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

Explanation

At time t the number of atoms present in a radioactive sample is,
`N = N_(0) e^(-lamda t)`
`At t = T_(1//2) , we have, N = (N_(0))/(2)`
`(N_(0))/(2) = N_(0) e^(-lamda(T_(1//2))`
`e^(lamda T_(1/2)) = 2`
`lamda T_(1/2) = log_(e) 2`
`lamda T_(1/2) = 2.303 log_(10) 2`
`lamda (T_(1/2)) = 2.303 times 0.3010 = 0.693`
`T_(1/2) = (0.693)/(lamda)`