The decay of Rb-87(t1 / 2=4.8 ×10^10 y) to Sr-87 has been used to determine the age of ancient r

step 1 If rubidium 87 decays to strontium 87, we can write a balanced nuclear equation and identify wha

The decay of Rb-87(t1 / 2=4.8 ×10^10 y) to Sr-87 has been...

The decay of $\mathrm{Rb}-87\left(t_{1 / 2}=4.8 \times 10^{10} \mathrm{y}\right)$ to $\mathrm{Sr}-87$ has been used to determine the age of ancient rocks and minerals. a. Write the balanced nuclear equation for this decay. b. If a sample of rock is found to be $0.100 \%$ by mass $\mathrm{Rb}-87$ and $0.00250 \% \mathrm{Sr}-87$, what is the age of the rock? Assume that there was no Sr-87 present when the rock formed.

The decay of $\mathrm{Rb}-87\left(t_{1 / 2}=4.8 \times 10^{10} \mathrm{y}\right)$ to $\mathrm{Sr}-87$ has
been used to determine the age of ancient rocks and minerals.
a. Write the balanced nuclear equation for this decay.
b. If a sample of rock is found to be $0.100 \%$ by mass $\mathrm{Rb}-87$ and $0.00250 \% \mathrm{Sr}-87$, what is the age of the rock? Assume that there was no Sr-87 present when the rock formed.

Key Concepts

Stoichiometric Calculations in Radiometric Dating

Stoichiometric calculations in the context of radiometric dating involve converting mass or percentage compositions of isotopes into moles or numbers of atoms, and using these values in decay equations. This process enables the determination of the original quantity of the radioactive isotope and the calculation of the elapsed time since the decay process began. Such calculations underpin the quantitative analysis required to derive accurate age estimates from isotopic measurements.

Nuclear Reaction Equations

Nuclear reaction equations represent the processes of radioactive decay by showing the transformation of a parent nucleus into a daughter nucleus along with any emitted particles or radiation. These equations must balance the nucleon number (mass number) and the proton number (atomic number), reflecting the conservation laws of physics. They provide a concise way to visualize the change in nuclear composition during a decay process.

Beta Decay

Beta decay is a type of radioactive decay in which a neutron is transformed into a proton with the emission of an electron (beta particle) and an antineutrino, or vice versa. In the context of nuclear transmutations, beta decay results in an increase (or decrease) of the atomic number by one while leaving the mass number unchanged. When an element undergoes beta decay, its identity changes, which is a key principle in the study of radioactive dating methods.

Exponential Decay and Half-Life

Exponential decay describes the process by which the number of undecayed radioactive nuclei decreases over time at a rate proportional to the current quantity. The half-life is the time required for half of the radioactive nuclei in a sample to decay. This concept is essential for calculating the age of a sample based on its remaining radioactive content, as it offers a measurable timescale for the decay process.

Radiometric Dating

Radiometric dating is a technique used to determine the age of rocks and minerals by comparing the abundance of a radioactive parent isotope to its stable daughter isotope. By applying the known half-life of the parent isotope and measuring the current isotopic ratios, scientists can calculate the time elapsed since the formation of the sample. This method is fundamental in fields such as geology and archaeology for establishing time scales.

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