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JEE Main 201910 AprilMorning Shift

Exam: JEE Main
Year: 2019
Date: 10 April
Shift: Morning Shift
Subject: Physics
Chapter: Nuclear Physics

JEE Main 2019 · 10 April · Morning Shift · Physics · Nuclear Physics

Two radioactive materials A and B have decay constants 10λ and λ ,...

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

1 / e

after a time:

Options

A $\dfrac{1}{10\lambda}$
B $\dfrac{1}{9\lambda}$
C $\dfrac{1}{11\lambda}$
D $\dfrac{11}{10\lambda}$

Correct answer

B. $\dfrac{1}{9\lambda}$

Step-by-step solution

{N}_{A} = {N}_{0}{e}^{- 10\lambdat}

{N}_{B} = {N}_{0}{e}^{- \lambdat}

\dfrac{{N}_{A}}{{N}_{B}} = \dfrac{1}{e} = {e}^{- 10\lambdat + \lambdat} = {e}^{- 9\lambdat}

1 = 9\lambdat

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

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