Question 383: Atoms & Nuclei

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 $30 \mathrm{~s}$. The effective half-life of the nucleus is calculated to be $\frac{\alpha}{11} \mathrm{~s}$. The value of $\alpha$ is __________.

Accepted Answer

$$ \Rightarrow {\lambda _{eff}} = {\lambda _1} + {\lambda _2}$$
$$ \Rightarrow {{\ln 2} \over {{t_{1/2}}}} = {{\ln 2} \over {{{({t_{1/2}})}_1}}} + {{\ln 2} \over {{{({t_{1/2}})}_2}}}$$
$$ \Rightarrow {t_{1/2}} = {{{{({t_{1/2}})}_1} 	imes {{({t_{1/2}})}_2}} \over {{{({t_{1/2}})}_1} + {{({t_{1/2}})}_2}}} = {{300 	imes 30} \over {300 + 30}}s = {{300} \over {11}}s$$
$$ \Rightarrow \alpha  = 300$$

Atoms & Nuclei

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 \mathrm{~s}. The effective half-life of the nucleus is calculated to be \frac{\alpha}{11} \mathrm{~s}. The value of \alpha is __________.

Choose the correct answer: