From amu to u: The Story of the Atomic Mass Unit

For most of the 20th century, chemists and physicists couldn’t agree on the mass of an atom. Not because they couldn’t measure it, but because they were using two different scales, both called “atomic mass units,” anchored to different standards. A mass reported by a physicist and the same mass reported by a chemist were not quite the same number. Resolving this required an international compromise that would reshape how we define atomic mass.

The Need for a Relative Scale

Atoms are extremely light: a single proton has a mass of roughly 1.67 × 10⁻²⁷ kg. Expressing atomic masses in kilograms is valid but cumbersome and gives little sense of how atoms compare to one another. Scientists instead developed a relative mass scale: choose one atom as the standard, assign it a precise mass value, and report every other mass relative to it. This is why the atomic masses on your periodic table are not in grams or kilograms; they are ratios, measured against a standard atom. The history of the atomic mass unit is the history of choosing that standard, and it took over 150 years to get it right.

The idea began with John Dalton, who in 1803 published the first table of relative atomic weights using hydrogen (the lightest element) as the reference, set to 1. In the 1810s, Jöns Jacob Berzelius shifted the reference to oxygen, which reacts with far more elements than hydrogen and was therefore more practical for chemical analysis. Jean Stas later refined Berzelius’s measurements with extraordinary precision, cementing oxygen as the accepted standard. By 1900, nearly all published atomic weights were based on oxygen = 16. The consensus seemed settled, but as measurement techniques improved in the 20th century, a hidden flaw in this oxygen standard came to light.

The First Standards: Two Types of “amu”

In the early 20th century, two slightly different mass scales emerged, both using the term “atomic mass unit” (amu). The coexistence of two scales with the same name created a subtle but significant conflict between chemistry and physics.

The “Chemical” amu

Around 1903, chemists formalized a scale based on naturally occurring oxygen, assigning the average mass of a natural oxygen atom a value of exactly 16 amu. Oxygen was a practical choice: it is abundant and forms compounds with many other elements, making it an ideal laboratory reference for determining relative weights through chemical analysis. But natural oxygen is a mixture of three stable isotopes (¹⁶O, ¹⁷O, and ¹⁸O), so the standard itself was an average, one that could shift slightly depending on the source of the oxygen sample.

The “Physical” amu

By the 1920s, physicists armed with the mass spectrometer could resolve individual isotopes and needed a sharper standard. They kept oxygen but pinned their scale to a single isotope, oxygen-16, assigning one ¹⁶O atom a mass of exactly 16 amu. A pure isotope is a more precise reference than a natural mixture, but this fix introduced a new problem: because natural oxygen contains small amounts of the heavier isotopes, the “chemical” amu was slightly larger than the “physical” amu (1 amu_chem ≈ 1.00028 amu_phys). Two fields, one unit name, two different numbers. This confusion persisted for decades.

The Resolution: The Unified Atomic Mass Unit (u)

The stalemate held until 1957, when Josef Mattauch, a German-Austrian physicist, championed a compromise first suggested to him by Alfred Nier: abandon oxygen entirely and base the scale on carbon-12. After several years of committee negotiations, IUPAP (physics) adopted the new standard in 1960 and IUPAC (chemistry) followed in 1961.

The modern standard is based on the isotope carbon-12 (¹²C). The unified atomic mass unit (u) is formally defined as: \[ \begin{align*} 1~\mathrm{u} &= \frac{1}{12}~\times~\text{mass of one neutral } {}^{12}\text{C atom in its ground state} \end{align*} \] The definition specifies “neutral” (including all 6 electrons) and “ground state” (lowest energy configuration) to ensure that every laboratory in the world measures exactly the same quantity. These conditions matter because, via E = mc², even small differences in energy configuration correspond to tiny differences in mass.

This new unit is also officially named the Dalton (Da) in honor of John Dalton. The terms are synonymous: 1 u ≡ 1 Da. In practice, u is more common in physics and general chemistry, while Da (and its multiple kDa) is standard in biochemistry and mass spectrometry.

In absolute terms, 1 u = 1.660 539 068 92 × 10⁻²⁷ kg (CODATA 2022).

Going Deeper: The 2019 SI Redefinition

Before 2019, the definitions of the amu and the mole were linked so that one mole of ¹²C atoms had a mass of exactly 12 grams. The 2019 SI redefinition broke that exact link by fixing Avogadro’s number to an exact value (6.022 140 76 × 10²³). As a result, 12 grams of ¹²C now contains very nearly, but not exactly, one mole of atoms. The discrepancy is roughly 1 part in 10⁹, negligible for any practical calculation. See The Mole: The Story of a Number for the full story.

Why Carbon-12?

Carbon-12 is a pure, single isotope, satisfying the need for precision. Carbon is easily purified and handled in the laboratory. And its mass is such that the new unified atomic mass unit (u) is numerically very close to both of the old “amu” standards, meaning existing scientific data did not need to be recalculated. Hydrogen-1 was considered but rejected. Calculations by Alfred Nier showed that carbon-12 required only a 42 ppm shift in existing chemical tables, whereas other candidates would have forced much larger revisions.

Summary and Modern Usage

The table below summarizes the three standards discussed in this note.

Table 1: Comparison of Atomic Mass Unit Standards

A Note on “amu”

In older texts and resources, you will frequently encounter the term “amu”. You can treat it as numerically identical to the modern, carbon-12 based unified atomic mass unit (u) or Dalton (Da). This textbook uses the modern u and Da symbols.

When you look up an element on the periodic table, the atomic mass listed (such as 12.011 for carbon or 15.999 for oxygen) is expressed in these units. These values are weighted averages that account for the natural abundance of each element’s isotopes. They are not whole numbers because nature provides a mixture of isotopes, and they are not in grams because they are ratios. A fluorine atom, for instance, has a mass of 18.998 u, meaning it is about 1.58 times as heavy as a carbon-12 atom. That shared standard keeps every entry on the table comparable.