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

Explanation

The number of radioactive nuclei .N. at any time t is given as `N(t)=N_(0)e^(-lambdat)`
where `N_(0)` is number of radioactive nuclei in the sample at some arbitrary time `t=0` and `lambda` is the radioactive decay constant.
Given : `lambda_(A)=8lambda_(B)=lambda,N_(0A)=N_(0B)=N_(0)`
`therefore" "(N_(B))/(N_(A))=(e^(-lambdat))/(e^(=8lambda t))`
`rArr" "(1)/(e)=e^(-lambdat)e^(8lambdat)=e^(7lambdat)`
`rArr" "-1=7lambdat or t=(-1)/(7lambda)`
Negative value of time is not possible.
So givne ratio in equation should be `(N_(B))/(N_(A))=e`.
Question is not properly framed.