The Atomic Mass Unit

Introduction

Relative atomic masses have no units, because they are ratios. But sometimes we want to state the actual mass of an atom, and grams give awkward numbers. The answer is a unit specially sized for atoms: the unified atomic mass unit , symbol u . With it, the mass of a carbon-12 atom is simply 12 u, and a hydrogen atom is about 1 u. This page explains what the unit is and just how small it is.

Core explanation

Definition. One unified atomic mass unit is one-twelfth of the mass of one atom of carbon-12 :

1 u = mass of one carbon-12 atom ÷ 12

This is the same quantity used as the reference on the carbon-12 scale, but now treated as a real unit of mass, like the gram or kilogram.

Its size. Measurements show that

1 u ≈ 1.66 × 10⁻²⁷ kg = 1.66 × 10⁻²⁴ g

That is about the mass of a single hydrogen atom, or almost exactly the mass of a single proton or neutron.

Masses in u. Using this unit, atom masses become friendly numbers:

Atom Mass in u (approx.) Mass in kg (approx.) --- --- --- Hydrogen-1 1.008 u 1.67 × 10⁻²⁷ kg Carbon-12 12 u (exactly) 1.99 × 10⁻²⁶ kg Oxygen-16 15.995 u 2.66 × 10⁻²⁶ kg Iron-56 55.93 u 9.29 × 10⁻²⁶ kg

u versus Ar. The number is the same, but the meaning differs slightly. "An average oxygen atom has a mass of 16.00 u" gives an actual mass with a unit. "Ar(O) = 16.00" gives a ratio with no unit. Both describe the same fact in two ways.

Other names. You may meet the older abbreviation amu (atomic mass unit). The name dalton , symbol Da , honours John Dalton and means exactly the same as u. Biochemists often describe large molecules, such as proteins, in kilodaltons (kDa): a protein of 50 kDa has a mass of about 50 000 u.

Converting. To change a mass in u into kilograms, multiply by 1.66 × 10⁻²⁷. To change kilograms into u, divide by 1.66 × 10⁻²⁷.

Formulae

1 u = (1/12) × mass of one ¹²C atom ≈ 1.66 × 10⁻²⁷ kg. Mass in kg = mass in u × 1.66 × 10⁻²⁷.

Step-by-step reasoning

To find the mass in kilograms of an atom with mass 23 u (sodium):

1. Write the conversion factor: 1 u ≈ 1.66 × 10⁻²⁷ kg. 2. Multiply: 23 × 1.66 × 10⁻²⁷ kg. 3. 23 × 1.66 = 38.2, so the mass is 38.2 × 10⁻²⁷ kg. 4. In standard form: 3.82 × 10⁻²⁶ kg.

Visual explanation

Think of a ladder of mass units. The kilogram suits people, the gram suits spoonfuls, the milligram suits grains of salt, and far, far below them all sits the u, sized so that one step of it matches roughly one hydrogen atom.

Real-world analogy

Astronomers measure distances between stars in light-years, not kilometres, because kilometres give absurdly large numbers. The atomic mass unit does the same job at the other extreme, giving sensible numbers for absurdly small masses.

Real-world example

In medicine and biology, antibody molecules are described as having a mass of about 150 kDa, and a water molecule about 18 Da. Using daltons lets scientists compare molecules from the tiniest to the largest on one convenient scale.

Why?

Why is 1 u so close to the mass of a hydrogen atom? A carbon-12 atom is built from twelve particles of almost equal mass (six protons and six neutrons) plus light electrons. One-twelfth of it is therefore close to the mass of one of those particles, and a hydrogen-1 atom is essentially one proton plus one electron.

Common misconception

"u and g are interchangeable." They are not. 1 u is about 1.66 × 10⁻²⁴ g, so writing "a carbon atom has a mass of 12 g" is wrong by a factor of about 6 × 10²³.

Worked example

Question: A gold atom has a mass of about 197 u. What is its mass in kilograms?

Reasoning: Mass = 197 × 1.66 × 10⁻²⁷ kg. 197 × 1.66 = 327, so the mass is 327 × 10⁻²⁷ kg.

Answer: About 3.27 × 10⁻²⁵ kg.

Quick check

1. What is the mass of one carbon-12 atom in u? Answer: Exactly 12 u.

Exam focus

Know the definition of 1 u as one-twelfth of the mass of a carbon-12 atom, and its approximate size, 1.66 × 10⁻²⁷ kg. Be clear that u is a unit of mass, whereas Ar is a pure number without units.

Advanced insight

In the 2019 revision of the SI, the kilogram was redefined using the Planck constant, and the Avogadro constant was given an exact value. The unified atomic mass unit is still defined through carbon-12, so its value in kilograms is now a measured quantity known to about ten significant figures rather than exactly.

Summary

The unified atomic mass unit, u (also called the dalton, Da), is one-twelfth of the mass of a carbon-12 atom, about 1.66 × 10⁻²⁷ kg. Atom masses in u are small, friendly numbers equal to their relative masses. The unit lets us state actual masses of atoms and molecules without awkward powers of ten.

Practice questions

1. Define the unified atomic mass unit. Answer: One-twelfth of the mass of one atom of carbon-12, about 1.66 × 10⁻²⁷ kg. 2. Convert 40 u (a calcium atom) into kilograms. Answer: 40 × 1.66 × 10⁻²⁷ = 6.64 × 10⁻²⁶ kg. 3. An atom has a mass of 5.31 × 10⁻²⁶ kg. What is its mass in u? Answer: 5.31 × 10⁻²⁶ ÷ 1.66 × 10⁻²⁷ ≈ 32 u, which matches sulfur. 4. What is the difference between saying "mass = 16 u" and "Ar = 16"? Answer: The first is an actual mass with a unit; the second is a ratio with no unit. They describe the same fact.