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Atoms are so light that measuring their masses in kilograms gives awkward numbers: a carbon atom has a mass of about 0.00000000000000000000000002 kg. Chemists use a far more convenient unit instead: the atomic mass unit, symbol u, also called the dalton (Da). On this scale, a carbon-12 atom has a mass of exactly 12, hydrogen about 1, and gold about 197. This article explains how the unit is defined, why carbon-12 was chosen, and how the unit links atoms to the moles and grams used in the lab.
Definition
One atomic mass unit is exactly one-twelfth of the mass of a single carbon-12 atom (in its ground state, at rest, unbound).
1 u = 1 Da ≈ 1.660539 × 10⁻²⁷ kg
So by definition, a carbon-12 atom has a mass of exactly 12 u.
The names unified atomic mass unit (u) and dalton (Da, named after John Dalton) mean the same thing. Chemists and physicists more often write u; biochemists usually use Da and kDa (kilodaltons) for large molecules such as proteins. An older abbreviation, amu, is still seen but is no longer recommended.
Masses of particles and atoms in u
| Particle or atom | Mass (u) |
|---|---|
| electron | 0.000549 |
| proton | 1.00728 |
| neutron | 1.00866 |
| hydrogen-1 atom | 1.00783 |
| carbon-12 atom | 12 (exactly) |
| oxygen-16 atom | 15.9949 |
| uranium-238 atom | 238.0508 |
Notice that an atom’s mass in u is always close to its mass number (the number of protons plus neutrons), because protons and neutrons each have a mass of about 1 u and electrons contribute very little. See mass number explained.
Why isn’t every atom’s mass a whole number?
If protons and neutrons are each about 1 u, why isn’t oxygen-16 exactly 16 u?
Two reasons:
- Protons and neutrons aren’t exactly 1 u. They’re slightly more (1.00728 and 1.00866 u).
- Mass defect. When protons and neutrons bind together into a nucleus, some mass is converted into the binding energy that holds the nucleus together (E = mc²). A nucleus weighs less than its separate parts. See mass defect and binding energy.
Carbon-12 is exactly 12 only because it’s the reference that defines the scale.
Relative atomic mass vs atomic mass
- The atomic mass of a particular isotope is its mass in u, e.g. chlorine-35 = 34.969 u.
- The relative atomic mass (Aᵣ) of an element is the weighted average of its isotopes’ masses, divided by 1 u, so it has no units. For chlorine, Aᵣ = 35.45.
See relative atomic mass calculations and atomic mass vs mass number vs molar mass.
The link to moles and grams
The atomic mass unit was designed to connect neatly with the mole:
An atom with a mass of x u has a molar mass of (very nearly) x g/mol.
- One carbon-12 atom: 12 u → one mole of carbon-12: 12 g
- One water molecule: about 18.02 u → one mole of water: 18.02 g
This works because Avogadro’s constant is the number of atomic mass units in one gram (to a very close approximation):
1 g ÷ 1.660539 × 10⁻²⁷ kg = 1 × 10⁻³ kg ÷ 1.660539 × 10⁻²⁷ kg ≈ 6.022 × 10²³
That’s why the numbers on the periodic table serve double duty: they’re the mass of an average atom in u and the mass of a mole in grams. See Avogadro’s number and what is molar mass?
(Since the 2019 redefinition of SI units, the mole is defined by fixing Avogadro’s constant exactly, so the equality “1 u × N_A = 1 g/mol” is now extremely close but no longer exact by definition. The difference, less than one part in a billion, is irrelevant for all practical chemistry.)
Worked examples
Example 1: What’s the mass in kilograms of one atom of gold-197 (196.967 u)?
196.967 × 1.660539 × 10⁻²⁷ = 3.271 × 10⁻²⁵ kg
Example 2: How many atomic mass units are in 1 gram?
1 × 10⁻³ ÷ 1.660539 × 10⁻²⁷ = 6.022 × 10²³ u (Avogadro’s number)
Example 3: A protein has a mass of 66.5 kDa (serum albumin). What’s the mass of one molecule in grams?
66,500 × 1.660539 × 10⁻²⁴ g = 1.10 × 10⁻¹⁹ g
And one mole of it has a mass of about 66,500 g (66.5 kg).
History: from hydrogen to oxygen to carbon
The reference for atomic masses has changed several times:
| Period | Reference | Problem |
|---|---|---|
| Early 1800s (Dalton) | hydrogen = 1 | hydrogen forms few compounds with metals, making many masses hard to measure directly |
| Later 1800s – 1961 | oxygen = 16 | chemists used natural oxygen (a mixture of isotopes), physicists used pure oxygen-16, giving two slightly different scales |
| 1961 onwards | carbon-12 = 12 | a single agreed scale for chemists and physicists |
The discovery of isotopes caused the oxygen problem: natural oxygen contains small amounts of oxygen-17 and oxygen-18, so “oxygen = 16” meant slightly different things to different scientists. In 1961, the International Union of Pure and Applied Chemistry (IUPAC) and the International Union of Pure and Applied Physics adopted carbon-12, which unified the scales and changed most atomic masses by only about 0.004%.
Carbon-12 was a good choice because carbon is common, forms many compounds and its isotope carbon-12 can be measured very precisely in mass spectrometers.
Where the unit is used
- Chemistry: atomic and molecular masses; every molar mass calculation.
- Mass spectrometry: results are plotted against m/z, with m in u (Da); high-resolution instruments measure masses to four or five decimal places, allowing molecular formulas to be identified. See mass spectrometry.
- Biochemistry: protein and DNA sizes in kDa or MDa (the ribosome has a mass of several megadaltons).
- Nuclear physics: mass defects and binding energies, often converted using 1 u ≈ 931.5 MeV.
Common mistakes
- Confusing u with g. One atom of carbon-12 is 12 u, not 12 g. Twelve grams is the mass of a whole mole of carbon-12 atoms.
- Giving relative atomic mass units. Aᵣ is a ratio and has no units; atomic mass in u, and molar mass in g/mol, do.
- Assuming masses are exact whole numbers. Only carbon-12 is exactly 12 u; every other atom’s mass has decimals.
- Mixing up Da and kDa. Protein masses in kDa must be multiplied by 1,000 before converting to grams per mole.
A useful check: the mass of any atom in u should be close to its mass number, and the mass of one mole in grams should be the same number as the mass of one particle in u.
Key takeaways
- 1 u (1 Da) is one-twelfth of the mass of a carbon-12 atom: about 1.66 × 10⁻²⁷ kg.
- Protons and neutrons are each about 1 u; electrons are about 0.00055 u.
- Atomic masses aren’t whole numbers because of the particles’ exact masses and the nuclear mass defect.
- An atom with mass x u has a molar mass of x g/mol, because Avogadro’s constant links u and grams.
- The carbon-12 standard (1961) replaced earlier hydrogen and oxygen scales, unifying chemistry and physics.
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