A radioactive sample is undergoing


A radioactive sample is undergoing $\alpha$ decay.

At any time $\mathrm{t}_{1}$, its activity is A and another time

$t_{2}$, the activity is $\frac{\mathrm{A}}{5}$. What is the average life

time for the sample ?


  1. $\frac{\ell \mathrm{n} 5}{\mathrm{t}_{2}-\mathrm{t}_{1}}$

  2. $\frac{t_{1}-t_{2}}{\ell n 5}$

  3. $\frac{\mathrm{t}_{2}-\mathrm{t}_{1}}{\ell \operatorname{n} 5}$

  4. $\frac{\ln \left(\mathrm{t}_{2}+\mathrm{t}_{1}\right)}{2}$

Correct Option: , 3


Let initial activity be $\mathrm{A}_{0}$

$\mathrm{A}=\mathrm{A}_{0} \mathrm{e}^{-\lambda \mathrm{t}_{1}}$   .........(i)

$\frac{A}{5}=A_{0} e^{-\lambda_{2}}$ ...........(II)

(i) $\div$ (ii)


$\lambda=\frac{\ln 5}{\mathrm{t}_{2}-\mathrm{t}_{1}}=\frac{1}{\tau}$

$\tau=\frac{\mathrm{t}_{2}-\mathrm{t}_{1}}{\ell \ln 5}$


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