In a large sample of ${ }^{235}U$ (which is alpha active}

 

If a radioactive sample contains N nuclides of radioactive element, then the probability of decaying

of a particular nucleus during 1 sec interval is $\frac{dN}{Ndt}=\lambda$

It means probability of a nucleus disintegration during 

one second is constant for all times. Number of nuclei left after one average life is 

$\mathrm{N}={\mathrm{N}}_0{e}^{-\lambda \times \frac{1}{\lambda }}=\frac{{\mathrm{N}}_0}{e}=0.37{\mathrm{N}}_0$

i.e., an appreciable quantity is still left after one average life.