JEE Main · 2016 · 03 Apr 2016 · Offline · Modern Physics

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Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be :

(A) $4 : 1$
(B) $1 : 4$
(C) $5 : 4$ ✓ Correct
(D) $1 : 16$

Answer: (C)

Solution

After time

t

a sample keeps

N = N_{0} (\frac{1}{2})^{t / T_{1/2}}

. In 80 minutes element A passes four of its 20-minute half-lives, leaving

\frac{N _{0}}{16}

, so it has decayed

N_{0} - \frac{N _{0}}{16} = \frac{15 N _{0}}{16}

. Element B passes two of its 40-minute half-lives, leaving

\frac{N _{0}}{4}

, so it has decayed

\frac{3 N _{0}}{4}

. The ratio of decayed nuclei is

\frac{15 N _{0} /16}{3 N _{0} /4} = \frac{15}{12} = \frac{5}{4}

JEE Main · 2016 · 03 Apr 2016 · Offline · Single correct option

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