7408/1 · 2 hours · 85 marks · 34% of A-Level · Sections 1 – 5
Section 1 - Measurements and their errors
All physical quantities have a numerical value and a unit. SI (Systeme International) base units underpin all derived units used in physics.
Common prefixes:
| Prefix | Symbol | Multiplier |
|---|---|---|
| Tera | T | 1012 |
| Giga | G | 109 |
| Mega | M | 106 |
| Kilo | k | 103 |
| Centi | c | 10-2 |
| Milli | m | 10-3 |
| Micro | μ | 10-6 |
| Nano | n | 10-9 |
| Pico | p | 10-12 |
| Femto | f | 10-15 |
Unit conversions to know:
Unit checking (dimensional analysis) is a powerful tool: if both sides of an equation have the same base units, the equation is dimensionally consistent. Use it to check unfamiliar formulae.
Combining uncertainties:
Error bars on graphs: each data point may be plotted with a vertical (and/or horizontal) error bar representing the uncertainty in that measurement. The bar extends by ±(absolute uncertainty) above and below the point.
Uncertainties in gradient and intercept of a best-fit straight line:
In practicals, the instrument with the largest percentage uncertainty dominates the overall result. Always calculate the percentage uncertainty for each measurement before deciding where to focus precision improvements.
Being able to estimate the order of magnitude of physical quantities is an important skill. Use known values as anchors and reason from them.
Estimation questions award marks for a valid method and a reasonable order of magnitude, not an exact answer. Show your working and justify any assumed values.
Section 2 - Particles and radiation
| Particle | Relative mass | Relative charge | Mass (SI) | Charge (SI) |
|---|---|---|---|---|
| Proton | 1 | +1 | 1.673 × 10-27 kg | +1.6 × 10-19 C |
| Neutron | 1 | 0 | 1.675 × 10-27 kg | 0 |
| Electron | 1/1836 | −1 | 9.11 × 10-31 kg | −1.6 × 10-19 C |
An atom is described as AZX where A = mass number (protons + neutrons) and Z = atomic number (protons only). Isotopes have the same Z but different A (same element, different number of neutrons).
The electron has a much higher specific charge than the proton because it has the same magnitude of charge but ~1836 times less mass. This is a commonly examined comparison.
The strong nuclear force holds the nucleus together against the electrostatic repulsion between protons. It acts between all nucleons (proton-proton, neutron-neutron, proton-neutron).
Radioactive decay modes:
Always check that both mass number and atomic number are conserved in a nuclear equation. Neutrinos and antineutrinos carry away energy and momentum but have negligible mass and no charge.
Every particle has a corresponding antiparticle with the same mass but opposite charge (and opposite quantum numbers).
| Particle | Antiparticle | Charge | Rest energy (MeV) |
|---|---|---|---|
| Electron (e-) | Positron (e+) | +1 | 0.511 |
| Proton (p) | Antiproton (p̄) | −1 | 938.3 |
| Neutron (n) | Antineutron (n̄) | 0 | 939.6 |
| Neutrino (νe) | Antineutrino (ν̄e) | 0 | ≈0 |
Particle and antiparticle have identical rest mass (and rest energy); they differ in charge and all other quantum numbers (baryon number, lepton number, strangeness).
Pair production and annihilation are direct applications of E = mc². In annihilation, two photons are produced (not one) to conserve momentum.
Four fundamental forces and their exchange particles (2.1.4):
| Force | Exchange particle | Acts on | Range |
|---|---|---|---|
| Strong nuclear | Gluons (pions at nuclear level) | Quarks / hadrons | ~10-15 m |
| Electromagnetic | Virtual photon (γ) | Charged particles | Infinite |
| Weak nuclear | W+, W- bosons | All quarks and leptons | ~10-18 m |
| Gravity | Graviton (theoretical) | All particles with mass | Infinite |
Feynman diagrams represent particle interactions using exchange particles. Key interactions to know:
Particle classification (2.1.5):
Strange particles: particles that are produced through the strong interaction but decay through the weak interaction (e.g. kaons). This accounts for why they are produced rapidly but decay relatively slowly. Strange particles are always created in pairs (strangeness is conserved in production). Strangeness (symbol S) is a quantum number: S = +1 for the K+ kaon (us̄); S = −1 for the K− antikaon (ūs).
Quarks (2.1.6):
| Quark | Symbol | Charge | Baryon number | Strangeness |
|---|---|---|---|---|
| Up | u | +2/3 e | +1/3 | 0 |
| Down | d | −1/3 e | +1/3 | 0 |
| Strange | s | −1/3 e | +1/3 | −1 |
| Anti-up | ū | −2/3 e | −1/3 | 0 |
| Anti-down | d̄ | +1/3 e | −1/3 | 0 |
| Anti-strange | s̄ | +1/3 e | −1/3 | +1 |
Conservation laws in particle interactions:
Le and Lμ are conserved separately: check each independently. A reaction producing e− must also produce ν̄e (not ν̄μ). In β− decay the antineutrino is an electron antineutrino (ν̄e), not a muon antineutrino. This is a frequent exam trap.
When electromagnetic radiation above a threshold frequency strikes a metal surface, electrons are emitted. This cannot be explained by wave theory - it provides evidence for the photon model of light.
Key observations that wave theory cannot explain: (1) instantaneous emission - no time delay; (2) threshold frequency - below it, no emission regardless of intensity; (3) maximum KE depends on frequency, not intensity. Each one-to-one photon-electron interaction explains all three.
Excitation by electron collision (2.2.2): a free electron collides with an atom and transfers energy to a bound electron, raising it to a higher energy level. Unlike photon absorption, the colliding electron does not need to supply exactly the right energy; it simply loses some of its kinetic energy. The atom then de-excites by emitting a photon of energy E = hf = Eupper − Elower.
Energy levels in atoms (2.2.3): electrons occupy discrete energy levels. Ground state is the lowest energy level (most negative). Energy is quantised; electrons can only have specific energies.
Wave-particle duality: particles exhibit wave behaviour and waves exhibit particle behaviour. de Broglie proposed that all moving particles have an associated wavelength.
Wave-particle duality: light behaves as a wave (diffraction, interference) and as a particle (photoelectric effect). Electrons behave as particles (ionisation, deflection in fields) and as waves (electron diffraction). The behaviour observed depends on the experiment.
Section 3 - Waves
Polarisation: a transverse wave is plane polarised when its oscillations are confined to a single plane (perpendicular to the direction of propagation). Unpolarised light oscillates in all planes simultaneously. Only transverse waves can be polarised; this is used as experimental evidence that light is a transverse wave.
Polarisation is evidence that light is a transverse wave. Know that crossed polarisers (90°) give zero transmission – no component of the polarisation lies along the analyser axis. Unpolarised light loses half its intensity through a single polariser.
Intensity of a wave is proportional to amplitude squared: I ∝ A². Doubling the amplitude increases intensity by a factor of 4.
The principle of superposition: when two or more waves overlap, the resultant displacement at any point is the algebraic sum of the individual displacements.
A stationary (standing) wave is formed when two waves of the same frequency and amplitude travel in opposite directions and superpose. Energy is stored, not transmitted.
For a string fixed at both ends: harmonics occur at L = nλ/2 (n = 1, 2, 3...). For an open pipe: same as string. For a closed pipe: only odd harmonics; L = nλ/4 (n = 1, 3, 5...).
Distinguish stationary and progressive waves: in a stationary wave, all points between two nodes oscillate in phase with each other (amplitude varies by position). In a progressive wave, phase varies continuously along the wave.
Interference occurs when two coherent waves overlap. Coherent sources have the same frequency and a constant phase difference.
White light interference: each wavelength produces its own fringe pattern with a different spacing. The central maximum (zero order) is white (all wavelengths overlap). Higher orders show coloured fringes: violet is closest to the centre (shortest λ, smallest spacing), red is furthest. The fringes overlap and become indistinct at high orders.
Laser safety: lasers produce intense, coherent, collimated beams and can cause permanent retinal damage. Never look directly into a laser beam or point it at people. Use laser safety goggles at appropriate wavelengths; ensure the beam is at bench level with no reflective surfaces nearby.
Young's double-slit experiment provides evidence for the wave nature of light. The fringes are equally spaced. Larger λ or larger D gives wider fringes; larger slit separation a gives narrower fringes.
Diffraction is the spreading of a wave as it passes through a gap or around an obstacle. Maximum diffraction occurs when the gap width is approximately equal to the wavelength.
Single slit diffraction: a monochromatic source passing through a narrow slit produces a pattern with a wide, bright central maximum flanked by alternating dark minima and weaker secondary maxima.
The single slit and double slit patterns combine: the double-slit interference fringes are modulated by the single-slit envelope. Fringes near the centre are bright; those near the single-slit minima disappear. This is why some orders are missing in double-slit patterns.
The diffraction grating produces very sharp, bright maxima (unlike the broad fringes from a double slit). Used to measure wavelengths of light precisely.
In the diffraction grating equation, check that nλ/d ≤ 1 before calculating θ. If nλ > d, that order does not exist. The zero-order maximum (n=0) is always straight ahead at θ = 0.
Refraction is the change in direction of a wave when it passes from one medium to another due to a change in wave speed.
Optical fibres (step-index) consist of a high-refractive-index core surrounded by a lower-refractive-index cladding. Light travels in the core and undergoes total internal reflection at the core-cladding boundary. The cladding: (1) enables TIR by providing a lower-index boundary; (2) protects the core; (3) prevents light leaking between adjacent fibres (crosstalk). Used in communications (digital signals) and medical imaging (endoscopes).
Modal dispersion in step-index fibres: rays entering at different angles travel different path lengths, causing pulse broadening. Reduced by using monomode fibres (very narrow core). Material dispersion occurs because different wavelengths travel at different speeds; reduced by using monochromatic light.
When light goes from dense to less dense (e.g. glass to air), it bends away from the normal. When it goes from less dense to denser, it bends towards the normal. Light speeds up in less dense media.
Section 4 - Mechanics and materials
Adding vectors: two vectors at right angles are added by calculation (Pythagoras for magnitude, trigonometry for direction). Vectors at any angle can be added by accurate scale drawing. For three coplanar forces in equilibrium, a closed triangle can be drawn the vectors form a closed loop placed head-to-tail.
Resolving vectors: Fx = F cos θ, Fy = F sin θ. Resolve each vector into horizontal and vertical components, sum each direction, then use Pythagoras for the resultant magnitude and trigonometry for its direction. Problems may also be solved using the closed triangle method.
An object is in equilibrium when the resultant force on it is zero and the resultant moment about any point is zero. This applies whether the object is at rest or moving at constant velocity.
A couple is a pair of equal and opposite coplanar forces that produce a pure turning effect (no resultant force).
Centre of mass: the single point through which the weight of an object appears to act. For a uniform regular solid, the centre of mass is at its geometric centre.
For an object in equilibrium: (1) resultant force = 0 (no acceleration), AND (2) resultant moment about any point = 0 (no angular acceleration). Both conditions must be met simultaneously.
Definitions:
Graphical methods for uniform and non-uniform acceleration:
The SUVAT equations apply to constant (uniform) acceleration in a straight line:
Acceleration due to gravity g ≈ 9.81 m s-2 downwards near Earth's surface.
Projectile motion: horizontal and vertical components are independent. No air resistance assumed.
Friction, drag and terminal speed:
To solve projectile problems: resolve the initial velocity into horizontal and vertical components, then treat each direction independently using the appropriate equations.
Understanding impulse and momentum underpins ethical transport design: crumple zones, airbags, and seatbelts all increase collision time, reducing the peak force on occupants. Impact forces are related to contact times (e.g. kicking a football, crumple zones, packaging). Quantitative questions may involve forces that vary with time.
Impulse = area under a force-time graph. A large force for a short time produces the same impulse (and change in momentum) as a small force for a long time. This is the principle behind crumple zones and airbags.
Conservation of energy: energy cannot be created or destroyed, only converted from one form to another. When resistive forces act, kinetic or potential energy is transferred to thermal energy; the total (Ek + Ep + energy dissipated against resistive forces) remains constant. Without resistive forces: Ek + Ep = constant.
Work is only done when the force has a component in the direction of motion. A centripetal force does no work because it is always perpendicular to the velocity.
Force-extension behaviour and material types:
Stress-strain graphs: gradient of the linear (Hooke's law) region = Young modulus; area under graph = elastic strain energy per unit volume. Ductile materials show a yield point then a long plastic region; brittle materials fracture near the elastic limit with no plastic region.
Required Practical 4: determination of the Young modulus by a simple method (e.g. measuring extension of a long wire under known loads using a vernier scale).
Appreciation of energy conservation in ethical transport design: materials that deform plastically absorb more energy (larger area under F-extension graph), informing the design of crumple zones and protective packaging.
The Young modulus is a property of the material (independent of dimensions). The spring constant k depends on both material and dimensions. Use a stress-strain graph to find E; use a force-extension graph to find k.
Section 5 - Electricity
I-V characteristics show how current varies with potential difference:
Ohm's law is a special case: for an ohmic conductor, I ∝ V under constant physical conditions. This gives a straight-line I–V graph through the origin with constant gradient (constant resistance).
NTC thermistor: resistance decreases as temperature increases (opposite to a metal). LDR (light-dependent resistor): resistance decreases as light intensity increases. Both are non-ohmic.
Ideal meters: unless otherwise stated, ammeters have zero resistance (no voltage drop across them) and voltmeters have infinite resistance (no current through them). Questions can be set with either I or V on the horizontal axis of a characteristic graph.
Current is the same at all points in a series circuit. The sum of potential differences across components in a series circuit equals the supply voltage. These are direct consequences of charge conservation and energy conservation.
Resistivity is a property of the material (not the sample). It depends on temperature: metals increase in resistivity with temperature; semiconductors (including NTC thermistors) decrease in resistivity with temperature. Only negative temperature coefficient (NTC) thermistors are assessed. Thermistor applications include temperature sensors; behaviour is shown on resistance–temperature graphs.
Superconductivity: some materials have zero resistivity at and below a critical temperature Tc (which depends on the material). The resistance drops suddenly to exactly zero. Applications include: production of strong magnetic fields (e.g. MRI scanners, particle accelerators) and reduction of energy loss in transmission of electric power. Note: critical field is not assessed.
Required Practical 5: determination of the resistivity of a wire using a micrometer, ammeter, and voltmeter.
Resistivity and resistance are different: resistance (R) depends on the material AND dimensions; resistivity (ρ) depends only on the material and temperature. To find the resistivity of a wire, measure R, L, and diameter (to find A = πr²).
Conservation of charge (Kirchhoff's First Law) and conservation of energy (Kirchhoff's Second Law) apply throughout all dc circuits. Currents, voltages, and resistances in series and parallel combinations follow directly from these principles.
Adding a resistor in series always increases total resistance. Adding a resistor in parallel always decreases total resistance. Use this as a quick sanity check on your answers.
A potential divider is used to supply a constant or variable potential difference from a power supply. The output voltage is taken across one of the resistors in a series chain.
Components used in the potential divider include variable resistors (to supply a variable output voltage), thermistors (output varies with temperature), and LDRs (output varies with light intensity). Note: the use of the potentiometer as a measuring instrument is not required.
If R2 increases (e.g. thermistor cools down → resistance rises), Vout increases. If R2 decreases, Vout decreases. This logic is essential for analysing sensor circuits.
Electromotive force (EMF, ϵ) is the total energy supplied per unit charge by the source: ϵ = E/Q. It differs from terminal pd because some energy is dissipated within the source due to internal resistance r.
Required Practical 6: investigation of the emf and internal resistance of electric cells and batteries by measuring the variation of the terminal pd of the cell with current in it.
As more current is drawn from a battery, the terminal pd falls because the "lost volts" (Ir) increase. A battery with a high internal resistance cannot deliver large currents without a significant voltage drop. This explains why old batteries struggle to start cars.