Two radioactive materials `X_(1)` and `X_(2)` have decay constants `10 lambda` and `lambda` respectively. If initially they have the same numbers of nucle, then the ratio fo the nclie of `X_(1)` to that `X_(2)` will be `1//e` after a time:

Options

A. `(1)/(10lambda)`
B. `(1)/(11 lambda0`
C. `(11)/(10lambda)`
D. `(1)/(9lambda)`

Answer

`(d)`

Explanation

`N_(1) = N_(0) e^(-10 lambda t), N_(2) = N_(0) e^(-lambda t)`
`:. (N_(1))/(N_(2)) = (e^(-lambda t))/(e^(-10lambda t)) = e^((-10lambda+ lambda t)) = e^(-9lambda t)`
`:' (N_(1))/(N_(2)) = (1)/(e)`
`:. e^(-1) = e^(-9 lambda t)`
`:. -9lambda t = -1` or `t = (1)/(9 lambda)`.