Two radioactive 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. `(lambda_Alambda_B)/((lambda_A-lambda_B))"In"(N_B/N_A)`
B. `(1)/((lambda_A+lambda_B))"In"(N_B/N_A)`
C. `(1)/((lambda_B-lambda_A))"In"(N_B/N_A)`
D. `(1)/((lambda_A-lambda_B))"In"(N_B/N_A)`

Answer

C

Explanation

`N_A e^(-lambda A^t)=N_B e^(-lambda B^t)`
or `e(lambda_B-lambda_A)t=(N_B//N_A)`
`therefore t=1/((lambda_B-lambda_A))"In"(N_B/N_A)`