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

The Need for a Relative Scale

Atoms are extremely light. The mass of a single proton is approximately 1.67 × 10−27 kg. Using standard units like kilograms to express the masses of different atoms is scientifically valid, but it is cumbersome and gives little sense of how heavy atoms are relative to one another.

To simplify this, scientists developed a relative mass scale. The strategy is to choose one specific atom as the “standard,” assign it a precise mass value, and then report the masses of all other atoms relative to that standard. The history of the atomic mass unit involves refining the choice of that standard to achieve better precision and universal agreement.

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). This created a subtle but significant conflict between the disciplines of chemistry and physics. The chemical scale was formalized around 1903, while the physical scale emerged in the 1920s with the development of mass spectrometry.

1. The “Chemical” amu

Chemists defined their scale using naturally occurring oxygen. They assigned the average mass of a natural oxygen atom a value of exactly 16 amu.

  • Why oxygen? Oxygen is abundant and forms compounds with a vast number of other elements, making it a practical laboratory standard for determining relative weights through chemical analysis.
  • The Problem: Natural oxygen is a mixture of three stable isotopes (16O, 17O, and 18O). This meant the standard itself was an average, dependent on natural abundances that could have minor variations.

2. The “Physical” amu

Physicists, using the mass spectrometer, could measure the masses of individual isotopes and required a more precise standard. They defined their scale using a single isotope, oxygen-16. They assigned the mass of one 16O atom a value of exactly 16 amu.

  • Why oxygen-16? It is the most abundant isotope of oxygen, and using a pure isotope is a fundamentally more precise definition than using a natural mixture.
  • The Problem: Because natural oxygen contains small amounts of the heavier isotopes, the “chemical” amu was slightly larger than the “physical” amu (1 amu (chemical) ≈ 1.00028 amu (physical)). This discrepancy, while small, was an obstacle to clear scientific communication.

The Resolution: The Unified Atomic Mass Unit (u)

In 1961, an international agreement between IUPAC (chemistry) and IUPAP (physics) established a new, single standard for all sciences, resolving the confusion.

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) because, via E = mc², even the small binding energy of electrons contributes measurably to an atom’s 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 absolute terms, 1 u = 1.660 539 068 92 × 10−27 kg (CODATA 2022). Before 2019, this value was defined so that one mole of 12C atoms had a mass of exactly 12 grams. Since the 2019 SI redefinition, the mole is instead defined by fixing Avogadro’s number exactly (6.022 140 76 × 1023). As a result, 12 grams of 12C now contains very nearly (but not exactly) one mole of atoms. The difference is negligible for all practical purposes (roughly 1 part in 1010).

  • Why carbon-12? Several factors made carbon-12 a practical choice. It 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 would have made all atomic masses greater than 1, requiring more extensive revision of existing tables.)

Summary and Modern Usage

Table 1: Comparison of Atomic Mass Unit Standards

In older texts and resources, you will frequently encounter the term “amu”. For all practical purposes in this course, you can treat it as being numerically identical to the modern, carbon-12 based unified atomic mass unit (u) or Dalton (Da). This textbook will use the modern u and Da symbols, as they represent the current standard.

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 represent weighted averages that account for the natural abundance of each element’s isotopes.