A radioactive nucleus of mass number A, initially at rest, emits an `alpha-` particle with a speed v. What will be the recoil speed of the daughter nucleus ?

Options

A. `(A-4)/(4v)`
B. `(4v)/(A-4)`
C. v
D. `v/4`

Answer

B

Explanation

According to the question
`""_(Z)X^(A)to""_(Z-2)Y^(A-4)+2He^(4)`
Let the recoil speed of daughter nucleus is v'. By the law of conservation of momentum, we have
Initial momentum=Final momentum
`0=(A-4)v'+4v`
or `(A-4)v'=-4vorv'=-(4v)/((A-4))`