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STD 12 - 13. Nuclei — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 13. Nuclei4 Marks
Question
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 $..............$
✓

Answer

c
$\frac{ dN _1}{ dt }=-\lambda_1 N \quad \frac{ dN _2}{ dt }=-\lambda_2 N$

$\frac{ dN }{ dt }=-\left(\lambda_1+\lambda_2\right) N$

$\Rightarrow \lambda_{\text {eq }}=\lambda_1+\lambda_2$

$\Rightarrow \frac{1}{t_{1 / 2}}=\frac{1}{300}+\frac{1}{30}=\frac{11}{300}$

$\Rightarrow t _{1 / 2}=\frac{300}{11}$

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