Question

A sample of rock from the moon was found to contain the elements $X$ and $Y$ in $1:7$ ratio by mole. Element $X$ is radioactive, it decays to $Y$ with half life of $6.93\times {10}^9$ years
$[X⟶Y{t}_{1/2}=6.93\times {10}^{9}yrs]$
What is the age of the rock?

• A. $2.079\times {10}^{10}$ years
• B. $1.33\times {10}^9$ years
• C. $1.94\times {10}^{10}$ years
• D. ${10}^{10}$ years

Answer 1

The correct option is A $2.079\times {10}^{10}$ years

$t=\frac{2.303\times 6.93\times {10}^9}{0.693}\times log(1+\frac{7}{1})$

$t=2.079\times {10}^{10}$ years