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

Explanation

Half life is the time during which half of the parent atoms decay.
We know, `N=N_(0)e^(- lambda t) ` where symbols have usual meaning
`N= (N_0)/( 2)` when `t= T = ` half life
Hence, `(N_0) /( 2) = N_(0) e^(-lambda T) to e^(- lambda T) = (1)/(2) to e^(lambda T)=2`
Therefore `lambda T= log_(e) 2 = 2.303 log 2 = 0.693 `
`therefore T= (0.693) /( lambda )`