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Question

A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is

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A
6h
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B
12 h
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C
24 h
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D
128 h
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Solution

The correct option is B 12 h
Let's say the permissible level is N, so initially we have 64N nuclei present.

We need to calculate the time taken to drop the number of nuclei from 64N to N.
We know, N = N0eλt
N0 is 64N here. So after subtituting this we get,
eλt=164
Or,
eλt=64.
Which gives,
λt=In 64.
Or,
t=In 64λ1)
Now we have half-life,t1/2 = 2h
Which gives, λ = In 2t1/2= In 22h
Now putting this value in equation 1)
t = In 64λ=In 64In 2×2h
Or,
t = 6 In 2In 2×2h=12h.

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