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JEE Main 2022 (28 Jul, Shift 1) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2022 (28 Jul, Shift 1)

Q47JEE Main 2022 · 28 JUL · SHIFT 1Medium

Law of Radioactive Decay

A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be _________ hours.

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

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Answer: 15

Activity must fall by a factor $64 = 2^6$ , i.e. 6 half-lives.
$t = 6\times2.5\text{ h} = 15$ h.
Minimum time = 15 hours.

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