Know that the random motion of microscopic particles in a suspension is evidence for the kinetic particle model of matter

Cambridge IGCSE Physics (0625) – Core Syllabus Notes

Assessment Objectives (AOs)

  • AO‑1: Knowledge and understanding of factual information, definitions and basic concepts.
  • AO‑2: Application of knowledge – translate between words, symbols and diagrams; solve routine problems.
  • AO‑3: Experimental skills – plan, carry out, analyse and evaluate investigations.


1. Motion, Forces & Energy (Unit 1)

1.1 Scalars & Vectors

  • Scalar quantities have magnitude only (e.g. distance, speed, mass).
  • Vector quantities have magnitude and direction (e.g. displacement, velocity, force).
  • Resultant vector: use the tip‑to‑tail method or components.

1.2 Kinematics

QuantitySymbolUnitFormula (uniform motion)
Distancesm
DisplacementΔsm
Speedvm s⁻¹v = s / t
Velocityum s⁻¹u = Δs / t
Accelerationam s⁻²a = Δu / t

Distance‑time and speed‑time graphs

  • Slope of a distance‑time graph = speed (horizontal) or velocity (inclined).
  • Area under a speed‑time graph = distance travelled.
  • Gradient of a speed‑time graph = acceleration.

1.3 Forces & Newton’s Laws

  • Resultant force, F = mass × acceleration (F = ma).
  • Weight, W = mg (g = 9.8 m s⁻²).
  • Frictional force, F_f = μ R (μ = coefficient of friction, R = normal reaction).

1.4 Momentum & Impulse

Momentum, 

= mv. Impulse, J = FΔt = change in momentum.

1.5 Work, Energy & Power

  • Work, W = F s cos θ (Joules).
  • Kinetic energy, E_k = ½ mv².
  • Gravitational potential energy, E_p = mgh.
  • Power, P = W / t = F v (W = J s⁻¹).

1.6 Pressure

Pressure, p = F / A (Pa). In fluids, p = ρ g h where ρ = density, g = 9.8 m s⁻², h = depth.


2. Thermal Physics (Unit 2)

2.1 Kinetic Particle Model (AO‑1)

  • All matter consists of tiny particles (atoms, molecules, ions) in constant motion.
  • State‑dependent motion:

    • Solids: particles vibrate about fixed positions in a regular lattice.
    • Liquids: particles are close together, slide past one another.
    • Gases: particles are far apart, move freely in all directions, colliding with each other and the container walls.

  • Temperature measures the average kinetic energy of the particles.
  • Absolute zero (0 K, –273 °C) is the theoretical point where particle motion ceases.

2.2 Brownian Motion – Direct Visual Evidence

When a dilute suspension of microscopic solid particles (e.g., pollen, chalk, milk fat) is placed in a liquid or gas, the particles jiggle erratically under a microscope. This is Brownian motion.

Why it supports the kinetic model

  1. The suspended particles are too large to be moved by any visible currents.
  2. Invisible molecules of the surrounding fluid, which are in constant random motion, collide with the suspended particles.
  3. Each collision transfers a tiny amount of momentum, causing a random change in direction.
  4. The cumulative effect of countless collisions produces the observed jittery path.

2.3 Quantitative Description (AO‑2)

  • Mean‑square displacement: ⟨x²⟩ = 2 D t
  • Diffusion coefficient: D = k_B T ⁄ (6π η r)

    • k_B = 1.38 × 10⁻²³ J K⁻¹ (Boltzmann constant)
    • T = absolute temperature (K)
    • η = viscosity of the fluid (Pa s)
    • r = radius of the suspended particle (m)

2.4 Heat Transfer & Specific Heat Capacity

ConceptFormulaUnits
Specific heat capacityQ = mcΔθJ kg⁻¹ K⁻¹
Latent heat (fusion/evaporation)Q = mLJ kg⁻¹
Thermal expansion (linear)ΔL = α L₀ Δθm
Thermal expansion (area)ΔA = 2α A₀ Δθ
Thermal expansion (volume)ΔV = 3α V₀ Δθ

2.5 Ideal‑Gas Relationships

  • pV = nRT (combined gas law for a fixed amount of gas).
  • At constant temperature, pV = constant (Boyle’s law).
  • At constant pressure, V / T = constant (Charles’s law).
  • At constant volume, p / T = constant (Gay‑Lussac’s law).

2.6 Temperature Conversions (AO‑2)

 T(K) = θ(°C) + 273   θ(°C) = T(K) – 273

2.7 Practical Investigation – Brownian Motion (AO‑3)

Aim

To observe Brownian motion and investigate how temperature and viscosity affect its intensity, thereby providing experimental evidence for the kinetic particle model.

Materials

  • Low‑power microscope (40×–100×)
  • Glass slides & cover slips
  • Suspension: fine chalk powder or milk in water (≈0.1 % w/v)
  • Thermostated water bath (10 °C–60 °C)
  • Viscous liquids for comparison (e.g., glycerol, syrup)
  • Thermometer, stopwatch, reticle/grid

Method (summary)

  1. Prepare a thin film of the suspension on a slide and cover with a cover slip.
  2. Focus on a single particle; record its (x, y) coordinates every 2 s for 30 s.
  3. Repeat at three temperatures (e.g., 15 °C, 30 °C, 45 °C).
  4. Repeat the whole set using a more viscous fluid (e.g., glycerol) at a fixed temperature.
  5. Calculate successive displacements, plot displacement versus time, and determine the mean‑square displacement.

Variables

  • Controlled: particle size, observation interval, magnification.
  • Independent: temperature, fluid viscosity.
  • Dependent: average displacement (or ⟨x²⟩) of the particle.

Safety

  • Handle hot water baths with gloves.
  • Never look directly at the microscope light source.
  • Dispose of liquids according to school safety rules.

Sample Data Table

TrialFluidTemperature (°C)Time (s)Coordinates (x, y) mmΔs (mm)

Error‑analysis checklist

  • Microscope resolution – can the particle’s centre be located accurately?
  • Slide or stage drift during observation.
  • Temperature stability of the bath.
  • Variation in particle size within the suspension.
  • Human reaction time when noting the time‑stamp.


3. Waves (Unit 3)

3.1 Wave Basics

  • Wave speed: v = f λ (v = speed, f = frequency, λ = wavelength).
  • Transverse waves – particle motion ⟂ to direction of travel (e.g., water surface waves, light).
  • Longitudinal waves – particle motion ‖ direction of travel (e.g., sound).

3.2 Reflection & Refraction

  • Law of reflection: angle of incidence = angle of reflection.
  • Refraction: sin i / sin r = v₁ / v₂ = n₂ / n₁ (Snell’s law). n = refractive index.

3.3 Diffraction & Superposition

  • Diffraction occurs when a wave passes an obstacle comparable to its wavelength – observed as spreading.
  • Superposition: when two waves occupy the same region, resultant displacement = algebraic sum of individual displacements.

3.4 Sound

PropertyTypical value
Speed in air (20 °C)≈ 340 m s⁻¹
Frequency range (human hearing)20 Hz – 20 kHz

  • Pitch ∝ frequency; loudness ∝ amplitude.
  • Echoes occur when the reflecting surface is > 17 m away (time ≈ 0.1 s).

3.5 Electromagnetic (EM) Spectrum (brief)

Radio → Microwave → Infra‑red → Visible → Ultra‑violet → X‑ray → Gamma‑ray. All travel at c = 3 × 10⁸ m s⁻¹ in vacuum.


4. Electricity & Magnetism (Unit 4)

4.1 Electric Charge & Current

  • Charge, q measured in coulombs (C). 1 C = 6.25 × 10¹⁸ electrons.
  • Current, I = Δq ⁄ Δt (A = C s⁻¹).

4.2 Potential Difference & Resistance

  • Potential difference (voltage), V = W ⁄ q (V = J C⁻¹).
  • Resistance, R = V ⁄ I (Ω = V A⁻¹).
  • Ohm’s law: V = IR (valid for ohmic conductors).

4.3 Power & Energy in Circuits

  • P = VI = I²R = V² ⁄ R (W = J s⁻¹).
  • Energy used, E = Pt (kWh = 3.6 MJ).

4.4 Series & Parallel Circuits

Circuit typeCurrentVoltageResistance
SeriesSame through each componentDividesR_total = ΣR
ParallelDividesSame across each branch1/R_total = Σ(1/R)

4.5 Magnetic Fields

  • Field lines emerge from north pole, enter south pole.
  • Force on a current‑carrying conductor: F = B I L sin θ (B = magnetic flux density, T).
  • Right‑hand rule for direction of B and force.

4.6 Electromagnetism

  • Moving charge creates a magnetic field (Oersted’s experiment).
  • Changing magnetic flux induces an emf (Faraday’s law): ε = – ΔΦ ⁄ Δt.
  • Applications: electric motors (convert electrical energy → mechanical), generators (reverse), transformers (step‑up/step‑down voltage).

4.7 Safety & Practical Tips (AO‑3)

  • Never touch live wires; use insulated tools.
  • Fuse rating must be ≥ expected current.
  • When measuring current, insert the ammeter in series; for voltage, connect voltmeter in parallel.


5. Nuclear Physics (Unit 5)

5.1 Atomic Structure & Radioactivity

  • Atom = nucleus (protons + neutrons) + electrons.
  • Isotopes: same Z (protons), different A (mass number).
  • Radioactive decay types:

    • α‑decay: emission of ⁴He nucleus (2 p + 2 n).
    • β‑decay: neutron → proton + electron + antineutrino (or reverse for β⁺).
    • γ‑decay: emission of high‑energy photon (no change in A or Z).

  • Half‑life, t½: time for half the nuclei in a sample to decay. N = N₀ (½)^{t⁄t½}.

5.2 Fission & Fusion

  • Fission: heavy nucleus splits into lighter fragments, releasing neutrons and large energy (e.g., ²³⁵U + n → ⁹⁴Kr + ¹⁴¹Ba + 3 n + ≈ 200 MeV).
  • Fusion: light nuclei combine (e.g., ²H + ³H → ⁴He + n + ≈ 17 MeV). Requires very high temperature to overcome Coulomb barrier.
  • Applications: nuclear power stations (controlled fission), medical isotopes, radiocarbon dating.

5.3 Radiation Protection (AO‑3)

  • Shielding: α – paper; β – aluminium; γ – lead or concrete.
  • Distance reduces dose by inverse‑square law.
  • Time: minimise exposure.


6. Summary – Linking Observation to the Kinetic Particle Model

ObservationInterpretation (kinetic model)
Microscopic particles jiggle in a still fluid.Collisions with rapidly moving invisible molecules transfer momentum → random motion.
Jitteriness increases with temperature.Higher temperature → greater average kinetic energy of molecules → more energetic collisions.
Motion is slower in viscous liquids.Viscosity dampens the effect of molecular impacts, reducing net displacement.
Gas pressure rises when temperature rises (constant volume).Faster molecules strike the container walls more often and with greater momentum.
Sound speed increases with temperature.Particle vibration speed rises, allowing pressure disturbances to travel faster.


7. Exam‑style Practice Questions

  1. Explain why the random motion of pollen grains in water provides evidence for the kinetic particle model.
  2. A student observes that Brownian motion becomes more vigorous when the water temperature is increased. Explain this using the kinetic model.
  3. Describe how the viscosity of a liquid influences the observed Brownian motion and why.
  4. Using the ideal‑gas equation, predict what happens to the pressure of a fixed mass of gas if its temperature is raised from 20 °C to 40 °C while the volume remains constant.
  5. Given D = k_B T ⁄ (6π η r), state how the mean‑square displacement changes if the particle radius is doubled, keeping all other factors constant.
  6. Calculate the work done when a 5 kg object is lifted 3 m vertically. State the energy store involved.
  7. A 12 V battery supplies a current of 2 A for 5 min. Determine the energy used in kWh.
  8. Sketch a distance‑time graph for an object moving with constant acceleration and label the gradient and area.
  9. State the three factors that affect the half‑life of a radioactive sample and give one practical application of each.
  10. Explain why sound cannot travel through a vacuum, referencing the particle model.


8. Quick Classroom Demonstrations

  • Brownian Motion: Place a drop of milk in warm water, view under low‑power microscope, and ask students to describe how the jitteriness changes with temperature.
  • Gas Pressure: Use a sealed syringe with a piston; heat the syringe and observe the piston move outward – discuss kinetic‑particle explanation.
  • Wave Reflection: Shine a laser onto a mirror at an angle and measure the reflected angle to confirm the law of reflection.
  • Magnetic Field: Sprinkle iron filings around a current‑carrying wire connected to a battery; the pattern shows the circular field lines.