An ancient rock is found to contain ⁴⁰Ar gas, indicating that 77% of the ⁴⁰K in the rock has decayed since the rock solidified. Any argon would have boiled out of liquid rock. The half-life of ⁴⁰K is 1.25 billion years. How long ago did the rock solidify?

Question

Quizplus · Accepted Answer

The decay of 77% of the original ⁴⁰K means that 23% remains. Using the formula for radioactive decay, N(t) = N0 * (1/2)^(t/T), where N(t) is the remaining quantity, N0 is the initial quantity, t is time, and T is the half-life, we solve for t: 0.23 = (1/2)^(t/1.25). Solving for t gives approximately 2.6 billion years.

An Ancient Rock Is Found to Contain 40Ar Gas, Indicating

An Ancient Rock Is Found to Contain ⁴⁰Ar Gas, Indicating