Question

Define half-life of a radioactive substance and write the relation of half-life with the following:
(a) Radioactive decay constant (disintegration constant)
(b) Mean life of a radioactive substance.

Answer 1

Half life of a radioactive substance(${\tau }_{1/2}$) measures the time it takes for a given amount of the substance to become reduced by half as a consequence of decay, and therefore, the emission of radiation.

It is related to radioactive decay constant $k$ as ${\tau }_{1/2}=\frac{ln2}{k}$.

Also its relation with mean life ${\lambda }_m=\frac{1}{k}$ is

${\tau }_{1/2}={\lambda }_{m}ln2$