Radioactive material 'A' has decay constant `'8 lamda'` and material 'B' has decay constant 'lamda'. Initial they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be `(1)/( e)` ?

Options

A. `(1)/(7 lamda)`
B. `(1)/(8 lamda)`
C. `(1)/(9 lamda)`
D. `(1)/(lamda)`

Answer

A

Explanation

(a) `lamda_A = 8 lamda, lamda_B = lamda`
`rArr N_B = (N_A)/( e) rArr N_0 e^(-lamda t) = (N_0 e^(-8 lamda t))/( e)`
`rArr - lamda t = - 8 lamda t - 1`
`rArr t = (-1)/(7 lamda)`
Best answer is `t = (1)/(7 lamda)`.