The radioactive potassium- 40 isotope decays to argon- 40...

The radioactive potassium- 40 isotope decays to argon- 40 with a half-life of $1.2 \times 10^{9}$ years. (a) Write a balanced equation for the reaction. (b) A sample of moon rock is found to contain 18 percent potassium- 40 and 82 percent argon by mass. Calculate the age of the rock in years. (Assume that all the argon in the sample is the result of potassium decay.)

Key Concepts

Exponential Decay Law

The exponential decay law describes how the quantity of a radioactive substance declines over time according to the formula N(t) = N?e^(–?t). Here, N? is the initial quantity, N(t) is the quantity at time t, and ? is the decay constant. This equation is central to radiometric dating techniques.

Decay Constant

The decay constant is a parameter that represents the probability per unit time of a nucleus decaying. It is mathematically related to the half-life through the formula ? = ln(2)/half-life and is essential in the exponential decay law used to model the decrease of radioactive materials over time.

Radiometric Dating

Radiometric dating is a method used to determine the age of objects or materials by measuring the relative proportions of a radioactive parent isotope and its daughter products. It relies on the known half-life of the parent isotope and the exponential decay law to calculate the time elapsed since the material formed.

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting particles or radiation. This spontaneous process occurs at a characteristic rate for each radioactive isotope and forms the basis for many scientific techniques, including dating geological and archaeological materials.

Half-Life

The half-life is the time required for half of the amount of a radioactive substance to decay. It provides a measure of the rate of decay and is crucial in calculations involving the exponential decrease of a radioactive isotope, allowing scientists to determine the age of samples based on remaining material.

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