A radioactive nucleus decays by two different processes. The half life of the first process is 5 minutes and that of the second process is 30 s. The effective half-life of the nucleus is calculated to be (α)/(11) s. The value of α is __________. Numerical answer type. Work it out, then open the answer.

Answer: 300. For two parallel decays λ = λ₁ + λ₂, so 1/T = 1/T₁ + 1/T₂. 1/T = 1/300 + 1/30 = 11/300 per s. T = 300/11 s, so α = 300.

A radioactive nucleus decays by two different processes. The half… | JEE Main 2023 (30 Jan, Shift 2)

Q36JEE Main 2023 · 30 JAN · SHIFT 2Medium

Law of Radioactive Decay

A radioactive nucleus decays by two different processes. The half life of the first process is 5 minutes and that of the second process is $30\text{ s}$ . The effective half-life of the nucleus is calculated to be $\frac{\alpha}{11}\text{ s}$ . The value of $\alpha$ is __________.

Numerical answer type. Work it out, then open the answer.

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Answer: 300

For two parallel decays $\lambda = \lambda_1 + \lambda_2$ , so $\frac{1}{T} = \frac{1}{T_1} + \frac{1}{T_2}$ .
$\frac{1}{T} = \frac{1}{300} + \frac{1}{30} = \frac{11}{300}$ per s.
$T = \frac{300}{11}$ s, so $\alpha = 300$ .

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