Two radioactive materials `X_1` and `X_2` have decay constants `10 lambda` and `lambda`, respectively. If initialy they have the same number of nuclei, then the ratio of the number of nuclei of `X_1` to that of `X_2` will be `1//e` after a time
(a) `1//10 lambda` (b) `1//11 lambda` (c) `11//10lambda` (d) `1//9lambda`

Options

A. `(1)/(10 lambda)`
B. `(1)/(10 lambda)`
C. `(1)1/(10 lambda)`
D. `(1)/(9 lambda)`

Answer

d

Explanation

`N_(x_(1)) =N_(0) e^(-10 lambda t)`
`N_(x_(2)) =N_(0) e^(-lambda t)`
`(N_(x_(1)))/(N_(x_(2)))=(1)/(e)=(e^(-10lambdat))/(e^(-lambdat))=e^(9lambda)`
`9 lambda t =1 rArr t=(1)/(9lambda)`.