JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Modern Physics

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Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as :
(where

λ

is the decay constant)

(A) $\frac{l n ( \frac{3}{2} )}{λ}$ ✓ Correct
(B) $\frac{l n 2}{λ}$
(C) $\frac{2 l n 2}{λ}$
(D) $\frac{1}{2} \frac{l n 2}{λ}$

Answer: (A)

Solution

For first-order decay

N = N_{0} e^{- λ t}

. When a quarter has decayed,

\frac{3}{4}

remain:

t_{1} = \frac{1}{λ} ln \frac{4}{3}

. When half has decayed,

\frac{1}{2}

remain:

t_{2} = \frac{1}{λ} ln 2

. The time gap is

t_{2} - t_{1} = \frac{1}{λ} (ln 2 - ln \frac{4}{3}) = \frac{1}{λ} ln \frac{3}{2} = \frac{l n ( 3/2 )}{λ}

JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Single correct option

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