(a) Define the terms (i) half-life $\left( { T }_{ 1/2 } \right)$ and (ii) average life $\left( \tau \right)$ .Find out their relationships with the decay constant $\left( \lambda \right)$ .
(b) A radioactive nucleus has a decay constant, $\lambda =0.3465\left( day \right) ^{ -1 }.$ How long would it take the nucleus to decay to 75% of its initial amount ?
(a)(i) Half life : The time taken by a radioactive nuclei to reduce to half of the initial number of radio- nuclei.
(ii)Average life : The ratio of total life time of all radioactive nuclei to the total number of nuclei in the sample.
Relation between half-life and decay constant
{ T }_{ 1/2 }=\frac { 0.693 }{ \lambda }
Relation between average life and decay constant
\tau =\frac { 1 }{ \lambda }
