Question

A radioactive isotope X with half - life of 6.93 × 109 years decay to Y which is stable. A sample of rock from the moon was found to contain both the element X and Y in the mole ratio 1 : 7.What is the age of the rock?

• A. 2.079 × 1010 years
• B. 1.94 × 1010 years
• C. 1.33 × 109 years
• D. 1010 years

Answer 1

Answer: (A)

2.079 × 1010 years

Answer 2

$\lambda t = In\left\lbrack \frac{n_{x} + n_{y}}{n_{x}} \right\rbrack$

$t = \frac{0.693 \times 10^{9}}{0.693} \times 2.303\log_{10}\left\lbrack \frac{1 + 7}{1} \right\rbrack = 2.079 \times 10^{10}years$