Question

A sample of rock from moon contains equal number of atoms of uranium and lead $(t_{\frac{1}{2}}$ for $U=4.5\times {10}^9$ years $)$. The age of the rock would be

• A. $4.5\times {10}^9$ years
• B. $9\times {10}^9$ years
• C. $13.5\times {10}^9$ years
• D. $2.25\times {10}^9$ years

Answer 1

The correct option is A $4.5\times {10}^9$ years

$t_{1/2}=\frac{0.693}{k}$

$\therefore k=\frac{0.693}{45x{10}^g}year{s}^{-1}$

It is an uranium dating technique,

$\therefore Age=\frac{2.303}{K}lo{g}_{10}[1+\frac{P{b}^{206}}{U^{238}}]$

$=\frac{2.303}{0.693}x45x{10}^{g}lo{g}_{10}[1+1]$

$=\frac{2.303x45x{10}^g}{0.693}lo{g}_{10}\left(2\right)$

Age = 4 x 10${}^g$ years