A freshly prepared radioactive source of half life 2 hours emits radiation of intensity which is 32 times the permissible safe level. The minimum time after which it would be possible to work safely with the source is

6 hours

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10 hours

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24 hours

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128 hours

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Solution

The correct option is B 10 hours
$\begin{matrix} N u m b e r o f n u c l e i i n t e r m s o f h a l f l i f e - N = \frac{N_{0}}{2^{t / t_{1 / 2}}} w h e r e i n V e r y u s e f u l t o d e t e r m i n e n u m b e r o f n u c l e i i n t e r m s o f h a l f l i f e \frac{t_{1}}{2} = 2 h r I n i t i a l i n t e n s i t y = 32 A A = \frac{A_{0}}{2^{t / t 1 /_{2}}} => A = \frac{32 A}{2^{t / 2}} o r 2^{t / 2} = 2^{5} t = 10 h r s \end{matrix}$
Hence,
option $(B)$ is correct answer.

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A freshly prepared radioactive source of half life 2 hours emits radiation of intensity which is 32 times the permissible safe level. The minimum time after which it would be possible to work safely with the source is

The correct option is B 10 hoursNumberofnucleiintermsofhalflife−N=N02t/t1/2whereinVeryusefultodeterminenumberofnucleiintermsofhalflifet12=2hrInitialintensity=32AA=A02t/t1/2=>A=32A2t/2or2t/2=25t=10hrsHence,option (B) is correct answer.