Decay constant of two radioactive samples is `lambda` and `3lambda` respectively. At `t = 0` they have equal number of active nuclei. Calculate when will be the ratio of active nuclei becomes `e : 1`.

Answer

`1//2lambda`

Explanation

`N_(1)=N_(01)e^(-lambdat)` and `N_(2)=N_(02) e^(-3lambdat)`
`N_(1)/N_(2)=(N_(01) e^(-lambdat))/(N_(02)e^(-3lambdat))=e^(2lambdat)=e^(2 lambdat) [ :' N_(01)=N_(02)` for `N_(1)/N_(2)=e/1]`
`:. 1=2 lambdatimplies t=1/(2 lambda)`