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The half-life of a radioactive isotope $X$ is $50 \mathrm{yr}$. It decays to another element $Y$ which is stable. The two elements $X$ and $Y$ were found to be in the ratio of $1: 15$ in a sample of a given rock. The age of the rock was estimated to be
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Verified Answer
The correct answer is:
$200 \mathrm{yr}$
We know that
$$
\begin{aligned}
\frac{N}{N_0} & =\left(\frac{1}{2}\right)^{t / t_1 / 2} \\
\frac{1}{16} & =\left(\frac{1}{2}\right)^{t / 50} \\
t & =4 \times 50 \\
t & =200 \mathrm{yr}
\end{aligned}
$$
$$
\begin{aligned}
\frac{N}{N_0} & =\left(\frac{1}{2}\right)^{t / t_1 / 2} \\
\frac{1}{16} & =\left(\frac{1}{2}\right)^{t / 50} \\
t & =4 \times 50 \\
t & =200 \mathrm{yr}
\end{aligned}
$$
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