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`.

Options

A. `17s`
B. `7s`
C. `5s`
D. `15s`

Answer

B

Explanation

Let `N_(0)=` initial number of nuclei
`n = N_(0) - N_(0)e^(-lambda xx)`
`1.75 n = N_(0) - N_(0)e^(-4lambda)`
`(1)/(1.75) = (1-e^(-2lambda))/(1-e^(-4lambda))`
`1+e^(-2lambda) = 1.75`
`e^(2lambda) = (1)/(0.75) = 1.33`
`2 lambda = ln (1.33)`
`tau = (1)/(lambda) = (2)/(ln(1.33)) = 7s`