At given instant there are 50% undecayed radioactive nuclei in a sample. After 20sec, the number of  undecayed nuclei reduces to 12.5% . Calculate mean life of the nuclei.

The no of undecayed nuclei is reduced  from 50% to 25% to 12.5% (i.e, two half ) in 20 sec. ∴The half life of the radioactive sample  =   T12=202   =10 s Now, Half life=  T12=0.693λ ⇒     λ=0.693t12 Mean life =   Ta=1λ=T120.693=100.693=14.43sec