Two redioactive nuclei A and B have disintegration constants `lamda_(A)andlamda_(B)` and initially `N_(A)andN_(B)` number of nuclei of them are taken, then the time after which their undisintegrated nuclei are same is

Options

A. `(lamda_(A)lamda_(B))/((lamda_(A)-lamda_(B)))"In"((N_(B))/(N_(A)))`
B. `(1)/((lamda_(A)+lamda_(B)))"In"((N_(B))/(N_(A)))`
C. `(1)/((lamda_(A)-lamda_(B)))"In"((N_(B))/(N_(A)))`
D. `(1)/((lamda_(A)-lamda_(B)))"In"((N_(B))/(N_(A)))`

Answer

C

Explanation

We have, `N_(A)e^(-lamdaAt)=N_(B)e^(-lamdaBt)`
`thereforee^((lamda_(B)-lamda_(A))t)=(N_(B))/(N_(A))`
`thereforeTime,t=(1)/(lamda_(B)-lamda_(A))In((N_(B))/(N_(A)))`