Question

A sample of rock from South America contains equal number of atoms of $U^{238}$ and $P{b}^{206}$. The age of the rock will be :

• A. $4.5\times {10}^{9}years$
• B. $9\times {10}^{9}years$
• C. $13.5\times {10}^{9}years$
• D. $2.25\times {10}^{9}years$

Answer 1

Answer: (A)

$4.5\times {10}^{9}years$

$K=\frac{2.303}{t}log\left(\frac{N_0}{N}\right)$
$\frac{0.693}{t_{1/2}}=\frac{2.303}{t}log\left(\frac{N_0}{N}\right)\left[\begin{array}{cc}{N}_0=1+1=2& \\ N=1& \end{array}\right]$
$\frac{0.693}{4.5\times {10}^9}=\frac{2.303}{t}log\left(\frac{2}{1}\right)$
$\therefore t=4.5\times {10}^{9}years$