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

Explanation

It is defined as the time period during which half of the original atoms of the radiactive element disintegrate.
Let `N_0` be the initial number of atoms of a radioactive sample.
After a time interval equal to the half life T , the number of atoms of the radioactive sample remaining will be `N_0/2`.
Then `N=N_0/2` at `t=T_1//2` (A lutte bigger if possible not early visible )
w.k.t `N=N_0e^(-lambdat)`
`cancelN_0/2=cancelN_0e^(-lambdaT_1//2) rArr 1//2=e^(-lambdaT_1//2) rArr 1/2=1/(e^(lambda)T_1//2) rArr 2=e^(lambda)T_1//2`
`lambdaT_1//2=log_e^2 rArr T_1//2=2.303log_10^2=2.303xx0.3010`=0.693
`T_(1//2)=0.693/lambda`