The half life of a radioactive nucleus is 50 days. The time interval (t2 - t1) between the time t2 when \frac{2} {3} of it has decayed and the time t1 when \frac{1} {3} of it had decayed is :  

  • Option 1)

    50 days

  • Option 2)

    60 days

  • Option 3)

    15 days

  • Option 4)

    30 days

 

Answers (1)

As discussed in @8784

After t2 time, only \frac{1}{3} remains.

\therefore \frac{N_{0}}{3}= N_{0}. e^{-\lambda t_{2}}              - 1

After t time, only \frac{2}{3} remains

\therefore \frac{2}{3}N_{0} = N_{0}.e^{-\lambda t_{1}}          -2

Divide equation 2 in equation 1, we get:

\frac{1}{2}= e^{\lambda\left ( t_{1}-t_{2} \right ) } on taking log.

or ln2 =   \lambda \left ( t_{2} - t_{1}\right )

or t_{2}- t_{1} = \frac{ln^{2}}{\lambda }= t_{\frac{1}{2}} = \:50\:days


Option 1)

50 days

This answer is correct

Option 2)

60 days

This answer is incorrect

Option 3)

15 days

This answer is incorrect

Option 4)

30 days

This answer is incorrect

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