There are two radioactive substance `A` and `B`. Decay consant of `B` is two times that of `A`. Initially, both have equal number of nuceli. After n half-lives of `A`,rates of disintegaration of both are equal. The value of `n` is .

Options

A. 1
B. 2
C. 4
D. all of these

Answer

A

Explanation

`lamda_(e)=2 lamda_(A)`
`(dN_(e))/(dt)=(dN_(A))/(dt)`
`lamda_(B)N_(B)=lamda_(A)N_(A) rArr lamda_(B)N_(0)e^(-lamda_(B)t)=lamda_(A)N_(0)e^(-lamda_(A)t)`
`2 lamda_(A)e^(-lamda_(B)t)=lamda_(A)e^(-lamda_(A)t)`
`2=e^((lamda_(B)-lamda_(A))t)`
`t = (lamda_(B)-lamda_(A))=l n2 rArrt = (l n2)/(lamda_(A))=t_(H_(A))`.