The argon-40 method of radioisotope dating was developed in the Geology Department at Stony Brook University to determine the age of rocks brought back from the moon. This method assumes that no argon-40 gas was trapped when the molten rock solidified, and that no argon-40 can escape from the solid rock. One sample that was analyzed had a ratio of potassium-40 to argon-40 of 0.100 (N_K/N_Ar = 0.100). Potassium-40 decays into argon-40 by positron emission with a half-life of 1.28 $\times$ 10⁹ years. How many years ago was this moon rock formed?

Question

Quizplus · Accepted Answer

Using the formula for the decay of potassium-40 to argon-40:
[K-40] = [K-40]0e^(-λt)
where [K-40] is the amount of remaining potassium-40, [K-40]0 is the initial amount of potassium-40, λ is the decay constant, and t is the time elapsed.
Also, using the fact that the ratio of potassium-40 to argon-40 is 0.100, we get:
[K-40]/[Ar-40] = 0.100 = ([K-40]0e^(-λt))/[Ar-40]
Solving for t, we get:
t = (1/λ)ln([K-40]0/[Ar-40])
Substituting the values given in the problem, we get:
t = (1/0.693)(1.28x10^9 years)(ln(1/0.100))
t ≈ 4.4x10^9 years
Therefore, the moon rock was formed approximately 4.4x10^9 years ago.

The Argon-40 Method of Radioisotope Dating Was Developed in the Geology