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JEE Main 2022 (29 Jun, Shift 2) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2022 (29 Jun, Shift 2)

Q42JEE Main 2022 · 29 JUN · SHIFT 2Easy

Law of Radioactive Decay

The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of x is ____________.

Numerical answer type. Work it out, then open the answer.

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Answer: 20

$6.25\% = \frac{1}{16} = \left(\frac{1}{2}\right)^4$ , so 4 half-lives.
$x = 4 \times 5 = 20$ years.
So $x = 20$ years.

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