Question 541: Atoms & Nuclei

Question

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

Accepted Answer

Half life $$T=20 \mathrm{~min}$$
Left fraction of activity $$\frac{1}{16}$$
$$
\begin{aligned}
\because \frac{\mathrm{R}}{\mathrm{R}_{0}} & =\left(\frac{1}{2}ight)^{\mathrm{t} / \mathrm{T}} \
\frac{1}{16} & =\left(\frac{1}{2}ight)^{\mathrm{t} / 20} \
\left(\frac{1}{2}ight)^{4} & =\left(\frac{1}{2}ight)^{\mathrm{t} / 20} \
4 & =\frac{\mathrm{t}}{20} \
\mathrm{t} & =80 \mathrm{~min}
\end{aligned}
$$

Answer

40 minutes

Answer

60 minutes

Answer

80 minutes

Answer

20 minutes

Atoms & Nuclei

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

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