The radioisotope potassium-40 decays to argon-40 by positron emission with a half-life of 1.3 × 10⁹ yr.A sample of moon rock was found to contain 78 argon-40 atoms for every 22 potassium-40 atoms.The age of the rock is

Question

Quizplus · Accepted Answer

The ratio of argon-40 to potassium-40 in the sample is 78/22, which simplifies to 39/11. This means that there are 39 argon-40 atoms for every 11 potassium-40 atoms.

We can use the following equation to solve for the age of the rock:

(age of rock) = (half-life) x ln(2) x (number of half-lives)

To determine the number of half-lives, we can use the ratio of argon-40 to potassium-40:

(39/11) = (1 - e^(-λt))

where λ is the decay constant, which is equal to ln(2)/half-life. Solving for t gives:

t = (1/λ) x ln((11/39) + 1)

Plugging in the given half-life and solving gives:

t = 2.8 × 10^9 yr

Therefore, the age of the rock is 2.8 × 10^19 yr, which corresponds to choice C.

The Radioisotope Potassium-40 Decays to Argon-40 by Positron Emission with a Half-Life