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Standard XII

Physics

Half Life and Average Life

A radioactive...

Question

A radioactive element $X$ converts into another stable element $Y$ .A radioactive element XX converts into another stable element YY. Half-life of XX is 3hrs. Initially, only X nuclei are present. After time 't', the ratio of number of nuclei of $X$ to that of $Y$ is found to be 1:7. Therefore.

t=3hrs

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t=6hrs

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t=9hrs

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t=15hrs

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Solution

The correct option is C t=9hrs
$\begin{matrix} 2X ⟶ 2 Y, half life is 3 hrs then X ⟶ Y also half life is 3 hrs \end{matrix}$
$After time t,$
$x : y is 1: 7$
$and initial x to final x is 8:1.$

$[t = \frac{t_{1 / 2}}{ln 2} ln (\frac{x_{initial}}{x_{final}})]$

$∴ t = \frac{3}{ln 2} ln 8$

$t= 9 hrs$

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A radioactive element X converts into another stable element Y.A radioactive element XX converts into another stable element YY. Half-life of XX is 3hrs. Initially, only X nuclei are present. After time 't', the ratio of number of nuclei of X to that of Y is found to be 1:7. Therefore.

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A radioactive element $X$ converts into another stable element $Y$ .A radioactive element XX converts into another stable element YY. Half-life of XX is 3hrs. Initially, only X nuclei are present. After time 't', the ratio of number of nuclei of $X$ to that of $Y$ is found to be 1:7. Therefore.