question_answer

The half life period of a radioactive element A is the same as the mean life of another radioactive element B. Initially both of them have the same number of atoms. The radioactive element B decays faster than A. Explain, why.                     

Answer:

                If \[\lambda \] and \[\lambda '\] are the decay constants of the elements A and B respectively, then \[{{T}_{1/2}}(A)=\tau (B)\] or            \[\frac{0.693}{\lambda }=\frac{1}{\lambda '}\] or \[\frac{\lambda }{\lambda '}=0.693\] If both the samples have N atoms each initially, then the ratio of their rates of disintegration will be \[\frac{R}{R'}=\frac{\lambda N}{\lambda 'N}=\frac{\lambda }{\lambda '}=0.693\] Clearly, \[R'>R\] i.e., the element B disintegrates faster than A.