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  • The mean lives of a radioactive sample are 30 years and 60 years for  - emission and  

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 remains is:

Option: 1

14 years 


Option: 2

20 years


Option: 3

28 years 


Option: 4

45 years


Answers (1)

best_answer

\text { Here, } \lambda_{(\alpha+\beta)}=\lambda_\alpha+\lambda_\beta

\frac{1}{\tau}=\frac{1}{\tau_\alpha}+\frac{1}{\tau_\beta} \quad\left(\text { As } \lambda=\frac{1}{\tau}\right)

\Rightarrow \frac{1}{\tau}=\frac{1}{30}+\frac{1}{60}=\frac{1}{20}

\therefore \quad \tau=20 \text { years }

\text { Now, } \mathrm{T}_{1 / 2}=\ln (2) \tau=13.86 \text { years }

One – fourth of sample will remain after 2 half life = 27.72 years.

Posted by

sudhir.kumar

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