Question

A sample pitch blende is found to contain 50% Uranium ($U^{238}$) 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 pitchblende deposit?

• A. $1.65\times {10}^8$ years
• B. $3.3\times {10}^8$ years
• C. $6.6\times {10}^8$ years
• D. $3.3\times {10}^9$ years

Answer 1

The correct option is B $3.3\times {10}^8$ years

A sample pitch blende is found to contain 50% Uranium ($U^{238}$)
Thus, the amount of Uranium ($U^{238}$) is 50
2.425% Lead contains only 93% of $P{b}^{206}$ isotope.
Thus, the amount of $P{b}^{206}$ present will be $2.425\times \frac{93}{100}=2.255$
The age of pitch blende deposit can be determined by the formula $t=\frac{2.303}{\lambda }log\frac{N_0}{N}$......(1)
$N_0=50+2.255=52.255$
$N=50$
Substitute values in equation (1)
$t=\frac{2.303}{\lambda }log\frac{N_0}{N}=\frac{2.303}{1.52\times {10}^{-10}y{r}^{-1}}\times log\frac{52.255}{50}=3.3\times {10}^8$