(a) Write the relation between half-life and average life of a radioactive nucleus.
(b) In a given sample two isotopes A and B are initially present in the ratio of . Their half-lives are years and years respectively. How long will it take so that the sample has these isotopes in the ratio of ?
The half-life of a radioactive nucleus is given by the relation
Average life
Therefore
(b) we have no. of particle with and the particle with .
And note; Half-life of is years and years of .
Decay constant of
Decay constant of
By using the radioactive decay equation,
Initially
We have to find t when
Which implies that