The Particle Model and Density
Atomic Structure and the Particle Model
Everything around you is made of atoms. An atom has a tiny, positively charged nucleus at its centre, made up of protons and neutrons. Negatively charged electrons orbit the nucleus at different distances. The nuclear radius is much smaller than the overall radius of the atom, and almost all of the atom’s mass is concentrated in the nucleus.
A typical atom has a radius of about \(1 \times 10^{-10}\) m. The nucleus is roughly 10,000 times smaller than the atom itself, meaning atoms are mostly empty space. To put this in perspective, if an atom were the size of a football stadium, the nucleus would be no bigger than a marble sitting at the centre — yet that marble would contain virtually all of the atom’s mass.
Inside the nucleus, protons carry a positive charge and neutrons carry no charge. The number of protons defines which element the atom belongs to (its atomic number). In a neutral atom, the number of electrons equals the number of protons, so the overall charge is zero. If an atom gains or loses electrons it becomes a charged particle called an ion.
The atom has a positively charged nucleus (protons + neutrons) surrounded by negatively charged electrons. The nuclear radius is much smaller than the atomic radius, and almost all the mass is in the nucleus.
How the Atomic Model Changed Over Time
Our understanding of the atom developed through key scientific discoveries. Each new model replaced the last when experimental evidence showed the old model could not explain what scientists observed. This is a powerful example of how the scientific method works — models are updated or replaced as new evidence emerges.
Thomson’s Model (1897): J.J. Thomson discovered the electron and proposed the “plum pudding” model — a sphere of positive charge with electrons embedded throughout, like plums in a pudding. This was the first model to include subatomic particles.
Rutherford, Geiger and Marsden (1909): The alpha particle scattering experiment fired positively charged alpha particles at a thin sheet of gold foil. Most alpha particles passed straight through, showing the atom is mostly empty space. However, a small number were deflected at large angles, and a few bounced straight back. This could only be explained by a tiny, dense, positively charged nucleus at the centre of the atom. The plum pudding model was abandoned.
Bohr’s Model (1913): Niels Bohr refined the nuclear model by suggesting electrons orbit the nucleus at specific, fixed energy levels (shells), rather than randomly. Electrons can only exist in these allowed orbits, and they jump between energy levels by absorbing or emitting specific amounts of energy. This explained the emission spectra of elements — the distinct colours of light produced when elements are heated.
Modern model: Later work showed that electrons do not follow neat circular orbits. Instead, they exist in “clouds” of probability around the nucleus. For GCSE, the Bohr model with its electron shells is the version you need to use and understand.
Particle Arrangements in the Three States of Matter
The particle model explains the properties of solids, liquids and gases based on how their particles are arranged and how they move. Although the particles are far too small to see directly, the model successfully predicts observable properties like shape, volume and compressibility.
In a solid, particles are held in fixed positions by strong forces of attraction. They vibrate about these positions but cannot move from place to place. This is why solids have a fixed shape and a fixed volume. The regular arrangement of particles in many solids forms a lattice structure.
In a liquid, particles are close together but can slide past each other because the forces between them are weaker than in a solid. Liquids have a fixed volume but take the shape of their container. In a gas, particles are far apart with negligible forces between them. They move rapidly in random directions, colliding with each other and the walls of their container. Gases fill any container they are placed in and can be compressed because of the large spaces between particles.
What Is Density?
Density tells you how much mass is packed into a given volume. A dense material has a lot of mass in a small volume. The equation is:
$$\rho = \frac{m}{V}$$
Where \(\rho\) is density (\(\text{kg/m}^3\)), \(m\) is mass (kg), and \(V\) is volume (\(\text{m}^3\)). You may also see density expressed in \(\text{g/cm}^3\). To convert, remember that \(1 \text{ g/cm}^3 = 1000 \text{ kg/m}^3\). You must be able to rearrange this equation to find mass (\(m = \rho \times V\)) or volume (\(V = \frac{m}{\rho}\)).
Density = mass ÷ volume. Solids generally have higher densities than liquids because their particles are more closely packed. Gases have much lower densities because particles are spread far apart.
Question: A metal block has a mass of 540 g and a volume of \(200 \text{ cm}^3\). Calculate its density in \(\text{g/cm}^3\).
Answer: Write the equation: \(\rho = \frac{m}{V}\). Substitute: \(\rho = \frac{540}{200} = 2.7 \text{ g/cm}^3\). This matches the density of aluminium. To express in SI units: \(2.7 \text{ g/cm}^3 = 2700 \text{ kg/m}^3\).
Investigating Density (PAG P1)
To measure the density of a regular solid (such as a cuboid), measure its mass on a balance and calculate its volume using a ruler: \(V = \text{length} \times \text{width} \times \text{height}\). For a cylinder, use \(V = \pi r^2 h\).
For an irregular solid (like a pebble), use a eureka (displacement) can. Fill the can until water is level with the spout. Gently lower the object into the water and collect the displaced water in a measuring cylinder. The volume of displaced water equals the volume of the object. Alternatively, use a measuring cylinder directly: record the initial water level, submerge the object, and read the new level. The difference is the object’s volume.
For a liquid, measure the mass of an empty measuring cylinder on a balance. Pour in the liquid and measure the total mass. The liquid’s mass equals the difference between the two readings. Read the volume from the measuring cylinder scale at the bottom of the meniscus, then apply \(\rho = \frac{m}{V}\).
In solids, particles are closely packed in a regular arrangement, giving high density. In liquids, particles are still close but less ordered, so density is slightly lower. In gases, particles are far apart with large gaps, so density is much lower — typically about 1000 times less than solids.
Crucially, mass is conserved during a change of state. When ice melts to water, the same number of particles is present but they occupy a slightly different volume. When water boils to steam, the mass stays the same but the volume increases enormously, so the density drops dramatically. An unusual exception is water itself: ice is slightly less dense than liquid water, which is why ice floats.
Common sources of error include: reading the measuring cylinder at an angle (parallax error), not drying the object before measuring its mass, and air bubbles clinging to the surface of an irregular solid during displacement. To improve accuracy, take repeat measurements and calculate a mean, use a balance with higher resolution, and ensure the object is fully submerged.