Question

An analysis of the rock shows that the relative number of $S{r}^{87}$ and $R{b}^{87}(t_{1/2}=4.7\times {10}^{10}year)$ atoms is $\mathrm{0.05.}$ What is the age of the rock ? Assume all $S{r}^{87}$ to be formed from $R{b}^{87}$ only.

• A. $7.62\times {10}^9$ year
• B. $1.43\times {10}^9$ year
• C. $3.28\times {10}^9$ year
• D. $4.32\times {10}^8$ year

Answer 1

Answer: (C)

$3.28\times {10}^9$ year

$\frac{AtomsofSr}{AtomsofRb}=0.05$
or $\frac{Atomsof(Sr+Rb)}{atomsofRb}=1.05$

so, $\frac{Initialno.ofatomsofRb}{Presentno.ofatomsofRb}=1.05$

$t=\frac{2.303}{\lambda }log\left(n_0/n\right)$

$=\frac{2.303}{0.693}\times 4.7\times {10}^{10}log\left(1.05\right)$

$=3.28\times {10}^{9}year$

Hence option (C) is correct.