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. `(2v)/(A+4)`
B. `(4v)/(A+4)`
C. `(4v)/(A-4)`
D. `(2v)/(A-4)`

Answer

C

Explanation

`underset(("parent nucleus"))(""^AX)to underset(("Daughter nucleus"))(""^(A-4)Y+alpha^(4))`
As the parent nucleus is at rest,then according to convervation of momentum.
`implies0=M_(gamma)V(gamma)+m_(alpha)V_(alpha)`
`impliesv_(gamma)=(4v)/(A-4)`,the recol speed of daughter nucleus.