In a piece of rock from the Moon, the ^87 Rb content is assessed to be 1.82 ×10^10 atoms per gr

step 1 So in this question, the number of 87 rb nuclei per gram on the moon rock is an r b 1 .82 multip

In a piece of rock from the Moon, the ^87 Rb content is...

In a piece of rock from the Moon, the ${ }^{87} \mathrm{Rb}$ content is assessed to be $1.82 \times 10^{10}$ atoms per gram of material and the ${ }^{87} \mathrm{Sr}$ content is found to be $1.07 \times 10^{9}$ atoms per gram. (a) Determine the age of the rock. (b) Could the material in the rock actually be much older? What assumption is implicit in the use of the radioactive dating method? (The relevant decay is ${ }^{87} \mathrm{Rb} \rightarrow{ }^{87} \mathrm{Sr}+\mathrm{e}^{-} .$ The half-life of the decay is $4.8 \times 10^{10} \mathrm{yr} .$

In a piece of rock from the Moon, the ${ }^{87} \mathrm{Rb}$ content is assessed to be $1.82 \times 10^{10}$ atoms per gram of material and the ${ }^{87} \mathrm{Sr}$ content is found to be $1.07 \times 10^{9}$ atoms per gram.
(a) Determine the age of the rock.
(b) Could the material in the rock actually be much older? What assumption is implicit in the use of the radioactive dating method? (The relevant decay is ${ }^{87} \mathrm{Rb} \rightarrow{ }^{87} \mathrm{Sr}+\mathrm{e}^{-} .$ The half-life of the decay is
$4.8 \times 10^{10} \mathrm{yr} .$

Key Concepts

Closed System Assumption

An implicit assumption in radiometric dating is that the rock has remained a closed system since its formation, meaning that no significant addition or loss of parent or daughter isotopes has occurred. This assumption is crucial because any alteration in the isotopic content due to external processes can lead to inaccurate age determinations.

Parent-Daughter Isotope Ratio

Measuring the ratio between the parent isotope and its daughter product is critical for radiometric dating. By applying the decay law, which describes how the parent isotope diminishes over time, scientists can calculate the time that has elapsed since the rock or material was last reset or formed.

Radiometric Dating

Radiometric dating is a technique used to date materials such as rocks by comparing the relative proportions of a radioactive isotope and its decay products. This method is based on the predictable and constant decay rate of the radioactive parent isotope into a daughter isotope, allowing scientists to calculate the time elapsed since the rock’s formation.

Half-life and Decay Constant

The half-life is the time required for half of the parent radioactive atoms in a sample to decay into daughter isotopes. The decay constant, which is related to the half-life by the equation ? = ln(2)/half-life, quantifies the rate at which the radioactive decay occurs. These concepts are essential for calculating the age of a rock from the measured isotopic ratios.

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