A lunar rock was analyzed for argon by mass spectrometry and...

A lunar rock was analyzed for argon by mass spectrometry and for potassium by atomic absorption. The results of these analyses showed that the sample contained $3.02 \times 10^{-5} \mathrm{mL} \mathrm{g}^{-1}$ of argon and $0.083 \%$ of potassium. The half-life of potassium- 40 is $1.248 \times$ $10^{9} \mathrm{y} \cdot$ Calculate the age of the lunar rock.

Key Concepts

Potassium-Argon Dating

Potassium-argon dating is a radiometric dating method that measures the decay of potassium-40 into argon-40 in rocks and minerals. By analyzing the quantities of potassium and argon, researchers can calculate the time that has elapsed since the rock solidified. This method is particularly useful for dating geological events in early solar system history.

Decay Constant

The decay constant is a parameter that quantifies the probability of decay per unit time of a radioactive isotope. It is mathematically related to the half-life by the equation ? = ln(2)/t1/2. The decay constant is critical in deriving the decay equations that are used to determine the age of a sample based on the ratio of remaining parent isotope.

Radioactive Decay and Half-Life

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. The half-life is the period of time required for half of the radioactive parent isotope to decay into its daughter isotope. This concept is fundamental in radiometric dating as it provides a fixed time scale for calculating the age of a sample.

Radiometric Dating

Radiometric dating is a method used to determine the age of rocks and other materials based on the known decay rates of radioactive isotopes. This technique involves measuring the concentration of parent and daughter isotopes in a sample and applying the principles of radioactive decay to calculate the time elapsed since the sample formed.

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