A 0.500 g sample of rock was found to have 2.45 ×10^-6 mol of potassium-40 (t1 / 2=1.3 ×10^9 yr

step 1 If we have a .5 gram sample of rock that contains a known moles of potassium 40 and a known mole

A 0.500 g sample of rock was found to have 2.45 ×10^-6 mol...

A $0.500 \mathrm{~g}$ sample of rock was found to have $2.45 \times 10^{-6}$ mol of potassium-40 $\left(t_{1 / 2}=1.3 \times 10^{9} \mathrm{yr}\right)$ and $1.22 \times$ $10^{-6} \mathrm{~mol}$ of argon- $40 .$ How old was the rock? (What assumption is made about the origin of the argon-40?)

Key Concepts

Radioactive Decay

This is the process by which unstable atomic nuclei lose energy by emitting radiation. It is fundamental to understanding how a parent isotope transforms into a daughter isotope over time. The decay process follows predictable statistical laws that allow scientists to estimate elapsed time based on the current amount of parent and daughter isotopes.

Half-Life

The half-life is the time required for half of the nuclei in a sample of a radioactive isotope to decay. It is a key parameter in calculating the age of a sample using radioactive decay, as it quantifies the decay rate of the isotope being studied.

Radiometric Dating

Radiometric dating is a technique used to determine the age of materials such as rocks by comparing the relative proportions of a radioactive parent isotope and its daughter products. By applying the known decay rates, scientists can calculate the time elapsed since the rock or material formed.

Parent-Daughter Isotope Ratio

The ratio between the amount of the parent isotope and the daughter product is central to the dating process. Accurate determination of these quantities allows for the application of decay relationships, which are then used to infer the age of the sample through mathematical models.

Assumption of Zero Initial Daughter Isotope

A crucial assumption in many radiometric dating methods is that no measurable amount of the daughter isotope was present at the time the rock formed. This assumption implies that all of the daughter product observed today is a result of the radioactive decay of the parent isotope, ensuring that the calculated age is not skewed by pre-existing daughter material.

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