A radioactive sample is undergoing $\alpha$ decay. At any time t1, its activity is A and another time t2, the activity is ${A \over 5}$. What is the average life time for the sample?
Solution
Let initial activity be A<sub>0</sub><br><br>A = A<sub>0</sub> e<sup>$-$$\lambda$t<sub>1</sub></sup> ........(i)<br><br>${A \over 5}$ = A<sub>0</sub> e<sup>$-$$\lambda$t<sub>2</sub></sup> .......(ii)<br><br>(i) $\div$ (ii)<br><br>5 = e<sup>$\lambda$(t<sub>2</sub> $-$ t<sub>1</sub>)</sup><br><br>$\lambda$ = ${{\ln 5} \over {{t_2} - {t_1}}} = {1 \over \tau }$<br><br>$\tau = {{{t_2} - {t_1}} \over {\ln 5}}$
About this question
Subject: Physics · Chapter: Atoms and Nuclei · Topic: Radioactivity
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