n : 1. Find n.