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13.Nuclei
medium
A radioactive isotope $X$ with a half-life of $1.37 \times {10^9}$ years decays to $Y$ which is stable. A sample of rock from the moon was found to contain both the elements $X$ and $Y$ which were in the ratio of $1 : 7$. The age of the rock is
A
$1.96 \times {10^8}$ years
B
$3.85 \times {10^9}$ years
C
$4.11 \times {10^9}$ years
D
$9.59 \times {10^9}$ years
Solution
(c) If in the rock there is no $Y$ element,
then the time taken by element $X$ to reduce to $\frac{1}{8}th$
the initial value will be equal to $\frac{1}{8} = {\left( {\frac{1}{2}} \right)^n}$ or $n =3$
Therefore, from the beginning three half life time is spent.
Hence the age of the rock is $= 3 \times 1.37 \times {10^9} = 4.11 \times {10^9}\,hrs.$
Standard 12
Physics
