Question

Two radioactive `X_(1)` and `X_(2)` have decay constants `10 lambda ` and `lambda` respectively . If initially 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)s`
B. `(1)/(11 lambda)`
C. `(11)/(10 lambda)`
D. `(1)/(9lambda)`

Answer 1

Correct Answer - d
`N_(1)=N_(0) e^(-10 lambda t)` and `N_(2)=N_(0) e^(-lambda t)`
`:. (N_(1))/(N_(2))=(e^(-10lambda t))/(e^(-lambda t))=(1)/(e^(lambda t))`
Given,
`(N_(1))/(N_(2))=(1)/(e) rArr(1)/e^(( lambda t))=(1)/(e)`
or `9 lambda t=1` or `t=(1/9 lambda)`.