NEET 2023 — Physics solution

NEET2023Physics

The half life of a radioactive substance is $20$ minutes. In how much time, the activity of substance drops to $(\frac{1}{16})^{t h}$ of its initial value?

A
$40$ minutes
B
$60$ minutes
C
$80$ minutes
D
$20$ minutes

Solution

After $n$ half-lives, activity falls to $(\frac{1}{2})^{n}$ of its initial value.

$(\frac{1}{2})^{n} = \frac{1}{16} = (\frac{1}{2})^{4} \Rightarrow n = 4$ .

Total time $= 4 \times 20 = 80$ minutes.

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