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

These notes condense statements P1.1a to P1.1f of the OCR GCSE (9-1) Physics A (Gateway Science) specification (J249), Version 5.0 (July 2026). All six statements are assessed in both tiers. For full explanations and worked examples, read the study guide, then test yourself with the practice questions.

Course links: OCR GCSE Physics hub, printable checklist, free 10-minute diagnostics, and the wider Matter revision notes.

P1.1a: the atomic model timeline

Scientist	Model or discovery	Why the model changed
Thomson	Plum pudding: ball of positive charge with electrons embedded	Electrons were found to be tiny negative particles inside atoms
Rutherford, with Geiger and Marsden	Nuclear model: small, dense, positive nucleus; electrons around it	Alpha particles fired at thin gold foil: most passed straight through, a few were deflected through large angles, a very few bounced almost straight back
Bohr	Electrons in orbits (energy levels) at fixed distances	Explained atomic stability and light emitted at particular wavelengths

Why a model changes: new experimental evidence cannot be explained by the old model. The new model must explain both the old and the new evidence.

Alpha scattering, in three linked lines:

1. Most alpha particles went straight through, so most of an atom is empty space.
2. Some were deflected by large angles, so the centre is positive and repels alpha particles.
3. A few came almost straight back, so the positive centre is very small, very dense and holds nearly all the mass.

Picture of the experiment (words and symbols):

• Alpha source, then thin gold foil, then detector.
• Most alpha particles: straight on through.
• Some: deflected by a large angle.
• Very few: almost straight back.

P1.1b: the nuclear atom

• Positively charged nucleus in the centre.
• Negatively charged electrons surrounding it.
• Nuclear radius much smaller than atomic radius (about ten thousand times smaller as an order of magnitude).
• Almost all the mass is in the nucleus. An electron’s mass is about one two-thousandth of a proton’s.
• Overall the atom is neutral.

Scale reminder: nucleus fills about (1 ÷ 10 000)³ = 1 × 10⁻¹² of the atom’s volume. If the atom were 100 m across, the nucleus would be 100 ÷ 10 000 = 0.010 m, so 1.0 cm.

P1.1c: sizes

Object	Size to recall
Atom or small molecule	About 1 × 10⁻¹⁰ m (an order of magnitude)

Standard form practice: 1 mm = 1 × 10⁻³ m, so a 1 mm line is about 1 × 10⁻³ ÷ 1 × 10⁻¹⁰ = 1 × 10⁷ atoms wide.

Terms. Atom: one particle of an element. Molecule: atoms joined together. Subatomic particles: protons, neutrons, electrons. “Particle” can mean any of these, so match the word to the question.

P1.1d: density

Definition: density is mass per unit volume.

Quantity	Symbol	Unit
Density	ρ	kg/m³ (or g/cm³)
Mass	m	kg (or g)
Volume	V	m³ (or cm³)

Relationship: ρ = m ÷ V, so m = ρ × V and V = m ÷ ρ.

Unit conversions:

• 1 g/cm³ = 1000 kg/m³
• 1 m³ = 1 000 000 cm³
• 1 cm³ = 1 mL; 1 litre = 1000 cm³ = 0.001 m³

Method in steps (calculation):

1. Write the formula and decide which quantity is unknown.
2. Convert all units to a matching set (kg and m³, or g and cm³).
3. Substitute, calculate, and round sensibly.
4. Convert the answer to the unit requested, with the unit written.

Worked reminder. A metal cylinder has volume 35 cm³ and mass 273 g. Density = 273 ÷ 35 = 7.8 g/cm³ = 7800 kg/m³.

Worked reminder (irregular solid). A pebble of mass 66.0 g raises the water in a measuring cylinder from 30.0 cm³ to 54.0 cm³. Volume = 24.0 cm³. Density = 66.0 ÷ 24.0 = 2.75 g/cm³ = 2750 kg/m³.

Worked reminder (unit conversion). 0.0040 m³ of liquid has mass 3.2 kg. Density = 3.2 ÷ 0.0040 = 800 kg/m³. In g/cm³ this is 0.80.

Measuring density (practical suggestions in the specification):

Object	Mass	Volume
Regular solid	Balance	Measure lengths with a ruler or calipers, then calculate
Irregular solid	Balance	Water displaced in a measuring cylinder or eureka can
Liquid	Container with liquid minus empty container	Measuring cylinder, read at the bottom of the meniscus with the eye level with it

P1.1e: density and the states of matter

State	Arrangement	Spacing	Density
Solid	Regular, fixed positions, vibrating	Close	High
Liquid	Irregular, move past each other	Close	Similar to the solid, usually a little lower
Gas	Random, move quickly	Far apart	Very low

• Same particles in each state, so mass per particle does not change. Only the spacing changes.
• Gas density is low because a given volume contains far fewer particles.
• Water: about 1000 kg/m³. Air: about 1.2 kg/m³.
• Between particles is empty space, not air.
• Ice is less dense than liquid water, which is why ice floats.

P1.1f: mass conserved

The mass stays the same during melting, boiling, expanding and compressing in a sealed container. Then:

ρ₁ × V₁ = ρ₂ × V₂

• Volume down, density up.
• Volume up, density down.
• Sealed rigid container heated: mass and volume both fixed, so density unchanged.

Worked reminder. 0.30 m³ of gas at 2.0 kg/m³ expands to 0.50 m³. Mass = 0.60 kg. New density = 0.60 ÷ 0.50 = 1.2 kg/m³.

Worked reminder (melting). 2.0 kg of ice (density 920 kg/m³) melts to water (density 1000 kg/m³). Ice volume = 2.0 ÷ 920 = 2.2 × 10⁻³ m³. Water volume = 2.0 ÷ 1000 = 2.0 × 10⁻³ m³. The volume falls and the mass stays 2.0 kg.

Must-know distinctions

• Heaviest part of an atom versus largest part. The nucleus is the heaviest part and the smallest in size.
• Atom versus molecule. A molecule contains more than one atom.
• Mass versus volume versus density. Mass is the amount of matter, volume the space, density the mass per unit space.
• Particle size versus particle spacing. Changing state changes spacing, not the size of particles.

Answer-writing patterns

• Describe how the model changed: name the old model, state the new observation, say why the old model could not explain it, then state the new model.
• Explain density differences: say what is different (spacing), what is the same (the particles), and link spacing to the number of particles in a given volume.
• Calculate: write the formula, substitute with units, give the answer with a unit, and round at the end rather than part way.
• Suggest a source of error: name the measurement (for example the meniscus reading or air bubbles on a sunk object) and say which way it shifts the result.

Quick self-test

1. Which scientist proposed the plum pudding model?
2. State two observations from the gold foil experiment and what each shows.
3. Which scientist introduced electron orbits at fixed distances?
4. Who worked with Rutherford to carry out the gold foil experiment?
5. State the typical size of an atom as an order of magnitude.
6. Define density.
7. A block has volume 50 cm³ and mass 400 g. Find its density in kg/m³.
8. Find the mass of 0.025 m³ of a liquid of density 1100 kg/m³.
9. Explain why a gas is much less dense than the solid of the same substance.
10. 0.40 kg of gas in a syringe is compressed from 0.20 m³ to 0.050 m³. Find the new density.

Answers

1. Thomson.
2. Most alpha particles went straight through, so most of the atom is empty space. A small number were deflected through large angles (a few bounced almost straight back), so there is a small, dense, positive nucleus.
3. Bohr.
4. Geiger and Marsden.
5. About 1 × 10⁻¹⁰ m.
6. Mass per unit volume.
7. 400 ÷ 50 = 8.0 g/cm³ = 8000 kg/m³.
8. 1100 × 0.025 = 27.5 kg, so 28 kg to two significant figures.
9. The particles are far apart in a gas, so a given volume holds far fewer particles and has far less mass, though the particles themselves are the same.
10. 0.40 ÷ 0.050 = 8.0 kg/m³.

Where marks are usually lost

• Describing the alpha scattering results without saying what each one shows about the atom.
• Giving the plum pudding model a nucleus, or the Rutherford model fixed orbits.
• Writing “the atom is mostly empty space” and not linking it to most alpha particles passing straight through.
• Calling the nucleus the biggest part of the atom rather than the heaviest.
• Mixing grams with m³ or kg with cm³ in a density calculation.
• Reading g/cm³ as 100 kg/m³ instead of 1000 kg/m³.
• Forgetting to subtract the starting volume when finding volume by displacement.
• Explaining low gas density by saying the particles are lighter or smaller, rather than further apart.
• Saying the mass changes when a substance melts or a gas is compressed.

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.