Two radioactive substances A and B have decay constants 5\lambda and \lambda respectively . At t=0, sample has the same number of the two nuclei . The time taken for the ratio of the number of nuclei to become \left ( \frac{1}{e} \right )^{2}will be

:

 

 

 

 

 

 

 

  • Option 1)

    \frac{1}{2\lambda }

  • Option 2)

    \frac{1}{4\lambda }

  • Option 3)

    \frac{1}{\lambda }

  • Option 4)

    \frac{2}{\lambda }

Answers (1)

\frac{N_{1}}{N_{2}}=\frac{N_0e^{-5\lambda t} }{N_0e^{-\lambda t}}=\frac{1}{e^{2}}

e^{-4\lambda t}=\frac{1}{e^{2}}

en \left ( e^{-4\lambda t} \right )=en \left ( \frac{1}{e^{2}} \right )

-4\lambda t=-2

t= \frac{1}{2\lambda }


Option 1)

\frac{1}{2\lambda }

Option 2)

\frac{1}{4\lambda }

Option 3)

\frac{1}{\lambda }

Option 4)

\frac{2}{\lambda }

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