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  • The mean lives of a radioactive material for and radiations are 1620 years and 520 years respective

The mean lives of a radioactive material for \alpha and \beta radiations are 1620 years and 520 years respectively. The material decays simultaneously for \alpha and \beta decay. The time after which one fourth of the material remains undecayed is -

Option: 1

540 years 


Option: 2

324 years


Option: 3

720 years


Option: 4

840 years


Answers (1)

best_answer

\tau=\frac{\tau_\alpha \tau_\beta}{\tau_\alpha+\tau_\beta}=\frac{1620 \times 520}{1620+520}

=394 \text { years }

\mathrm{t}=\text { time of decay }=2.303 \log _{10} \frac{\mathrm{N}_0}{\mathrm{~N}} \times \tau

=2.303 \times \log _{10} 4 \times 394

=540 \text { years }

Posted by

manish painkra

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