The radioisotope potassium40 decays to argon40 by positron e

The radioisotope potassium-40 decays to argon-40 by positron emission with a half-life
of 1.3 10⁹ yr. A sample of rock was found to contain 40 mmoles of argon-40 atoms and
210 mmoles of potassium-40 atoms. The age of the rock is

Solution

Assume sample was 100% K-40 at start.

The sample contains 78% Ar-40 and 22% K-40. We will use 0.22, the decimal percent of K-40 remaining:

(1/2)^n = 0.22

where n is the number of half-lives.

n log 0.5 = log 0.22

n = 2.18

(2.18) (1.3 x 10^9) = 2.8 x 10^9 yrs