Nuclear Physics Question 8
Question 8 - 30 January - Shift 2
A radioactive nucleus decays by two different process. 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 $\frac{\alpha}{11} s$. The value of $\alpha$ is
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Answer: (300)
Solution:
Formula: Radioactive Decay
$ \begin{aligned} & \frac{dN_1}{dt}=-\lambda_1 N \quad \frac{dN_2}{dt}=-\lambda_2 N \\ & \frac{dN}{dt}=-(\lambda_1+\lambda_2) N \\ & \Rightarrow \lambda _{\text{eq }}=\lambda_1+\lambda_2 \\ & \Rightarrow \frac{1}{t _{1 / 2}}=\frac{1}{300}+\frac{1}{30}=\frac{11}{300} \\ & \Rightarrow t _{1 / 2}=\frac{300}{11} \end{aligned} $
