A nucleus `""_(Z)X^(A)` emits an `alpha`- particle with the velocity v. The recoil speed of the daughter nucleus is

Options

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

Answer

B

Explanation

According to low of conservation of linear momentum,
`0 = m_(D)v_(D) + m_(alpha) v_(alpha)`
where subscripts D and `alpha` represent daughter neucles and `alpha`-particle respectively.
`0 = (A - 4)v_(D) + 4v`
`v_(D) = - (4v)/(A - 4)`
Negative sign shows the recoil of the daughter nucleus.