Question

A nucleus of 210 84 Po originally at rest emits α-particle with speed v what will be the recoil speed of the daughter nucleus 

(A) [v / (214)] 

(B) [(4v) / (214)] 

(C) [(4v) / (206)] 

(D) [v / (206)]

Answer 1

The correct option is (C) [(4v) / (206)].

Explanation:

according to conservation of momentum,

m₁v₁ + m₂v₂ = 0

m₁ = mass number of α particle = 4 

v₁ = velocity of α particle = v 

m₂ = mass number of daughter nucleus = 210 – 4 = 206 

v₂ = velocity of daughter nucleus 

∴ 4v₁ + 206v₂ = 0 

∴ 206v₂ = – 4v₁ 

∴ v₂ = [(– 4v₁) / (206)] 

∴ v₂ = [(– 4v) / (206)] = [(4v) / (206)] (magnitude)