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JEE Main 2021 (25 Jul, Shift 2) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2021 (25 Jul, Shift 2)

Q53JEE Main 2021 · 25 JUL · SHIFT 2Easy

Law of Radioactive Decay

The nuclear activity of a radioactive element becomes $\left(\frac{1}{8}\right)^{th}$ of its initial value in 30 years. The half- life of radioactive element is _____________ years.

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

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Answer: 10

$\frac{A}{A_0} = \left(\frac{1}{2}\right)^n = \frac{1}{8} \Rightarrow n = 3$ half-lives.
$3T = 30$ years $\Rightarrow T = 10$ years.
Half-life = 10 years.

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