Two radiouctive materials `X_(1)` and `X_(2)` have decayconstants `10lambda` 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,

Options

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

Answer

D

Explanation

According to law of Radioactive decay,
`N(t) = N_(0)e^(-lambda t)`
Decay constants are `10lambda and lamda`, then,
`rArr N_(0)e^(-10lambda)/(N_(0)e^(-lambda t)) = 1/e`
`e^(-9lambdat) = e^(-1)`
`:. T = 1/9lambda`.