(a) Write the relation between half-life and average life of a radioactive nucleus.
(6) In a given sample two isotopes A and B are initially present in the ratio of 1 :2. Their half-lives are 60 years and 30 years respectively. How long will it take so that the sample has these isotopes in the ratio of 2 : 1?

Explanation

To solve the problem, we will break it down into two parts:

### Part (a): Relation between Half-life and Average Life of a Radioactive Nucleus

1. **Definition of Half-life (T½)**: The half-life of a radioactive substance is the time required for half of the radioactive nuclei in a sample to decay.

2. **Definition of Average Life (τ)**: The average life (or mean life) of a radioactive nucleus is the average time that a nucleus exists before it decays.

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