From atom to nucleus: how small is small?

An atom is mostly empty space around a tiny centre. To talk about that centre we need a new unit.

• A typical atom is about 10⁻¹⁰ m across. That is 0.1 nanometres, or one ångström.
• A nucleus is between about 10⁻¹⁵ m and 10⁻¹⁴ m across. The unit for this scale is the femtometre (fm): 1 fm = 10⁻¹⁵ m. A single proton is a bit under 2 fm across, and a big nucleus such as lead is roughly 14 fm across.

So the nucleus is smaller than the atom by a factor of roughly 10⁴ to 10⁵. Put the other way round, the ratio of nuclear size to atom size is about 10⁻⁵. If you blew a nucleus up to the size of a pea (about 1 cm), its atom would be somewhere between 100 m and 1 km across. That is anything from a football pitch to a small town, with a pea in the middle.

Almost all the mass is in the nucleus. A proton and a neutron each weigh about 1.67 × 10⁻²⁷ kg. An electron is about 1,836 times lighter. Add up an atom and the nucleus carries more than 99.9 percent of the mass, even though it fills only about 10⁻¹⁵ of the volume (a millionth of a billionth).

That makes nuclear matter extremely dense: roughly 2 × 10¹⁷ kg per cubic metre. A sugar-cube volume (1 cm³) of it would weigh in the region of 200 million tonnes. You will never meet such a thing on Earth in bulk, but the nucleus inside every atom is made of it. (Neutron stars are the large-scale version of this stuff.)

How do we know? In 1909, Hans Geiger and Ernest Marsden, working in Ernest Rutherford's laboratory, fired alpha particles (fast, positively charged helium nuclei) at a very thin sheet of gold foil. The popular picture at the time, J. J. Thomson's "plum pudding", spread the positive charge through the whole atom, so every alpha particle should have sailed through with only a tiny nudge.

What they saw instead:

• Almost all the alpha particles passed straight through.
• A very small fraction were deflected through large angles, and a few came almost straight back.

In 1911 Rutherford worked out what that meant: nearly all the positive charge and mass must sit in a tiny, dense core, with the rest of the atom empty. Rutherford later described a large bounce-back as being almost as unbelievable as firing a big shell at tissue paper and having it come back at you. He called the core the nucleus.