Rubidium is used in "atomic clocks" and other precise...

Rubidium is used in "atomic clocks" and other precise electronic equipment. The average atomic mass of ${ }_{37}^{85} \mathrm{Rb}(84.912 \mathrm{amu})$ and ${ }_{37}^{87} \mathrm{Rb}(86.909 \mathrm{amu})$ is
85.47 amu. Calculate the natural abundances of the rubidium isotopes.

Key Concepts

System of Linear Equations

Solving for the isotopic abundances often involves setting up a system of linear equations: one equation reflects that the sum of the abundances equals one (or 100%), and another represents the weighted average of the masses. Solving these equations simultaneously provides the fractional abundances necessary to reconcile the observed average atomic mass with the individual isotopic masses.

Average Atomic Mass

The average atomic mass of an element accounts for the masses of each naturally-occurring isotope weighted by their relative abundances. It reflects the measured atomic mass found on periodic tables, which is calculated as the summation of the products of the isotopic masses and their fractional abundances.

Isotopes

Isotopes are variants of a particular chemical element that have the same number of protons but different numbers of neutrons in their nuclei. This difference in neutron number leads to different atomic masses for each isotope, which becomes important in calculating the overall properties of the element as they occur naturally.

Weighted Average Calculation

Weighted average calculation involves multiplying each isotope's mass by its fraction of occurrence (natural abundance) and summing these values to produce the average atomic mass. This method is central in determining either the average atomic mass given the abundances or finding the abundances if the average mass is known.

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