A radioactive sample decays by beta emission. In the first 2 seconds, n beta-particles are emitted. In the next 2 seconds, 0.25n beta-particles are emitted. What is the half-life of the radioactive nuclei?

2 sec
4 sec
1 sec
None of these

Correct answer: 1 sec

Solution

Let x = e^(-2*lambda). Decays in first 2s = N₀*(1-x) = n. Decays in next 2s = N₀*x*(1-x) = 0.25n. Dividing: x = 0.25 = 1/4. So e^(-2*lambda) = 1/4 => lambda = ln2 s⁻¹. T_(1/2) = ln2/lambda = ln2/ln2 = 1 s.

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