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

Answer

D

Explanation

Fraction remains after n half-lives
`(N)/(N_(0))=((1)/(2))^(n)=((1)/(2))^(t//T)`
Given, `N=(N_(0))/(e)`
`implies (N_(0))/(eN_(0))=((1)/(2))^(5//T) or (1)/(e)=((1)/(2))^(5//T)`
Taking log on both sides, we get
`log1-loge=(5)/(T) "log"(1)/(2)`
`-1=(5)/(7)(-log2) implies T=5log_(e)2`
Now, let t' be the time after which activity reduces to half
`((1)/(2))=((1)/(2))^(t'//5log_(e)2) implies t'=5log_(e)2`