Q90 / 90 · JEE Main 2021 (20 Jul Shift 2) · Physics

A radioactive substance decays to ${(\frac{1}{16})}^{th}$ of its initial activity in $80$ days. The half life of the radioactive substance expressed in days is ________.

Correct answer: 20

Solution

$N_{0} \overset{t_{\frac{1}{2}}}{⟶} \frac{N_{0}}{2} \overset{t_{\frac{1}{2}}}{⟶} \frac{N_{0}}{4} \overset{t_{\frac{1}{2}}}{⟶} \frac{N_{0}}{8} \overset{t_{\frac{1}{2}}}{⟶} \frac{N_{0}}{16}$

$4 \times t_{\frac{1}{2}} = 80$

$t_{\frac{1}{2}} = 20$ days

Hence, the correct answer is 20.

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Solution

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A radioactive substance decays to ${(\frac{1}{16})}^{th}$ of its initial activity in $80$ days. The half life of the radioactive substance expressed in days is ________.