Write the expression for the half life of a radioactive element.

Explanation

We have `N=N_0e^(-lambdat)`
When `t=T_(1/2), N=V_0/2`
`therefore N_0/2=N_0e^(-lambdaT_(1/2))`
`therefore e^(lambdaT_(1/2))=2`
`lambdaT_(1/2)=ln2=log_e2`
`T_(1/2)=(log_e^2)/lambda=(2.303log_10^2)/lambda=0.693/lambda`