A geologist measured the amount of 40K in a rock; she determined that there was about 10 grams of 40K and 10 grams of 40Ar.
What would be the approximate age of that rock?
To determine the approximate age of the rock, we can use the concept of radioactive decay. Potassium-40 (40K) is a radioactive isotope that decays over time into Argon-40 (40Ar) with a known decay rate.
The decay of 40K to 40Ar occurs via a process called potassium-argon (K-Ar) dating. The half-life of 40K is approximately 1.25 billion years. This means that it takes 1.25 billion years for half of the 40K in a sample to decay into 40Ar.
Given that there are initially 10 grams of 40K and 10 grams of 40Ar, we can assume that the rock was initially composed entirely of 40K. This implies that there has been a complete decay of 40K, and all the 10 grams of 40Ar present in the rock resulted from this decay.
Since each 40K atom decays to one 40Ar atom, and the half-life is 1.25 billion years, we can calculate the number of half-lives that have occurred by dividing the total age by the half-life. In this case:
Total age = (10 grams of 40Ar) / (10 grams/half-life) = 1 half-life
Therefore, the approximate age of the rock is one half-life or approximately 1.25 billion years.