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

we know that

Number of nuclei in terms of half life

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

and it is also given that $N_0=64N_s$

where $N_s$ is corresponding to safe limit

and $t_{\frac{1}{2}}=2h$

so we get

$N_s=64N_se^{-\frac{ln2*t}{2}}$

after solving we get t=12 hours

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