OCR GCSE Physics A: Atomic model, atomic size and density (J249)

This guide covers statements P1.1a to P1.1f of Topic P1 (Matter) in the OCR GCSE (9-1) Physics A (Gateway Science) specification (J249), Version 5.0 (July 2026). None of these statements is in bold in the specification, so all of them are assessed in both the Foundation Tier and Higher Tier papers. It teaches the history of the atomic model, the structure and size of an atom, and density, including density across the states of matter. Use it with the revision notes and the practice questions. The wider topic is in OCR GCSE Physics: Matter.

Course pages: OCR GCSE Physics hub and the printable checklist. To find your weak spots first, try the free 10-minute diagnostics.

What this unit covers

Statement	You must be able to	Tier
P1.1a	Describe how and why the atomic model has changed over time (Thomson, Rutherford with Geiger and Marsden, Bohr)	Both
P1.1b	Describe the atom as a positively charged nucleus surrounded by negatively charged electrons, with the nuclear radius much smaller than the atom’s and almost all the mass in the nucleus	Both
P1.1c	Recall the typical size of atoms and small molecules (order of magnitude)	Both
P1.1d	Define density	Both
P1.1e	Explain density differences between states of matter using particle arrangements	Both
P1.1f	Apply density = mass / volume to changes where mass is conserved	Both

The specification’s own note on common errors is worth remembering. People confuse subatomic particles, atoms and molecules, and they slip when converting units of volume. Both points come up below.

P1.1a: how the atomic model changed

A model is a way of picturing something we cannot see directly. It is kept while it explains the evidence and replaced when new evidence disagrees with it. The specification asks for how and why, so always give the evidence behind each change.

Thomson: the plum pudding model. Thomson’s work on electrons showed that atoms contain tiny negative particles. Since atoms are neutral overall, he pictured a ball of positive charge with electrons spread through it, like fruit in a pudding. In this model the charge and mass are spread evenly through the atom.

Rutherford, Geiger and Marsden: the nuclear model. Geiger and Marsden, working with Rutherford, fired alpha particles (which are positively charged) at a very thin gold foil and detected where they went. The results:

• Most alpha particles went straight through. So most of the atom is empty space.
• A small number were deflected through large angles, and a very few came almost straight back. So there must be a small, dense, positively charged centre that repels them.

The plum pudding model could not explain large deflections, because spread-out positive charge would only deflect a particle slightly. Rutherford therefore proposed a small central nucleus holding the positive charge and nearly all the mass, with electrons around it.

Bohr: electrons at set distances. Bohr adapted the nuclear model by placing the electrons in orbits (energy levels) at fixed distances from the nucleus. This explained why atoms are stable and why they give out light only at particular wavelengths.

Model	Positive charge	Electrons	Key evidence
Plum pudding (Thomson)	Spread through the atom	Embedded in it	Discovery of the electron
Nuclear (Rutherford)	Small central nucleus	Around the nucleus, far away	Alpha scattering by gold foil
Bohr	Nucleus	In orbits at fixed distances	Atoms emit light of particular wavelengths

Scientists checked and built on each other’s work, and that teamwork is part of how models develop.

P1.1b: the nuclear atom

An atom has a positively charged nucleus surrounded by negatively charged electrons. Three facts to state:

1. The nucleus carries all the positive charge.
2. The radius of the nucleus is much smaller than the radius of the atom. The nucleus is roughly ten thousand times smaller across, though the exact ratio depends on the atom.
3. Almost all the mass is in the nucleus, because an electron has only about one two-thousandth of the mass of a proton or neutron.

Worked example (scale model). If an atom were enlarged to 100 m across (a stadium), how big would the nucleus be, taking it as 10 000 times smaller?

Nucleus = 100 m ÷ 10 000 = 0.010 m = 1.0 cm. It is a marble in the middle of a stadium.

Because volume depends on the cube of the radius, the nucleus occupies a fraction of about (1 ÷ 10 000)³ = 1 × 10⁻¹² of the atom’s volume. Yet it holds almost all the mass. This is why the nucleus is extremely dense and why the atom is mostly empty space.

P1.1c: sizes to recall

The specification says to know that atoms and small molecules are typically 1 × 10⁻¹⁰ m across. This is an order of magnitude, not an exact value. Different atoms differ a little, and bigger molecules are larger.

Worked example. How many atoms of diameter 1 × 10⁻¹⁰ m fit in a row across a hair 0.080 mm wide?

0.080 mm = 8.0 × 10⁻⁵ m. Number = 8.0 × 10⁻⁵ ÷ 1 × 10⁻¹⁰ = 8 × 10⁵, or about 800 000 atoms.

Be careful with terms. A molecule is two or more atoms joined together. “Particle” is a general word and can mean an atom, a molecule or a subatomic particle, so use the exact word the question uses.

P1.1d: defining density

Density is the mass of a substance per unit volume. Written as a relationship:

density (kg/m³) = mass (kg) ÷ volume (m³), or ρ = m ÷ V

Density tells you how much matter is packed into a given space. A block of lead and a block of wood can have the same volume, but the lead has far more mass, so its density is greater.

Units need care because the specification gives kg and m³.

• 1 m³ = 1 000 000 cm³ (because 100 × 100 × 100 = 1 000 000).
• 1 g/cm³ = 1000 kg/m³.
• 1 cm³ = 1 millilitre, so 1 litre = 1000 cm³ = 0.001 m³.

Worked example 1 (regular solid). A brass block measures 3.0 cm × 4.0 cm × 2.0 cm and has mass 204 g. Find its density in kg/m³.

Volume = 3.0 × 4.0 × 2.0 = 24 cm³. Density = 204 ÷ 24 = 8.5 g/cm³ = 8.5 × 1000 = 8500 kg/m³.

Worked example 2 (find mass). A tank holds 0.60 m³ of petrol of density 740 kg/m³. Find the mass.

Rearrange: m = ρ × V = 740 × 0.60 = 444 kg, or 440 kg to two significant figures.

Worked example 3 (find volume). What volume does 2.4 kg of cooking oil of density 920 kg/m³ occupy?

V = m ÷ ρ = 2.4 ÷ 920 = 2.6 × 10⁻³ m³, which is 2600 cm³ (2.6 litres).

Worked example 4 (irregular solid). A stone of mass 87.5 g is lowered into a measuring cylinder holding 40.0 cm³ of water. The level rises to 52.0 cm³.

Volume of stone = 52.0 − 40.0 = 12.0 cm³. Density = 87.5 ÷ 12.0 = 7.29 g/cm³ = 7290 kg/m³ (3 s.f.).

The specification suggests measuring length, volume and mass to calculate density, and investigating Archimedes’ principle using eureka cans. The method for an irregular solid is: measure its mass on a balance, then find its volume from the water it displaces (in a measuring cylinder or a eureka can), then divide. For a liquid, measure the mass of a measuring cylinder empty and then with liquid, subtract, and read the volume from the scale at eye level. The main error sources are reading the meniscus, trapped air bubbles on a sunk object, and forgetting to subtract the container’s mass.

P1.1e: density and the states of matter

Density depends on how many particles are packed into a space and on how heavy they are. For one substance, the particles are the same in every state, so the difference comes from the spacing.

State	Arrangement	Spacing	Density
Solid	Regular pattern, fixed positions, vibrating	Very close, touching	High
Liquid	Irregular, free to move past each other	Close, mostly touching	Slightly lower than the solid
Gas	Random, far apart, moving quickly	Large gaps	Very low

In a gas the particles are far apart, with nothing between them (not air, not “vapour”; the gaps are empty space). So a given volume contains far fewer particles and far less mass.

Water as a liquid has a density of about 1000 kg/m³, while air is about 1.2 kg/m³. The ratio is 1000 ÷ 1.2 = about 830, so water is some hundreds of times denser. That is why a change of state from liquid to gas, such as boiling, produces a large increase in volume.

Most solids are slightly denser than their liquids because the regular arrangement packs particles a little closer. Water is an unusual case: ice is less dense than liquid water, which is why ice floats. If a question asks about this, say that the arrangement of the particles in ice takes up more space than in liquid water.

P1.1f: mass conserved, volume changes

When a substance changes state, expands, or is compressed in a sealed container, the mass stays the same, because no particles are gained or lost. So:

mass = ρ₁ × V₁ = ρ₂ × V₂

If the volume changes, the density changes in the opposite direction.

Worked example 5 (gas compressed). A sealed syringe holds 0.050 m³ of gas of density 1.2 kg/m³. It is compressed to 0.0125 m³ with no gas escaping. Find the new density.

Mass = 1.2 × 0.050 = 0.060 kg. New density = 0.060 ÷ 0.0125 = 4.8 kg/m³. The volume fell to a quarter, so the density rose four times.

Worked example 6 (melting). A block of ice of mass 4.6 kg has density 920 kg/m³. It melts to water of density 1000 kg/m³. Find the change in volume.

Volume of ice = 4.6 ÷ 920 = 5.0 × 10⁻³ m³. Volume of water = 4.6 ÷ 1000 = 4.6 × 10⁻³ m³. Volume decreases by 0.4 × 10⁻³ m³, which is 4.0 × 10⁻⁴ m³. The mass is unchanged at 4.6 kg throughout.

A useful check. If a gas is heated in a rigid, sealed container, both mass and volume stay the same, so the density does not change. If it is heated in a balloon that expands, the volume rises and the density falls.

Common errors

• Mixing units, for example dividing grams by m³. Convert first.
• Treating 1 g/cm³ as 100 kg/m³. It is 1000 kg/m³.
• Saying the nucleus is the biggest part of the atom. It is the heaviest part, not the largest.
• Saying electrons are in the nucleus, or that the nucleus is negative.
• Describing the plum pudding model as having a nucleus.
• Saying particles themselves “expand” when a substance is heated. The spacing changes, not the particles.
• Writing “gases have no mass”. They have a small density, not zero.

Next steps

Test yourself with the practice questions, then condense with the revision notes. The other density material for this course is in OCR GCSE Physics: Matter revision notes and Matter practice questions.

Official syllabus

OCR GCSE (9-1) Physics A (Gateway Science) specification (J249), Version 5.0 (July 2026), for first assessment in 2018, published by OCR. Statements P1.1a to P1.1f.