# A freshly prepared radioactive source of half life 2 hrs emits radiation of intensity which is 32 times the permissible safe value of intensity. Which of the following is the minimum time after which it would be possible to work safely with this source? Option 1) 16 hrs Option 2)  5 hrs   Option 3) 10 hrs Option 4) 32 hrs

Number of nuclei in terms of half life -

$N=\frac{N_{0}}{2^{t/t_{1/2}}}$

- wherein

Very useful to determine number of nuclei in terms of half life

$\frac{t_{1}}{2}=2hr$

Initial intensity =32A

$\because A=\frac{A_{0}}{2^{t/t1/_{2}}}$

$=> A=\frac{32A}{2^{t/2}}$

$or \: 2^{t/2} =2^{5}$

$t=10hrs$

Option 1)

16 hrs

Option is incorrect

Option 2)

5 hrs

Option is incorrect

Option 3)

10 hrs

Option is correct

Option 4)

32 hrs

Option is incorrect

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