Question

A radioactive isotope $X$ with half life of $1.37\times {10}^9$ years decays to $Y$, which is stable. A sample of rock from moon was found to contain both the elements $X$ and $Y$ in the ratio $1:7$. What is the age of the rock?

Answer 1

Total sample = $8x$

$\frac{0.693}{t_{1/2}}=\frac{2.303}{t_{age}}\log \left(\frac{N_0}{N}\right)$

$\frac{0.693}{1.37\times {10}^9}=\frac{2.303}{t_{age}}{\log }_{10}\left(\frac{x+7x}{x}\right)$

$\therefore t_{age}=4.11\times {10}^9$ years