The mean lives of a radioactive sample are 30 | vedclass

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Question

${\lambda _{(\alpha  + \beta )}} = {\lambda _\alpha } + {\lambda _\beta }$

$ \Rightarrow \frac{1}{{{T_{\frac{1}{2}(\alpha  - \beta )}}}}

Vedclass · Accepted Answer

$40$

Vedclass · Answer

${\lambda _{(\alpha  + \beta )}} = {\lambda _\alpha } + {\lambda _\beta }$

$ \Rightarrow \frac{1}{{{T_{\frac{1}{2}(\alpha  - \beta )}}}} = \frac{1}{{{T_{\frac{1}{2}(\alpha )}}}} + \frac{1}{{{T_{\frac{1}{2}\left( \beta  ight)}}}}$

$\Rightarrow \frac{1}{T_{\frac{1}{2}(x+\beta)}}=\frac{1}{30}+\frac{1}{60}=\frac{1}{20}$

$	herefore {{m{T}}_{\frac{1}{2}(\alpha  + \beta )}} = 20$ years.

$	herefore $ One-fourth of sample will remain after $2$ half life $=40$ years.

The mean lives of a radioactive sample are $30$ years and $60$ years for $\alpha$-emission and $\beta $ -emission respectively. If the sample decays both by $\alpha$- emission and $\beta $-emission simultaneously, the time after which, only one-fourth of the sample remain is :- ........... $years$

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