Question

A sample of uranium rock from moon contains equimolar amounts of $U^{238}$ and $P{b}^{206}$. The age of the rock will be $(t_{\frac{1}{2}}for{U}^{238}=4.5\times {10}^{9}yrs)$

• A. $4.5\times {10}^{9}yrs.$
• B. $9.0\times {10}^{9}yrs.$
• C. $13.5\times {10}^{9}yrs.$
• D. $2.25\times {10}^{9}yrs.$

Answer 1

The correct option is A

$4.5\times {10}^{9}yrs.$

$1+\frac{Pb}{U}=1+1=2=\frac{U+Pb}{U}=\frac{N_0}{N}$
Hence, $t=\frac{2.303}{\lambda }log\frac{N_0}{N};\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{4.5\times {10}^9}$
Thus, $t=\frac{2.303\times 4.5\times {10}^9}{0.693}log2=4.5\times {10}^{9}yr.$