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A sample of radioactive element has a mass of 10 gm at an instant t = 0. The approximate mass of this element in the sample after two mean lives is

1. 6.30 gm
2. 1.35 gm
3. 2.50 gm
4. 3.70 gm

Correct answer: 3.70 gm

Solution

After one mean life, the remaining mass is 1/e of the initial mass. After two mean lives, the remaining mass is (1/e)^2 times the initial mass. Substituting e ≈ 2.718, the remaining mass is approximately 10 × (1/2.718)^2 ≈ 3.70 gm.

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