Question

In a moon rock sample the ratio of the number of stable argon-40 atoms present to the number of radioactive potassium-40 atoms is 7:1. Assume that all the argon atoms were produced by the decay of potassium atoms, with a half life of 2.5 x 10${}^9$ yr. The age of the rock is

• A. 2.5 x 10${}^9$ yr
• B. 5.0 x 10${}^9$ yr
• C. 7.5 x 10${}^9$ yr
• D. 10${}^{10}$ yr

Answer 1

Answer: (C)

7.5 x 10${}^9$ yr

Ratio of argon-40 : potassium-40 $=7:1$
let, In the beginning potassium-40 $=1$
After x-half lives potassium-40 $=(\frac{1}{2}{)}^x$
After x-half lives argon-40 $=1-(\frac{1}{2}{)}^x$
so,
Ratio of argon:potassium $=\frac{1-(\frac{1}{2}{)}^x}{(\frac{1}{2}{)}^x}=\frac{7}{1}$
$=\Rightarrow 2^x-1=7$
$=\Rightarrow x=3$
$\therefore$ 3 half-lives so, Age of rock is $7.5\times {10}^9$ years.