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? A) 2.6 billion years B) 0.50 billion years C) 1.8 billion years D) 0.30 billion years

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