Atomic mass unit
u, dalton Da · 1/12 of the mass of a carbon-12 atom · 1.660 539 069·10⁻²⁷ kg
Weighing an atom in grams is impossible; comparing one atom with another is easy — send both around a circle in a magnetic field and see which one bends further. That is how nineteenth-century chemists worked: their tables consist of ratios, not of masses. All that remained was to choose what to take as the unit. Dalton took hydrogen, Berzelius took oxygen, and a century and a half later it turned out that physicists and chemists had different oxygen: some measured the isotope, others the natural mixture, and the scales diverged in the fourth digit. In 1961 the argument ended in a compromise both sides accepted reluctantly: the unit became a twelfth of a carbon-12 atom. Ever since, every periodic table on every wall has counted masses from one particular atom that nobody has ever laid eyes on.
01 · Definition
The atomic mass unit is one twelfth of the mass of a carbon-12 atom at rest, unbound and in its ground state. The unit's second and equally valid name is the dalton, and in biochemistry it long ago displaced the first: kilodaltons and megadaltons speak of proteins and viruses, while «u» has stayed with atoms and nuclei.
The qualifications in the definition are not pedantry. The atom must be free, because inside a molecule part of the mass goes into the bond. It must be in its ground state, because an excited atom is heavier — energy has mass. And it must be at rest, because a moving atom is heavier by exactly its kinetic energy divided by the square of the speed of light. All three corrections sit in the tenth digit, and all three matter: mass spectrometry has long worked to finer precision than that.
The unit's most curious property is that it comes out fractional for almost everything. The mass of carbon-12 is exactly twelve, by definition; the mass of any other nuclide differs from its mass number. Oxygen-16 weighs 15.9949, helium-4 weighs 4.0026, uranium-235 weighs 235.0439. The reason is not imprecise measurement but the fact that a bound nucleus is lighter than its parts: the binding energy has been subtracted from the mass. That very shortfall is the source of all nuclear power, and these are the handiest units in which to see it.
A peculiarity of its own appeared in 2019. Until then the kilogram was set by a cylinder at Sèvres and the Avogadro number was measured; after the reform everything turned over: the Avogadro number was fixed exactly, the kilogram was tied to the Planck constant — and the dalton, previously exact by definition, became a measured quantity. Today it is known to a relative uncertainty of three tenths of a billionth, and the molar mass of carbon-12 equals twelve grams per mole no longer exactly, but only within that uncertainty.
Four hydrogen nuclei weigh 4.0313 u; the helium made from them weighs 4.0026. The difference of 0.0287 u departs as light, and that is seven tenths of a percent of the original mass. It sounds like little, yet the Sun processes six hundred million tonnes of hydrogen a second, and four million tonnes of that turn into radiation — every second, for five billion years. Uranium fission gives back only nine hundredths of a percent, eight times less; the whole difference between a reactor and a star fits into the fourth digit of the atomic mass unit.
02 · Conversion
Enter a value — the sheet converts it into the rest
Three families: the mass scale, what weighs the same, and energy by Einstein's formula.
The coincidence between the dalton and the gram per mole is not an identity but a consequence of how the Avogadro number was chosen. Before 2019 it was exact by construction; now the molar mass of carbon-12 is 12.000 000 013 grams per mole with an uncertainty in the last digit, and for any laboratory work it is still twelve. The difference matters in two places: in precise measurements of isotopic composition, and when reading older manuals, where «amu» may mean the oxygen-16 scale, which differs from the present one by three hundredths of a percent.
| Notation | What it means | Value | Where it occurs |
|---|---|---|---|
| u (Da) | atomic mass unit | 1.0000 | nuclides and molecules |
| kDa | kilodalton | 0.0010 | proteins |
| MDa | megadalton | 0.00000 | viruses, ribosomes |
| kg | in SI units | 1.661·10⁻²⁷ kg | conversion via 1.6605·10⁻²⁷ |
| г | in grams | 1.661·10⁻²⁴ g | the same, more familiar |
| g/mol | molar mass | 1.0000 | numerically equal to u |
| MeV/c² | rest energy | 931.494 | nuclear physics |
| mₑ | in electron masses | 1822.89 | 1 u = 1822.89 mₑ |
mass defect = sum of nucleon masses − mass of the nucleus
03 · Orders of magnitude
decimal logarithm of mass, daltonsNucleons and light atoms
04 · Measuring instruments
What an atom is weighed with
A beam of ions passes through electric and magnetic fields that send particles of different mass to different places on a photographic plate. Francis Aston built such an instrument in 1919 and within a few years found two hundred and twelve isotopes, explaining at a stroke why atomic masses in the table are not whole numbers: an element is a mixture. The precision reached a thousandth of a percent, and even that was enough to reveal the mass defect.
A single ion is held by magnetic and electric fields while its orbital frequency is listened to: that frequency is inversely proportional to the mass. Two frequencies are then compared — the ion under study and a carbon ion — and the mass ratio comes out with eleven significant figures. This is the most precise measuring technique in all of physics; it is what verifies that the mass defect in nuclear reactions agrees with the energy released, which is to say it verifies Einstein's formula itself.
A laser pulse lifts molecules off the substrate, an electric field gives them all the same energy, and then it only remains to measure who crosses the tube first: the heavy ones lag behind. The method works even on proteins of hundreds of kilodaltons, which no other technique can weigh whole. This is where the word «dalton» lives: in biochemistry mass is always called that, and «u» would sound odd.
An instrument that weighs not atoms but the kilogram: the gravitational force on a sample is balanced by the force on a coil in a magnetic field, and the result is expressed through the Planck constant. It does not measure the atomic mass unit, but it sets the far end of the bridge between the atom and the weight. This is exactly why the dalton lost its exactness after 2019: its link to the kilogram now runs through measured quantities rather than through a definition.
05 · Writing rules
One unit, two names, prefixes only for one
The dalton is a unit with a name of its own, and prefixes are attached to it; they are not attached to «u».
The abbreviation «amu» is obsolete and ambiguous besides: in literature before 1961 it meant the oxygen scale, not the carbon one. Kilodaltons are the right form for large molecules; there is no point writing sixty-four thousand daltons. In the symbol for the dalton only the first letter is capital, because the unit is named after a person, while «u» is lowercase because «unit» is not a name. And finally: the mass of uranium-235 is not 235 but 235.0439 u — the whole number here is only the mass number, the count of nucleons, and confusing it with the mass means losing the very quantity everything was calculated for.
06 · Neighbouring units
The dalton stands between the kilogram, the mole and the electronvolt.
a bridge via the Planck constant
the same number, but in grams
mass expressed as energy
Next to it in Simetrium stand kilogram, mole, electronvolt and barn.
07 · Historical section
A century and a half of arguing what the unit should be
John Dalton took hydrogen as the unit — not on principle, but because nothing lighter was known. He did not measure absolute masses and could not; his entire table consisted of ratios derived from the weight proportions of reactions. It contains many errors: he took water to be HO, so oxygen came out twice as light as it really is. But the idea that every element has a characteristic number of its own proved everlasting, and in the end his name went to the unit.
Jöns Jacob Berzelius moved the support to oxygen: it combines with almost everything, and masses can be determined through it more precisely than through capricious hydrogen. Oxygen was first taken as one hundred, then as sixteen — so that hydrogen would stay near unity. The resulting scale stood for more than a century and entered every reference book, and nobody then suspected that oxygen comes in different kinds.
The discovery of oxygen isotopes raised an awkward question: physicists working with the mass spectrometer took pure oxygen-16 as sixteen, while chemists went on using the natural mixture, which is heavier. For thirty years two scales lived side by side, differing by two and a half ten-thousandths, and every table needed a note saying whose it was. The compromise was found in carbon-12: it shifted chemical masses by only four hundredths of a per mille and suited both sides as a reference line in the mass spectrum.
Before the reform the dalton was exact by definition and the Avogadro number was measured. Since May 2019 it is the other way round: the Avogadro number is fixed, the kilogram is expressed through the Planck constant, and the dalton has become a measured quantity with an uncertainty in the tenth digit. Along with it, the familiar equality of carbon's molar mass to twelve grams per mole ceased to be an identity. There are no practical consequences for a single calculation in chemistry, but there is an elegant metrological moral: only what has been decreed can be exact.
A unit that lives on ratios
The atomic mass unit is almost never measured directly — what is measured are mass ratios, and therein lies its metrological peculiarity. A Penning trap compares the orbital frequencies of two ions and yields a ratio to eleven digits; converting that ratio into kilograms adds an uncertainty orders of magnitude larger than the comparison itself. That is why a table of nuclide masses expressed in daltons is more precise than any of those masses expressed in kilograms: within its own scale it holds the tenth or eleventh digit, whereas the link between the scale and the kilogram is known only to the tenth. Hence a simple practical rule: mass differences — the defect in a nuclear reaction, for instance — are computed in daltons or straight in electronvolts and never converted to kilograms as an intermediate step, or the conversion uncertainty will be added to a difference sitting in the tenth digit. And hence, too, the elegant upshot of the 2019 reform: by decreeing the Avogadro number exact, the metrologists left the dalton measured — that is, they acknowledged that the link between the world of atoms and the world of weights remains a matter of experiment rather than agreement.
Catalogue · units of measurement
A sheet for every quantity
Seven SI base units, twenty-two derived ones with names of their own, and the non-SI units that neither engineering nor everyday life can do without. Each has its own sheet: definition, conversion, instruments, writing rules. In 36 languages.
Atom and nucleus: units of this scale
mass, energy, cross-sectionWhat familiar things weigh
in daltonsSI base units
the kilogram and the molePassport language
36 languages. The symbols u and Da are international; what is translated are instrument names, nuclides and the notes to the scales.