A sample of rock from moon contains atoms of uranium and lead in the ratio 1: 3. Then age of' rock will be (${\mathrm{t}}_{1/2}$ for uranium $=4\times {10}^9$ years) :

$\begin{array}{l}{\mathrm{t}}_{1/2}=\frac{0.693}{\mathrm{k}}\\ \therefore \mathrm{k}=\frac{0.693}{45\times {10}^{\mathrm{\Xi }}}{\text{ years }}^{-1}\end{array}$

It is an uranium dating technique,

$\begin{array}{l}\therefore \text{ Age }=\frac{2.303}{\mathrm{K}}{\log }_{10}\left[1+\frac{{\mathrm{Pb}}^{206}}{{\mathrm{U}}^{238}}\right]\\ =\frac{2.303}{0.693}\times 45\times {10}^g{\log }_{10}[1+1]\\ =\frac{2.303\times 45\times {10}^g}{0.693}{\log }_{10}\left(2\right)\end{array}$

$\text{ Age }=4\times {10}^9\text{ years }$