What is the kinetic energy of the recoiling daughter nucleus?

Question

A nucleus of mass 228 u, initialy at rest,
undergoes alpha decay.
If the alpha particle emitted has a kinetic
energy 3.06 Mev, what is the kinetic energy
of the recoiling daughter nucleus?
Answer in units of Mev.

Answer 1

A nucleus of mass 228 u, initialy at rest,
undergoes alpha decay.
If the alpha particle emitted has a kinetic
energy 3.06 Mev, what is the kinetic energy
of the recoiling daughter nucleus?
Answer in units of Mev.

 

========================

 

Let mass of alpha is m=4u

     velocity of alpha is v

     velocity of daughter nucleus is V

 

     mass of daughter nucleus will be M=228-4=224(u)

 

From momentum conseervation we have:  mv=MV

So, V=v*m/M

Energy of daughter will be,

 

T=MV^2/2=Mv^2*m^2/M^2=(mv^2/2)*m/M=3.06(mev)*4/224 = 0.0546 (MeV)

 

Message if questions;

good luck:)