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Isotopes and average atomic mass

Atoms of the same chemical element all have the same number of protons, but they can contain different numbers of neutrons. Such variants are isotopes.

An isotope is commonly written

$$^{A}_{Z}X,$$

where $X$ is the element symbol, $Z$ is the proton number, and

$$A=Z+N$$

is the mass number, the total number of protons and neutrons. For example, carbon-12 and carbon-13 both have $Z=6$, but contain six and seven neutrons respectively.

Atomic masses are conveniently measured in unified atomic mass units, symbol $\mathrm u$, defined so that a neutral carbon-12 atom has mass exactly $12,\mathrm u$.

A naturally occurring element may contain several isotopes. The atomic mass listed for such an element is therefore generally a weighted average rather than an integer. If isotope $i$ has fractional abundance $f_i$ and atomic mass $m_i$, then

$$\bar m=\sum_i f_i m_i,$$

with $\sum_i f_i=1$.

For chlorine, using approximate natural abundances and isotopic masses,

$$\bar m\approx(0.7578)(34.969,\mathrm u)+(0.2422)(36.966,\mathrm u) \approx35.45,\mathrm u.$$

This explains why periodic-table atomic masses such as chlorine's are usually not whole numbers. The average describes a macroscopic sample with the stated isotopic composition; an individual chlorine atom is one isotope, not an atom of mass $35.45,\mathrm u$.