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(1) How is mean life of a radioactive element related to its half life?
(2) A radioactive sample has activity of 10,000 disintegrations per second after 20 hours . After next 10 hours, its activity reduces to 5,000 dps. Find out its half - life and initial activity.

Explanation

### Step-by-Step Solution

**(1) Relationship between Mean Life and Half-Life of a Radioactive Element**

The mean life (τ) of a radioactive element is related to its half-life (t₁/₂) through the following equations:

1. The mean life (τ) is defined as the average time a particle exists before decaying:
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