Question

What is the relation between half life and average life ?

Answer 1

1. The half life of the reaction is the time in which the concentration of a reactant is reduced to one half of its initial concentration.
2. It is represented as ${\mathrm{t}}_{1/2}$.
3. For zero order reaction, ${\mathrm{t}}_{1/2}\mathrm{\alpha }\left[{\mathrm{R}}_{°}\right]$ and for first order it is independent of initial concentration.
4. The average life or the mean life is the expected life for the radioactive substance.
5. Half life of radioactive substance is given by $$\begin{gathered} {\mathrm{t}}_{1/2}=\frac{0.693}{\mathrm{k}} \\ \mathrm{where}\mathrm{k}\mathrm{is}\mathrm{the}\mathrm{rate}\mathrm{constant} \end{gathered}$$
6. And average life is given by $\mathrm{\tau }=\frac{1}{\mathrm{k}}$
7. The relation between half life and average life is $$\begin{gathered} {\mathrm{t}}_{1/2}=0.693\frac{1}{\mathrm{k}} \\ {\mathrm{t}}_{1/2}=0.693\mathrm{\tau } \end{gathered}$$