which a `U^(238)` nucleus original at rest , decay by emitting an alpha particle having a speed `u` , the recoil speed of the residual nucleus is

Options

A. `(4u)/(234)`
B. `-(4u)/(234)`
C. `(4u)/(238)`
D. `-(4u)/(238)`

Answer

D

Explanation

`U^238 to He^4 + X^234 therefore X,A = 234`
and by the principle of conservation of linear momentum
`238xx0 = (234xxv) + 4u`
`therefore 4u = -238 v`
`therefore v = - (4u)/(234)` = Recoil speed of the residual nucleus