Question

A radioactive isotope $X$ with half-life of $6.93\times {10}^9$ years decay to $Y$ which is stable. A sample of rock from the moon was found to contain both the elements $X$ and $Y$ in the mole ratio $1:7$. What is the age of the rock?

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

Answer 1

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

at time $\underset{n_0-x}{X}\to \underset{x}{Y};\frac{n_0-x}{x}=\frac{1}{7};n_0=\frac{8x}{7};$

$\lambda =\frac{0.693}{6.93\times {10}^9}\Rightarrow {10}^{-10}year{s}^{-1}$

$t=\frac{2.303}{\lambda }log\left(\frac{w_0}{w_0-x}\right)$

$=\frac{2.303}{{10}^{-10}}log\left(8\right)$

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

Hence option (A) is correct.