Question

${}^{40}K$ isotop of potenssum has half life of $1.37\times {10}^9$ years trn isotop of which is stble. In a particular sample of moon rock, the ration of postassium atoms to argon atoms was found to be 1:7. The age of the rock the rock, assuming that oringinally there was no was no arong present, is

• A. $4.11\times {10}^9$
• B. $2.74\times {10}^9$
• C. $5.48\times {10}^{{}^9}$
• D. $1.37\times {10}^{{}^9}$

Answer 1

Answer: (C)

$5.48\times {10}^{{}^9}$

$\begin{array}{c}\text{Ratio of}k\text{atoms intial to final is}\\ \frac{k_{in}}{k_f}=8\end{array}$

$\begin{array}{c}t=\frac{t_{1/2}}{\ln 2}\ln \left[\frac{k_i}{k_f}\right]\\ t=\frac{1.37\times {10}^9}{\ln 2}\ln 8\\ t=5.48\times {10}^9\text{years}\end{array}$