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

Let initial number of nulclei in A and B is `N_(0)`
Number of nuclei of A after time t is
" "`N_(A)=N_(0)e^(-lambdat)`
Similarly number of nuclei of A after time is
" " `N_(B)=N_(0)e^(-lambdat)`
It is given that `(N_(A))/(N_(B))=(1)/(e)" " [beforeN_(B)gtN_(A)]`
Now, form Eqs (i) and (ii)
" "`(e^(-lambdat))/(e^(-lambdat)=1/e`
Rearranging
`rArr e^(-1)=e^(-lambdat)rArr7lambdat=1Time t=(1)/(7lambda)`