There are two radioactive sunstances A and B Decay constant of B is two times that of A Intially bothe have equal number of nuclei. After n half lives of A rate of disintegration of both are equla. The value of n is

Options

A. `1`
B. `2`
C. `4`
D. All of the above

Answer

a

Explanation

Let `lambda_(A) =lambda and lambda_(B) =2 lambda`. Initially, rate of disintergaration of `A` is `lambda N_(0)` and that of `B` is `2 almbda N_(0)`. After one half-life of `A`, rate of disntigration of `A` will come become `lambdaN_(0)//2` (half-life of `B =one` half the half -life of `A`. So, after one half-life of A or two half-lives of `B`,
`((- dN)/(dt))=((-dN)/(dt))_(B)`
`:. n=1`.