Question

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 1

Let half life of A =$T_1$

Mean life of A =${\tau }_1$

Mean life of B = ${\tau }_2$

${\lambda }_2$ and${\lambda }_1$ disintegration constant of A and B respectively.

$T_1=ln{\tau }_1={\tau }_2=\frac{1}{{\lambda }_2}$........ (1)

$T_1=\frac{ln2}{{\lambda }_2}$.......... (2)

${\lambda }_1={\lambda }_{2}ln2$ [$ln2$ = 0.693]

So,${\lambda }_2>{\lambda }_1$

ie, disintegration constant of B is greater than that of A. So B disintegrates faster than A.