Radioactive decay of 40k atoms in an igneous rock has resulted in a ratio of 25 percent 40k atoms to 75 percent 40ar and 40ca atoms how many years old is the this rock

The answer is 6×10⁹ years.

K-Ar dating is radioactive dating method used to measure a time elapsed since the rock is cool enough to trap Ar after a radioactive decay of 40K to 40Ar. It can be expressed as:

where:
- elapsed time
- half-life of K40
- amount of K40
- amount of Ar40

We know that a half-life of K40 is 1.251×10⁹ years:


We do not know absolute value of amount of K40 and Ar40, but we know percentage and can express them as following:



So:


⇒ t = 6×10⁹

Thus, the rock is old 6×10⁹ years.