13.Nuclei
medium

From a newly formed radioactive substance (Half life $2$ hours), the intensity of radiation is $64$ times the permissible safe level. The minimum time after which work can be done safely from this source is ..........$hours$

A

$6 $

B

$12$

C

$24$

D

$128$

(IIT-1983)

Solution

(b) $\frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^n}$

$\Rightarrow \frac{1}{{64}} = {\left( {\frac{1}{2}} \right)^6}$

$= {\left( {\frac{1}{2}} \right)^n} \Rightarrow n = 6.$

After $6$ half lives intensity emitted will be safe.  

Total time taken $ = 6 \times 2 = 12\,hrs.$

Standard 12
Physics

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