The nuclear atom: (c) relative sizes of atom and nucleus

The idea

The nucleus is extremely small compared with the whole atom. A typical atomic diameter is of the order of 10⁻¹⁰ m, while a typical nuclear diameter is of the order of 10⁻¹⁵ m to 10⁻¹⁴ m. The ratio of atomic diameter to nuclear diameter is therefore about 10⁵, meaning the atom is roughly one hundred thousand times wider than its nucleus. Because volume depends on the cube of the radius, the atom's volume is about 10¹⁵ times the nuclear volume. This explains why most alpha particles pass straight through the atom in scattering experiments, while only those passing very close to the nucleus are strongly deflected.

What earns the marks

• A typical atomic diameter is of the order of 10⁻¹⁰ m.
• A typical nuclear diameter is of the order of 10⁻¹⁵ m to 10⁻¹⁴ m.
• The ratio of atomic diameter to nuclear diameter is about 10⁵, so the atom is roughly 100000 times wider than the nucleus.
• Because volume scales with the cube of radius, the atomic volume is about 10¹⁵ times the nuclear volume.
• The large difference in size means the atom is mostly empty space, which is consistent with alpha-particle scattering results.

Common mistakes and how to put them right

• Treating the ratio of diameters as the ratio of volumes.

  Put it right: Volume depends on the cube of the radius, so the volume ratio is about 10¹⁵, not 10⁵.

• Using 10⁻¹⁵ m as the atomic diameter.

  Put it right: That is the order of the nuclear diameter, while the atomic diameter is about 10⁻¹⁰ m.

• Thinking the nucleus occupies a large fraction of the atom.

  Put it right: The nucleus is tiny, so the atom is mostly empty space.

Exam tips

• Quote orders of magnitude rather than exact values, and state the unit clearly.
• Show the ratio calculation explicitly, for example 10⁻¹⁰ m divided by 10⁻¹⁵ m equals 10⁵.
• If asked about volume, remember to cube the radius ratio rather than using the diameter ratio directly.