Q

# 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)

$\frac{1}{10\lambda}$

Views

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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