Question:
After 2 h $\frac{1}{16} th $ of initial amount of a certain radioactive isotope remains undecayed. The half-life of the isotope is
After 2 h $\frac{1}{16} th $ of initial amount of a certain radioactive isotope remains undecayed. The half-life of the isotope is
Updated On: Jul 2, 2022
- 15 min
- 30 min
- 45 min
- 60 min
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The Correct Option is B
Solution and Explanation
If N be the number of radioactive substance, left at some instant of time and $N_0$ be the number of atoms initially present in the substance, then number of atoms left after n-half lives is given by N = $N_0 \big(\frac{1}{2}\big)^n .$
Given, $\frac{N}{N_0} = \frac{1}{16}$
$\therefore \frac{1}{16} = \big(\frac{1}{2}\big)^n$
$ \frac{1}{16} = \frac{1}{2^4}$
$\Rightarrow n = 4$
Also $ n = \frac{t}{T^{1/2}}$
$ T_{1/2} = \frac{t}{n} = \frac{2}{4} \times 60 \, min = 30 \, min$
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