Question

A sample of pitch blende is found to contain $50\%$ uranium and $2.425\%$ lead. Of this lead only $93\%$ was $P{b}^{206}$ isotope. If the disintegration constant is $1.52\times {10}^{-10}y{r}^{-1}$, how old could be the pitch blende deposits?

Answer 1

Moles of $U^{238}=\frac{50}{100\times 238}=2.1\times {10}^{-3}$
Moles of ${Pb}^{206}=\frac{2.425}{100}\times \frac{93}{100\times 206}=0.109\times {10}^{-3}$
$N_0=(x+y)=2.1\times {10}^{-3}+0.109\times {10}^{-3}=2.209\times {10}^{-3}$
$N=x=2.1\times {10}^{-3}$
$\lambda =\frac{2.303}{t}\log \left(\frac{N_0}{N}\right)$
$1.52\times {10}^{-10}=\frac{2.303}{t}\log \frac{2.209\times {10}^{-3}}{2.1\times {10}^{-3}}$
$t=3.3\times {10}^8$ years