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

Answer

B

Explanation

Given that the decay constants for the materials A and B are `lambda_(A)=8 lambda` and`lambda_(B)=lambda`.
Let in time t the ratio of number of nuclei of material ‘B’ to that of ‘A’ be -`1/e`
`N_(A)=1/eN_(B)`, Decay constant is `lambda., N_(A) =N_(0)e^(-lambda.t)`
Applying the law of radioactive decay
`N_(A)/N_(B) =(e^(-8lambdat))/(e^(-lambdat)) =e^(-7lambdat)`
`1/e=e^(-7lambdat)`
`t=1/(7lambda)`