Half life of a radioactive isotope X is 50 years. It decays to another element Y which is stable. tw

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13.Nuclei

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The half life of a radioactive isotope $X$ is $50$ years. 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..........$years$

A

$150 $

B

$200 $

C

$250$

D

$100 $

(AIPMT-2011)

Solution

$\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{n}$

where $n$ is number of half lives

$\therefore \quad \frac{1}{16}=\left(\frac{1}{2}\right)^{n}$ or $\left(\frac{1}{2}\right)^{4}=\left(\frac{1}{2}\right)^{n}$ or $n=4$

Let the age of rock be $t$ years.

$\because \quad n=\frac{t}{T_{1 / 2}}$

or $t=n T_{1 / 2}=4 \times 50$ years $=200$ $years$

Standard 12

Physics

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