Atomic Mass

The Problem with Tiny Masses

Atoms are unimaginably small. A single hydrogen atom has a mass of roughly $1.67 \times 10^{-24}$ grams — a decimal so small it is nearly impossible to work with directly. In the early days of chemistry, scientists had no way to weigh individual atoms. What they could do was compare the mass of one atom to another.

This is the core idea behind atomic mass: it is a relative quantity, not an absolute one. You never need to know the actual gram-mass of an atom; you only need to know how many times heavier it is than some chosen standard.

The Historical Standard: Hydrogen = 1

The lightest element known was hydrogen. Early chemists (including John Dalton) arbitrarily assigned hydrogen a mass of 1 (with no units). Every other element's mass was then expressed relative to this. For example, if an oxygen atom was found to be 16 times heavier than a hydrogen atom, its atomic mass was recorded as 16.

This system worked, but it had a flaw: different scientists used different standards (some used oxygen = 16, others used hydrogen = 1), leading to confusion.

The Modern Standard: Carbon-12

In 1961, an international agreement settled the matter once and for all. The standard chosen was the carbon-12 isotope (written as $^{12}\text{C}$). This isotope was assigned a mass of exactly 12 atomic mass units.

Definition of the Atomic Mass Unit

One atomic mass unit (amu, now symbolised as u) is defined as:

In grams, this works out to:

This number is the conversion factor between the atomic scale and the gram scale.

Finding the Mass of a Hydrogen Atom in amu

We know the actual mass of a hydrogen atom in grams:

To express this in atomic mass units, we divide by the value of 1 u:

Carrying out the division:

This is usually rounded to 1.0080 u.

Similarly, the mass of an oxygen-16 atom ($^{16}\text{O}$) works out to 15.995 u. …