A radioactive element decays by `beta-emission`. A detector records `n` beta particles in `2 s` and in next `2 s` it records `0.75 n` beta particles. Find mean life correct to nearest whole number. Given ln `|2| = 0.6931`, ln `|3|=1.0986`.

Explanation

We know that
`N=N_(0)e^(-lamdat)`
After 2 seconds `N_(1)=N_(0)e^(-lamdaxx2)`
After (2+2) second `N_(2)=N_(0)e^(-lamdaxx4)`
According to given conditions
`N_(0)-N_(1)=n`
or `N_(0)-N_(0)e^(-2lamda)=n`……….i
and `N_(0)e^(-2lamda)-N_(0)e^(-4lamda)=0.75n`........ii
After solving above equations we get
`lamda=0.145s`
Mean life `T=1//lamda=6.9s`