Question

Another isotope used for radioactive dating non-organic materials is potassium-40. Potassium-40 decays to argon-40 with a half life of 1,270,000,000 years. A sample of moon rock was found to still contain 22 grams of potassium-40 out of 100 originally. What is the age of the rock?

Answer 1

The age of the rock is 2,941,140,000 years.

Step-by-step explanation:

Potassium-40 decays to argon-40 with a half-life of 1,270,000,000 years. To find the age of the rock, we need to determine how many half-lives it has gone through. We start with 100 grams of potassium-40 and end up with 22 grams, which means there is 1/5th (or 0.2) of the original amount left. To find the number of half-lives, we take the logarithm base 0.5 of 0.2:

Number of half-lives = log0.5(0.2) = 2.3219

Since each half-life is 1,270,000,000 years, we multiply 2.3219 by the half-life to get the age of the rock:

Age of the rock = 2.3219 * 1,270,000,000 years = 2,941,140,000 years