The C R C Handbook, a large reference book of chemical and...

The $C R C$ Handbook, a large reference book of chemical and physical data from which many of the values in this book are taken, lists two isotopes of rubidium $(Z=37) .$ The atomic mass of $72.15 \%$ of rubidium atoms is 84.9118 amu. Through a typographical oversight, the atomic mass of the second isotope is not printed. Calculate that atomic mass.

Key Concepts

Algebraic Equation Setup for Weighted Averages

Setting up an algebraic equation for weighted averages involves assigning variables to unknown quantities and using the known values of isotopic masses and abundances to form an equation. This equation expresses the total weighted contribution of each isotope to the average atomic mass, allowing for the solving of unknown isotopic masses when the overall average and other contributions are known.

Weighted Average

Weighted average is a method of calculating an overall average in which each component contributes proportionally based on its assigned weight or relative frequency. In the context of atomic masses, the average atomic mass of an element is computed by multiplying the mass of each isotope by its fractional abundance and summing the results.

Isotopic Abundance

Isotopic abundance refers to the proportion or percentage of each isotope present in a natural sample of an element. This concept is crucial in determining the average atomic mass, as different isotopes have different masses and contribute differently to the overall atomic mass according to their abundance.

Atomic Mass

Atomic mass is the mass of an individual atom, typically measured in atomic mass units (amu). The average atomic mass that is commonly cited for an element is not the mass of a single isotope, but rather the weighted average of the masses of all the isotopes present, each multiplied by its natural abundance.

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