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Solve it, - Atoms And Nuclei - JEE Main-4

 

Two radioactive materials A and B have decay constants 10\lambda and \lambda, respectively.

If initially they have the same number of nuclei, then the ratio of the number of nuclei of A 

to  that of B will be \frac{1}{e} after a time:

  • Option 1)

    \frac{1}{9\lambda}

  • Option 2)

    \frac{1}{11\lambda}

  • Option 3)

    \frac{11}{10\lambda}

  • Option 4)

    \frac{1}{10\lambda}

 
Answers (1)
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Number of nuclei after disintegration -

N=N_{0}e^{-\lambda t} or A=A_{0}e^{-\lambda t}

- wherein

Number of nucleor activity at a time is exponentional function

 

 

\lambda_{a} = 10 \lambda

\lambda_{b} =  \lambda

\frac{N_{A}}{N_{B}}=\frac{N_{o}e^{-10\lambda t}}{N_{o}e^{-\lambda t}}=\frac{1}{e}

e^{-9\lambda t}=e^{-1}

-9\lambda t=-1

9\lambda t=1

t=\frac{1}{9\lambda}


Option 1)

\frac{1}{9\lambda}

Option 2)

\frac{1}{11\lambda}

Option 3)

\frac{11}{10\lambda}

Option 4)

\frac{1}{10\lambda}

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