A radioactive sample is undergoing


A radioactive sample is undergoing $\alpha$ decay. At any time $t_{1}$, its activity is $A$ and another time $t_{2}$ the activity is $\frac{A}{5} .$ What is the average life time for the sample?

  1. (1) $\frac{t_{2}-t_{1}}{\ln 5}$

  2. (2) $\frac{1 n\left(t_{2}+t_{1}\right)}{2}$

  3. (3) $\frac{t_{1}-t_{2}}{1 n 5}$

  4. (4) $\frac{1 n 5}{t_{2}-t_{1}}$

Correct Option: 1



For activity of radioactivesample

$A=A_{0} e^{-\alpha t_{1}} \ldots(1)$

$\frac{A}{5} A_{0} e^{-\alpha t_{2}} \ldots(2)$

From $(1) /(2)$


$\ln (5)=\left(t_{2}-t_{1}\right) \lambda \Rightarrow \lambda=\frac{\ln (5)}{t_{2}-t_{1}}$

avg. life $=\frac{1}{\lambda} \Rightarrow \frac{t_{2}-t_{1}}{\ln (5)}$

Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now