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13.Nuclei
medium
A radio isotope $X$ with a half-life $1.4 \times 10^{9}\; years$ decays of $Y$ which is stable. A sample of the rock from a cave was found to contain $X$ and $Y$ in the ratio $1: 7$. The age of the rock is ........ $ \times 10^9\; years$
A
$2.4$
B
$1.4$
C
$4.2$
D
$5.2$
(AIPMT-2014)
Solution
Here, $\frac{X}{Y}=\frac{1}{7}$
$\frac{X}{X+Y}=\frac{1}{1+7}=\frac{1}{8}=\frac{1}{2^{3}}=\left(\frac{1}{2}\right)^{3}$
$n=3$
$\frac{t}{T}=3$
$t=3 T=3 \times 1.4 \times 10^{9} years$
$t=4.20 \times 10^{9} years$
Standard 12
Physics
