Know that the forces and distances between particles (atoms, molecules, ions and electrons) and the motion of the particles affects the properties of solids, liquids and gases

Cambridge IGCSE Physics 0625 – 2.1.2 Particle Model

Objective

To understand how the forces and distances between particles (atoms, molecules, ions and electrons) and the motion of those particles determine the observable properties of solids, liquids and gases.

1. Core ideas of the particle model

• All matter is made up of tiny particles that are in continual random motion – whether they are atoms, molecules, ions or electrons.
• Two types of inter‑particle forces act:

  • Attractive forces – pull particles toward one another.
  • Repulsive forces – prevent particles from occupying the same space.

• The magnitude of both forces depends strongly on the distance between particles; the dependence is steep (approximately exponential) and becomes negligible when particles are far apart.

2. Inter‑particle distances and forces in the three states of matter

3. Motion of particles and temperature

The average kinetic energy of particles in a substance is directly proportional to its absolute temperature:

\(\displaystyle \langle Ek \rangle = \frac{3}{2}\,k{\mathrm B}\,T\)

• Solid: particles vibrate about fixed lattice positions.
• Liquid: particles vibrate and also translate, allowing flow.
• Gas: particles move freely in random directions, colliding with each other and with container walls.

Absolute zero (0 K) is the temperature at which the average kinetic energy would be zero; in reality particles retain only residual quantum motion.

4. Gas pressure – microscopic explanation (force / area)

• Pressure is the result of many tiny impacts of gas particles on the walls of the container.
• Each impact exerts a force; pressure \(p\) is the total force divided by the wall area \(A\):
  

  \(\displaystyle p = \frac{\sum F_{\text{impacts}}}{A}\)

• Increasing the temperature raises particle speed → more frequent and more forceful impacts → pressure rises (if volume is constant).
• Decreasing the volume forces particles into a smaller space → impact frequency increases → pressure rises (if temperature is constant).

For an ideal gas this can be expressed as

\(\displaystyle p = \frac{1}{3}\,\rho\,\overline{v^{2}}\)

where \(\rho\) is the gas density and \(\overline{v^{2}}\) the mean‑square speed of the molecules.

Quick diagram description (for revision)

Imagine a single molecule of mass \(m\) travelling with speed \(v\) perpendicular to a wall of area \(A\). After an elastic bounce it reverses its momentum, giving a change in momentum \(\Delta p = 2mv\). If the molecule strikes the wall every \(\Delta t\) seconds, the average force is \(F = \Delta p / \Delta t\). Summing over the huge number of molecules gives the pressure formula above.

5. How forces and motion determine macroscopic properties

These links are required explicitly by the syllabus:

• Density – Stronger attractive forces pull particles closer together, giving solids a higher mass per unit volume than liquids or gases.
• Compressibility – Weak forces (gases) allow particles to be forced closer together, so gases are highly compressible; strong forces (solids) make them essentially incompressible.
• Viscosity – Resistance to flow depends on the strength of intermolecular attractions; liquids with strong forces (e.g., honey) are more viscous than those with weak forces (e.g., water).
• Thermal conductivity – Energy is transferred by collisions. Closely packed particles (metals, solids) conduct heat efficiently, whereas widely spaced gas particles conduct poorly.
• Surface tension (liquids) – Cohesive attractive forces at the surface create a “skin” that resists external force.

6. Phase changes – microscopic view

• Melting: Heat supplies kinetic energy that overcomes part of the attractive forces. Inter‑particle distances increase slightly, allowing particles to slide past each other while the temperature remains constant.
• Boiling / evaporation: Surface particles acquire enough kinetic energy to break all attractive forces and escape into the gas phase.
• Condensation: Gas particles lose kinetic energy; attractive forces become dominant, pulling particles together into the liquid state.
• Freezing: Further loss of kinetic energy lets attractive forces lock particles into fixed positions, forming a solid.

7. Brownian motion and “light‑fast” molecules

• Brownian motion – The erratic jiggling of tiny solid particles (e.g., pollen) suspended in a liquid is caused by continual bombardment from the rapidly moving molecules of the liquid.
• The colliding particles are molecules (or atoms if the liquid is mono‑atomic). Their high speeds (often called “light‑fast” in the syllabus) transfer momentum to the suspended particle, setting it into motion.
• This phenomenon provides direct, visual evidence that microscopic particles are in continual random motion.

8. Effect of temperature and volume on a gas (syllabus 2.1.3 – brief reminder)

• At constant volume: Raising the temperature increases the average kinetic energy of the molecules → particle speed rises → pressure increases (Gay‑Lussac’s law).
• At constant temperature: Reducing the volume forces more molecules to strike the walls per unit time → pressure increases (Boyle’s law).

9. Summary checklist

• All three states consist of particles in continual random motion.
• Remember the typical inter‑particle distances: solid ≈ 0.1 nm, liquid ≈ 0.2 nm, gas > 1 nm.
• Stronger attractive forces → higher density, lower compressibility, higher surface tension.
• Particle speed ↔ temperature ↔ kinetic energy; absolute zero corresponds to zero average kinetic energy.
• Gas pressure = total force from particle impacts ÷ area; \(p = \frac{1}{3}\rho\overline{v^{2}}\).
• Heating a solid → melting → boiling; cooling a gas → condensation → freezing.
• Brownian motion shows that fast‑moving molecules can set suspended particles into motion.