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A radioactive element $X$ converts into another stable element $Y$ . Half life of $X$ is 4 hrs initially only nuclei of $X$ are present. After time $t$ , the ratio of number of nuclei of $X$ to $Y$ is $1: 15$ Therefore
Option: 1
$t=6 \, \mathrm{hrs}$

Option: 2
$t=8 \, \mathrm{hrs}$

Option: 3
$t=12 \, \mathrm{hrs}$

Option: 4
$t=16 \, \mathrm{hrs}$

Answers (1)

best_answer

$X \quad \rightarrow \quad Y$

$t=0$ $\text { No }$ $0$

$t=t$ $N_0-N$ $N .$

given $\frac{N_X}{N_Y}=\frac{1}{15}$ $\Rightarrow \quad \frac{N_0-N}{N}=\frac{1}{15}$

$\Rightarrow 15 N_0-15 N=N \Rightarrow N=\frac{15}{16} N_0 .$

$\Rightarrow \text { Number of nuclei of } X \text { remain }$

$=N_0-\frac{15}{16} N_0=\frac{N_0}{16}=\frac{N_0}{2^4}=\frac{N_0}{2^{t / t 1 / 2}} .$

$\Rightarrow t=4 t_{1 / 2}=16 \mathrm{hrs} .$

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Ajit Kumar Dubey

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