Question

The half-life of ${}_{92}^{238}U$ is $4.5\times {10}^9$ years. Uranium emits a $\alpha -$particle to give thorium. Calculate the time required to get the product which contains equal masses of thorium and uranium.

Answer 1

$t_{1/2}=4.5\times {10}^9$ years

$t=?$

$t=\frac{2.303}{\frac{0.693}{4.5\times {10}^9}}log(1+\frac{n_{Th}}{n_U})$

$t=\frac{2.303\times 4.5\times {10}^9}{0.693}\times log(1+\frac{\frac{1}{293}}{\frac{1}{238}})$

$t=4.58\times {10}^9$ years