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

Answer

A

Explanation

Given , `lambda _(A) = 8 lambda , lambda_(B) = lambda`
`N_(B) = (N_(A))/(e) implies N_(o) e^(-lambda B^(t)) = N_(o) (e^(-lambda A^(t)))/(e)`
`e^(-lambda t) = e^(-8 lambda t - 1)`
Comparing both side powers
`-lambda t = - 8 lambda t - 1-1 = 7 lambda t t = - (1)/(7 lambda)`