A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3:2. The ratio of their nuclear sizes will be . The value of 'x' is:-
Show answer and solution
Answer: 2
Solution
By conservation of momentum, m₁v₁ = m₂v₂, so m₁/m₂ = v₂/v₁ = 2/3.
Since mass number A ∝ R³, we have R₁/R₂ = (A₁/A₂)^(1/3) = (2/3)^(1/3) = (2/3)^(1/3).
This equals (x/3)^(1/3), so x = 2.
Since mass number A ∝ R³, we have R₁/R₂ = (A₁/A₂)^(1/3) = (2/3)^(1/3) = (2/3)^(1/3).
This equals (x/3)^(1/3), so x = 2.
[JEE Main 2023 · 25 Jan · Shift 2]