Question

A sample of ${}^{238}U$ (half-life $=4.5$$\times {10}^9$ years) ore is found to contain 23.8 g of $238U$ and 20.6 g of ${}^{206}Pb$. Calculate the age of the ore.

• A. $t=4.5\times {10}^9$ years
• B. $t=4.4\times {10}^9$ years
• C. $t=5.5\times {10}^9$ years
• D. None of these

Answer 1

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

$(1+\frac{\left[Pb\right]}{\left[U\right]})=2^y$
$(1+\frac{20.6/206}{23.8/238})=2^y$
$2=2^y$
$y=1$
$\frac{t}{t_{50}}=1$
$t=4.5\times {10}^9$ years