Half-lives of two radioactive elements A and B are 20 minute and 40 minute respectively. Initially the samples have equal nuclei. After 80 minute, the ratio of decayed number of A and B nuclei will beA. $1: 4$B. $5: 4$C. $1: 16$D. $4: 1$

Home » Half-lives of two radioactive elements A and B are 20 minute and 40 minute respectively. Initially the samples have equal nuclei. After 80 minute, the ratio of decayed number of A and B nuclei will beA. B. C. D.

Half-lives of two radioactive elements A and B are 20 minute and 40 minute respectively. Initially the samples have equal nuclei. After 80 minute, the ratio of decayed number of A and B nuclei will be
A. $1: 4$
B. $5: 4$
C. $1: 16$
D. $4: 1$

Physics

Half-lives of two radioactive elements A and B are 20 minute and 40 minute respectively. Initially the samples have equal nuclei. After 80 minute, the ratio of decayed number of A and B nuclei will be
A. $1: 4$
B. $5: 4$
C. $1: 16$
D. $4: 1$

Correct answer is B.

$\begin{array}{l} \mathrm{n}=\mathrm{n}_{0} \mathrm{e}^{-\alpha t} \\ \alpha_{\mathrm{A}}=\ln 2 / 20 \\ \alpha_{\mathrm{B}}=\ln 2 / 40 \end{array}$
After 80 min, remaining number of nuclei for $\mathrm{A}, \mathrm{n}_{\mathrm{A}}=\mathrm{n}_{0} / 16$
After 80 min, remaining number of nuclei for $\mathrm{B}, \mathrm{n}_{\mathrm{B}}=\mathrm{n}_{\mathrm{o}} / 4$
Decayed number of nuclei for A, $\Delta \mathrm{n}_{\mathrm{A}}=\frac{15}{16} \mathrm{n}_{\mathrm{o}}$
Decayed number of nuclei for $\mathrm{B}, \Delta \mathrm{n}_{\mathrm{B}}=\frac{3}{4} \mathrm{n}_{\mathrm{o}}$
Ratio of decayed number of nuclei is
$\frac{\Delta \mathrm{n}_{\mathrm{A}}}{\Delta \mathrm{n}_{\mathrm{B}}}=\frac{15 / 16}{3 / 4}=5: 4$

i

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