Potassium-40 Fossil Dating Calculation

Potassium-40 Fossil Dating Calculation

Potassium-40 has a half-life of 1.25 billion years and decays to argon-40. If a fossil has a 40K/40Ar ratio of approximately 26%, how old is the fossil?

Estimation: You can do a very quick estimation by considering that 26% is close to 25%. Two half-lives have passed: one from 100% to 50% concentration, and the other from 50% to 25% concentration. Therefore, 2 * 1.25 billion years = 2.50 billion years.

Exact Calculation: The formula to calculate the age of the fossil is based on the decay of Potassium-40 according to its half-life. The exact calculation yields an age of 2.43 billion years.

Potassium-40 has a half-life of 1.25 billion years and decays to argon-40. how old is a fossil that has a 40K/40Ar ratio of ~ 26%?

You can do a very quick estimation by telling the ~ 26% is close to 25%, end then two half-life have passed: one from 100% to 50% concentration, and other from 50% to 25% concentration. So, 2 * 1.25 billion years = 2.50 billion years. The answer, then is that the fossil is 2.50 by old. Given that this method has an accuracy of +/- 10% this answer is good enough. For didactical purposes, I am goint to show you the exact procedure. C = Co * e^ (- kt) Half-life time => C = Co / 2 => C / Co = (1/2) = e ^ (-kt) => -kt = ln(1/2) => kt = ln(2) t = 1.25 by => k (1.25) = ln(2) => k = ln(2) / 1.25 = 0.5545 => C/Co = e ^ (-kt) In the problem C/Co = 26/100 => 0.26 = e^ (-0.5545t) => -0.5545t = ln (0.26) => t = - ln (0.26) / 0.5545 = 2.43 by. So with the exact procedure you obtain 2.43 by while with the estimation that ~26% is close to 25% you obtain 2.50 by.