Question

There are $0.618 \,\mu g$ of ${ }^{206} Pb$ and $0.238 \, \mu g$ of ${ }^{238} U$ in a rock. If $T_{50}$ of ${ }^{238} U$ is $1.5 \times 10^9 \,yr$, age of the rock is

• A. $1.5 \times 10^9\, yr$
• B. $3.0 \times 10^9\, yr$
• C. $4.5 \times 10^9\, yr$
• D. $0.75 \times 10^9\, yr$

Answer 1

Answer: (B)

Based on rock-dating
$(1+\frac{[ Pb ]}{[ U ]}=(2)^n$
$\left(1+\frac{\frac{0.618 \times 10^{-6}}{206}}{\frac{0.238 \times 10^{-6}}{238}}\right)=(2)^n$
$(2)^2=(2)^n $
$n=2 $
$2=\frac{t}{T_{50}} $
$t=2 \times T_{50}=3 \times 10^9\, yr$