The half-life of a radioactive substance is 20 minutes . In how much time, the activity of the substance drops to 1/16^th of its initial value? - Physics MCQ NEET 2023 2026 | ExamTest.live

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

Solution & Step-by-step Explanation

The activity A after n half-lives is: A = A_{0} (\frac{1}{2})^{n} Given \frac{A}{A _{0}} = \frac{1}{16} = (\frac{1}{2})^{4} .So, n = 4 half-lives.Total time t = n \times T_{1/2} = 4 \times 20 = 80 minutes .

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

20 minutes

40 minutes

60 minutes

80 minutes

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