Question

Potassium-40 is a radioactive isotope of potassium, a very common element in terrestrial rocks, which decayrs to Ar-40 with a half-life of 1.28x10^9 years. By measuring the ratio of Ar-40 to K-40, geologists can determine the age of ancient rocks.

40 K ----> 40 Ar + 0/1e+

40 K ----> 40 Ca + 0/-1e-

A) Why might K-40 decay by two different pathways?

B) Only about 11% of the K-40 decays to Ar-40. If the ratio of Ar-40 to K-40 is found to be 0.435, how old is the rock?

C) Why don't geologists measure the 40Ca:40K ratio instead?

Answer 1

C) The ratio of the parent to the daughter elements is then used to calculate the age of the rock based on the known half-life decay rate of 40K into 40Ar – which is around 1.25 billion years. Actually, 40K decays into two different daughter products – 40Ca and 40Ar. However, since the original concentration of calcium (40Ca) cannot be reasonably determined, the ratio of 40K vs. 40Ca is not used to calculate the age of the rock.

A)This is a dating technique used for samples considerably older than 60,000 years. It is called potassium-argon dating and is based upon the detected ratio of ⁴⁰Ar to ⁴⁰K in a given sample.Natural potassium is composed of 0.01% radioactive potassium-40 which decays spontaneously according to two routes. 11% converts to calcium-40 by beta decay and 89% converts to inert argon-40 by electron capture (EC). The latter route has a half-life of 1.28 x 10⁹ years.

B)