A nucleus of mass `M+Deltam` is at rest and decays into two daughter nuclei of equal mass `(M)/(2)` each. Speed of light is c.
The speed of daughter nuclei is

Options

A. `csqrt((Deltam)/(M+mDeltam))`
B. `c(Deltam)/(M+Deltam)`
C. `csqrt((2Deltam)/(M))`
D. `csqrt((Deltam)/(M))`

Answer

C

Explanation

Total kinetic energy of products
`=` Total energy released `(P^(2))/(2m) + (P^(2))/(2m)`
= {mass defect) `c^(2)` (where `m = (M)/(2)` given)
`rArr 2(P^(2))/(2m) = [(M + Deltam) - ((M)/(2) + (M)/(2))] xx c^(2)`
`2 xx [(P^(2))/(2 ((M)/(2)))] = (Delta m)c^(2)`
`rArr (2((M)/(2)v)^(2))/(M) = (Delta m)c^(2) rArr v = c sqrt((2 Delta m)/(M))`