JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Modern Physics

Two radioactive materials A and B have decay constants

10 λ

and

λ

, 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:

(A) $\frac{1}{11 λ}$
(B) $\frac{1}{10 λ}$
(C) $\frac{1}{9 λ}$ ✓ Correct
(D) $\frac{11}{10 λ}$

Answer: (C)

Solution

Let both samples start with

N_{0}

nuclei. After time

t

, material A has

N_{1} = N_{0} e^{- 10 λ t}

and material B has

N_{2} = N_{0} e^{- λ t}

. The given ratio

\frac{N _{1}}{N _{2}} = \frac{1}{e}

becomes

e^{- 9 λ t} = e^{- 1}

, so

9 λ t = 1

and

t = \frac{1}{9 λ}

JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Single correct option

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