Question

A sample of uranium ore was found to contain 0.28 g ${}^{206}Pb$ and 1.67 g of ${}^{238}U$. Assuming that all Pb came from the decay of ${}^{238}U$, what is the age of the ore?
(Given $T_{50}$ of ${}^{238}U$ is $4.51\times {10}^9$ years).

• A. $2\times {10}^9$ years
• B. $1.2\times {10}^9$ years
• C. $4\times {10}^9$ years
• D. $6.2\times {10}^9$ years

Answer 1

Answer: (B)

$1.2\times {10}^9$ years

Number of moles of U - 238 present $=\frac{1.67}{238}=0.007017$

Number of moles of Pb - 206 present $=\frac{0.28}{206}=0.001359$

$\lambda =\frac{0.693}{t_{1/2}}=\frac{0.693}{4.51\times {10}^9}$

$t=\frac{2.303}{\lambda }log\frac{a}{a-x}$

$t=\frac{2.303}{0.693}\times 4.51\times {10}^9\times log\frac{0.007017+0.001359}{0.007017}$

$t=1.2\times {10}^9$ years.