IB Physics

Teach to this depth — Go well past SI unit recall. Distinguish random from systematic error. Define precision and accuracy independently. Derive combined uncertainty for addition, subtraction, multiplication, division, and powers using absolute and fractional forms. Propagate uncertainty through multi-step calculations. Express results as (value ± uncertainty) with correct significant figures and units. Read a vernier calliper and micrometer screw gauge.

Connects to — Every experiment and IA; uncertainty propagation recurs whenever a quantity is derived from measurements; significant figures discipline runs through all Paper 1 numerical answers.

IA & investigative angle — The foundation of all IA lab work. A student who cannot propagate uncertainty correctly cannot write a valid conclusion. Tier 1 practice should demand full uncertainty calculation chains, not just formula recall.

Teach to this depth — Define vector and scalar with examples drawn from every later topic. Add and subtract vectors graphically (tip-to-tail) and analytically (resolving into components). Find the resultant magnitude and direction. Resolve any vector into perpendicular components in a chosen coordinate system. Multiply a vector by a scalar.

Connects to — Forces in Phase B depend entirely on vector resolution; projectile motion requires independent component treatment; momentum and impulse are vector quantities; electric and gravitational fields are vectors; EM induction uses the component of a field.

IA & investigative angle — Vector resolution is the single most-applied mathematical skill in IB Physics. Tier 2 practice must require students to draw the diagram first — the error almost always lives in the diagram, not the algebra.

Teach to this depth — Plot data with correct scales, labelled axes with units, and error bars. Draw best-fit lines through error bars (not through points). Determine gradient and intercept with units and uncertainty from a worst-fit line. Linearise non-linear relationships by choosing the right variable transformation (e.g. plot T² vs L for a pendulum). Understand what the gradient and intercept represent physically. Identify outliers. Read and interpret displacement–time, velocity–time, and force–extension graphs as physical stories.

Connects to — Every experimental topic; the IA demands a linearised graph with a physically meaningful gradient; Paper 3 data-analysis questions are this topic assessed under timed conditions.

IA & investigative angle — Linearisation is the key discriminator between a shallow IA and a deep one. Teach students to ask: what variable transformation makes this relationship linear, and what will the gradient mean? Tier 2 practice should include graph interpretation, gradient extraction with uncertainty, and linearisation design.

Teach to this depth — Recognise and use SI prefixes from femto to giga. Estimate quantities to the nearest order of magnitude using physical reasoning. Know the approximate values of key physical constants: mass of a proton, size of an atom, speed of light, charge of an electron, Planck’s constant. Use powers-of-ten notation confidently in multi-step calculations.

Connects to — Nuclear physics (femtometre scales); astrophysics (parsec to kilometre conversions); every calculation where a student must judge whether an answer is physically plausible.

IA & investigative angle — Estimation questions appear in Paper 1 as order-of-magnitude MCQs. Answers marked wrong purely due to a unit error or a factor-of-1000 slip — often rooted in weak prefix fluency — are avoidable here.

Teach to this depth — Define displacement, velocity (average and instantaneous), and acceleration precisely. Derive the four kinematic equations from first principles using v–t graphs. Interpret displacement–time and velocity–time graphs fluently: gradient = velocity, area = displacement, curvature = changing acceleration. Apply the kinematic equations to free-fall and vertical-motion problems. Distinguish distance from displacement, speed from velocity.

Connects to — Projectile motion splits kinematics into two independent components; Newton’s laws explain why objects accelerate; energy and momentum use velocity as input; SHM position and velocity equations mirror the kinematics form; spacetime diagrams in Special Relativity are a graphical kinematics tool.

IA & investigative angle — A classic IA: measuring g by free fall, or verifying a kinematic relationship using video analysis. Tier 2 practice must include graph-reading and derivation — not only numerical substitution into SUVAT.

Teach to this depth — Resolve initial velocity into horizontal and vertical components. Treat horizontal motion as uniform (constant velocity) and vertical motion as free fall (constant downward acceleration g) simultaneously and independently. Solve for time of flight, range, maximum height, and final velocity — including launching from a height, launching at an angle above or below horizontal, and symmetrical trajectories. Derive the parabolic form of the trajectory algebraically.

Connects to — Circular motion requires a velocity direction that changes while magnitude stays constant — the same vector decomposition thinking; charged-particle trajectories in uniform electric fields (Phase D) are structurally identical to projectile motion.

IA & investigative angle — Projectile investigation (varying launch angle or height) is a well-structured IA context. Tier 2 practice should include non-symmetric launches and derivation of the range equation.

Teach to this depth — State all three laws precisely and distinguish clearly between them. Draw complete, correctly labelled free-body diagrams with one arrow per force, labelled with type and agent. Apply Newton’s second law in component form to multi-body systems. Identify Newton’s third-law pairs (same type, opposite direction, different bodies). Apply to connected bodies: Atwood machines, pulleys, and systems on inclines.

Connects to — Every mechanics topic depends on correct force identification; circular motion adds centripetal acceleration to the FBD; gravitation extends Newton’s second law to orbital contexts; electric and magnetic forces are treated identically to mechanical forces in later phases.

IA & investigative angle — Extended-response exam questions often ask students to justify the shape of a v–t graph in terms of the net force. Tier 2 practice must include multi-body systems and situations where the net force is zero.

Teach to this depth — Resolve forces on inclined planes by choosing axes parallel and perpendicular to the slope. Distinguish static and kinetic friction; apply the friction model (F ≤ μN for static; F_k = μ_k N for kinetic). Analyse tension in ropes and strings in elevator, pulley, and Atwood contexts. Analyse equilibrium situations using ΣF = 0 in all directions, including non-collinear force systems.

Connects to — Circular motion requires identifying the net centripetal force in complex situations; fluid resistance extends the friction concept; EM induction opposes motion — a force argument underlies Lenz’s law.

IA & investigative angle — A friction investigation (varying normal force or surface type) is a classic, well-controlled IA. Tier 2 practice should emphasise the FBD stage, since errors in the diagram propagate through the entire solution.

Teach to this depth — Define work as W = Fd cos θ with correct sign convention. Derive and apply the work–energy theorem. Define kinetic energy, gravitational PE, elastic PE (½kx²), and internal energy. Apply conservation of energy to systems with multiple energy types. Define power as rate of work done; use P = Fv for constant-force situations. Analyse energy dissipation through friction — energy is conserved but mechanical energy is not.

Connects to — Momentum provides a complementary tool — impulse for short-time collisions, energy for before-after comparisons; SHM involves continuous KE–PE exchange; thermodynamics generalises energy transfer to heat and internal energy; orbital motion combines KE and gravitational PE.

IA & investigative angle — Energy conservation investigations (ball rolling down a ramp, bungee-cord stretch) are strong IA contexts. Tier 2 practice should require students to justify which method — energy or Newton — is more efficient, and why.

Teach to this depth — Define momentum p = mv as a vector. Define impulse J = FΔt = Δp. State and apply conservation of linear momentum to 1D and 2D collisions. Distinguish elastic (KE conserved) from inelastic (KE not conserved) collisions. Interpret the area under a force–time graph as impulse. Apply Newton’s second law in the correct general form: F = Δp/Δt.

Connects to — Kinetic theory derives gas pressure from momentum transfer to walls; nuclear reactions (Phase F) apply momentum conservation alongside energy conservation; rocket propulsion is an application of Newton’s third law and momentum.

IA & investigative angle — Collision investigations (air track or dynamics trolleys) allow precise momentum measurement. Tier 2 practice must include 2D collisions and the elastic/inelastic distinction.

Teach to this depth — Define angular velocity ω and relate to linear speed v = rω and period T. Define centripetal acceleration a = v²/r = ω²r directed toward the centre. Identify the centripetal force as the net inward force provided by existing forces (tension, gravity, friction, normal force) — not a new force. Analyse vertical circles, banking, and conical pendulums. Explain why centrifugal force is not real in an inertial frame.

Connects to — Gravitation: orbital motion is circular motion with gravity as the centripetal force; SHM: the circular-motion phasor model generates SHM position equations; charged particles in magnetic fields move in circles.

IA & investigative angle — Conical pendulum or banking-angle investigation. Tier 2 practice must include vertical circles (where normal force varies with position) and banking — both are frequent HL exam targets.

Teach to this depth — State and apply Newton’s law of universal gravitation. Define gravitational field strength g = F/m = GM/r². Define gravitational potential V = −GM/r and gravitational potential energy E_p = mV. Derive Kepler’s third law T² ∝ r³ from Newton’s law and circular motion. Analyse orbital speed, total energy, and escape velocity. Understand how atmospheric drag affects an orbit — energy loss paradoxically causes orbital speed to increase.

Connects to — Electric fields (Phase D) are structurally identical — Coulomb’s law parallels Newton’s law and the potential formulas are analogous; gravitational potential is the template for electric potential; stellar physics uses gravitational collapse and orbital mechanics.

IA & investigative angle — Gravitational field investigation using a pendulum (measuring g, comparing to accepted value). Tier 2 practice must include potential-energy derivations, escape velocity, and the Kepler’s third law calculation.

Teach to this depth — Define SHM by the condition a = −ω²x. Derive and use x = A sin(ωt + φ), v = Aω cos(ωt + φ), a = −Aω² sin(ωt + φ). Derive the period of a mass–spring system T = 2π√(m/k) and a simple pendulum T = 2π√(L/g). Track continuous KE–PE exchange and show total energy E = ½mω²A² is constant. Analyse damping: light, heavy, and critical. Introduce forced oscillations and resonance — amplitude peaks when driving frequency equals natural frequency.

Connects to — Waves: SHM is the transverse motion of every particle in a transverse wave; resonance generalises to standing waves and RLC circuits; damping appears in EM induction contexts.

IA & investigative angle — Pendulum or mass–spring investigation — varying length, mass, or amplitude. Measure ω experimentally and compare to the theoretical prediction. Tier 2 practice must include the energy equation derivation and graph interpretation.

Teach to this depth — Define and distinguish transverse and longitudinal waves. Define amplitude, wavelength, period, frequency, wave speed, and phase. Apply v = fλ. Define wavefronts and rays. Understand the physical differences between mechanical and electromagnetic waves — what oscillates, what medium is needed, propagation speed. Know the electromagnetic spectrum with approximate wavelengths and frequencies for each region.

Connects to — All of Phase C builds on this foundation; the Doppler effect manipulates f and λ; sound waves are longitudinal mechanical waves; all optics is wave behaviour at boundaries; the wave nature of light leads directly to quantum physics in Phase F.

IA & investigative angle — Phase mock should include wave-diagram interpretation. Tier 1 practice: given a wave diagram, identify all six wave properties with correct units.

Teach to this depth — State the principle of superposition. Distinguish constructive and destructive interference and relate to path difference (nλ vs (n+½)λ). Apply Young’s double-slit formula d sin θ = nλ and the small-angle approximation. Analyse single-slit diffraction: central maximum width, condition for first minimum a sin θ = λ. Understand why diffraction is maximised when slit width ≈ wavelength. Interpret double-slit intensity patterns modulated by the single-slit envelope.

Connects to — Standing waves are interference between two identical waves travelling in opposite directions; X-ray diffraction determines crystal structure; Compton scattering requires the photon to have wave properties; electron diffraction (Phase F) confirms de Broglie’s hypothesis.

IA & investigative angle — Laser diffraction investigation — measuring slit width or wavelength from fringe patterns. Tier 2 practice must include path-difference derivations from geometry, not formula substitution alone.

Teach to this depth — Derive standing waves as the superposition of two identical waves travelling in opposite directions. Define nodes and antinodes and their spacing (λ/4 between adjacent node and antinode). Establish boundary conditions: fixed ends = nodes, open ends = antinodes. Derive the harmonic series for strings and open/closed pipes. Connect resonance frequency to the standing wave condition. Apply to musical instruments as a real physical context.

Connects to — SHM gave the resonance concept; standing waves give it geometric form; nuclear models use standing-wave concepts; cavity resonance in lasers is an advanced application.

IA & investigative angle — Melde’s experiment (standing waves on a string) or Kundt’s tube. Measuring wave speed in a string as a function of tension — a clean, controllable IA.

Teach to this depth — Explain qualitatively why observed frequency changes when source or observer moves. Apply the Doppler equations for sound (source moving, observer moving, and both). Apply the formula for light: use the non-relativistic form and introduce the relativistic correction for fast-moving sources. Connect galactic redshift to Hubble’s law as a preview of astrophysics. Distinguish redshift from blueshift.

Connects to — Stellar physics uses Doppler shift of absorption lines to measure radial velocities; Hubble’s law derives from the cosmological Doppler shift; special relativity modifies the formula for high speeds.

IA & investigative angle — Tier 2 practice: identify which form of the Doppler formula applies in a given scenario, calculate the observed frequency, and comment on the direction of the shift.

Teach to this depth — Apply the law of reflection. Define refractive index n = c/v and apply Snell’s law n₁ sin θ₁ = n₂ sin θ₂. Derive the critical angle condition and explain total internal reflection. Apply TIR to optical fibre and prism contexts. Understand dispersion — different wavelengths refract at different angles, causing white light to separate in a prism.

Connects to — Diffraction gratings use refraction and geometry; thin-film interference involves refracted and reflected rays; lenses require Snell’s law at every surface.

IA & investigative angle — Tier 2 practice: multi-boundary Snell’s law calculation, critical angle determination, and TIR explanation in context.

Teach to this depth — Derive and apply the grating equation d sin θ = nλ for maxima. Understand how the grating resolves wavelengths more sharply than a double slit — more slits produce narrower maxima. Analyse thin-film interference: path difference from film thickness, phase change on reflection at a denser medium (180° shift), and conditions for constructive and destructive interference.

Connects to — Stellar spectroscopy uses diffraction gratings to resolve emission and absorption lines; the phase-change rule on reflection echoes an important boundary condition in wave physics.

IA & investigative angle — Tier 2 practice: determine the wavelength of light from a grating measurement; predict whether a thin film produces constructive or destructive interference for a given thickness.

Teach to this depth — Apply the thin-lens equation 1/f = 1/u + 1/v and the magnification formula M = −v/u. Construct ray diagrams for converging and diverging lenses and concave and convex mirrors. Analyse the compound microscope and refracting telescope: angular magnification, normal adjustment, and instrument length. Understand chromatic and spherical aberration qualitatively. Distinguish real from virtual images physically and in ray diagrams.

Connects to — Thin lenses use Snell’s law at both surfaces; the telescope angular magnification is a ratio of focal lengths derived from geometry; aberrations connect to the wave nature of light.

IA & investigative angle — Measuring the focal length of a lens experimentally. Comparing theoretical magnification of a constructed telescope or microscope to measured values — an excellent IA with clear uncertainty analysis.

Teach to this depth — State and apply Coulomb’s law F = kq₁q₂/r². Define electric field strength E = F/q. Draw electric field lines for point charges, parallel plates, and combined charge configurations. Understand that field inside a conductor is zero in electrostatic equilibrium. Distinguish the field patterns for conductors and insulators.

Connects to — Electric potential follows from the field; capacitance stores charge in an electric field; the parallel structure with gravitation (Coulomb vs Newton) is a unifying theme of the entire course.

IA & investigative angle — Tier 2 practice: calculate the net field at a point due to two charges; draw the field lines for a dipole; identify where the field is zero.

Teach to this depth — Define electric potential V = kQ/r and electric potential energy E_p = qV. Understand that V is a scalar but E is a vector — a conceptual subtlety that resolves many calculation errors. Draw and interpret equipotential surfaces. Apply the work done in moving a charge: W = qΔV. Relate field to potential: E = −ΔV/Δd. Apply to parallel plates: E = V/d.

Connects to — Capacitance: energy stored in a capacitor is ½CV²; charged particle acceleration through a potential difference uses E_k = qV; the analogy with gravitational potential is strong and should be made explicit.

IA & investigative angle — Tier 2 practice: calculate the work done in moving a charge between two equipotentials; find the speed of a proton accelerated through a given potential difference.

Teach to this depth — Define current I = ΔQ/Δt and relate to drift velocity: I = nqvA. Define resistance R = V/I and resistivity ρ = RA/L. Apply Ohm’s law and recognise ohmic and non-ohmic behaviour from I–V graphs. Calculate power dissipated: P = IV = I²R = V²/R. Understand the physical origin of resistance in terms of electron collisions with the lattice.

Connects to — DC circuits build directly on these definitions; resistivity connects to semiconductor physics; the drift-velocity model is extended in the Hall effect context.

IA & investigative angle — Tier 2 practice: determine whether a given I–V graph represents ohmic or non-ohmic behaviour; calculate the resistivity of a material from measured dimensions and resistance.

Teach to this depth — Apply Kirchhoff’s current and voltage laws to multi-loop circuits. Derive and apply series and parallel resistance formulas. Model a battery with internal resistance r: terminal voltage V = ε − Ir. Analyse the variation of terminal voltage with current (gradient = −r, y-intercept = ε). Use potential dividers. Analyse circuits with combinations of series and parallel elements. Understand why voltmeters need very high resistance and ammeters very low resistance.

Connects to — Capacitance (Phase D) extends the circuit to include reactive elements; the potential divider is the basis of sensor circuits; the normal equations behind regression (Phase E analogy in mathematics) use the same linear system structure.

IA & investigative angle — Determining the internal resistance and EMF of a battery from a V–I characteristic graph — a classic, well-structured IA with excellent scope for uncertainty analysis. Tier 2 practice must include multi-loop circuits and internal resistance problems.

Teach to this depth — Describe the magnetic field patterns around a long straight wire, inside a solenoid, and around a bar magnet. Apply F = BIL sin θ to a current-carrying conductor using the left-hand rule. Apply F = qvB sin θ to moving charges. Understand that magnetic force is always perpendicular to velocity — it does no work and cannot change the kinetic energy of a particle.

Connects to — Charged particles in fields (next topic) combine electric and magnetic forces; electromagnetic induction uses F = qv × B as its microscopic basis; the Hall effect balances electric and magnetic forces.

IA & investigative angle — Tier 2 practice: determine the direction of the force on a current in a given field; identify the direction of force on a moving charge in a 3D configuration.

Teach to this depth — Analyse the circular motion of a charged particle in a uniform magnetic field: r = mv/qB. Analyse the velocity selector: when qE = qvB, only particles with v = E/B pass through undeflected. Describe the mass spectrometer and cyclotron as applications. Analyse the Hall effect — the steady state when electric and magnetic forces balance.

Connects to — Nuclear physics (Phase F): charged particles in particle detectors (bubble chambers, cloud chambers) are analysed using r = mv/qB; the cyclotron is a direct precursor to particle accelerators.

IA & investigative angle — Analysing the path of a charged particle from a bubble chamber photograph — a classic IB data-analysis question type. Tier 2 practice should include combined E and B field problems.

Teach to this depth — Define magnetic flux Φ = BA cos θ. State and apply Faraday’s law: ε = −ΔΦ/Δt (the magnitude equals the rate of change of flux). Apply Lenz’s law to determine the direction of the induced current using a physical argument (the induced current opposes the change that caused it). Analyse the AC generator: derive ε = ε₀ sin(ωt). Define RMS values: V_rms = V₀/√2. Understand the ideal transformer — turns ratio and the reason for high-voltage power transmission.

Connects to — Faraday’s law is a consequence of the force on charges (F = qv × B) in a moving conductor; the transformer is the practical application of mutual induction; AC analysis connects to wave-form mathematics from Phase C.

IA & investigative angle — Induced EMF as a function of rotation rate or field strength — a direct experimental test of Faraday’s law. Tier 2 practice must include situations where flux changes due to a changing B, a changing area, or a changing angle.

Teach to this depth — Define capacitance C = Q/V. Derive the energy stored: E = ½CV² = ½QV = Q²/2C. Analyse charging and discharging through a resistor: Q = Q₀e^−t/RC, where RC is the time constant. Apply to series and parallel capacitor combinations. Understand the effect of a dielectric — relative permittivity increases capacitance. Use the parallel-plate formula C = ε₀ε_rA/d.

Connects to — Capacitor charging and discharging mirrors radioactive decay mathematically (both are exponential) — the cross-phase connection should be made explicit; energy storage in a capacitor is analogous to elastic PE.

IA & investigative angle — Capacitor charging and discharging investigation — determining the time constant and comparing to the theoretical value RC. A clean, well-controlled IA with excellent scope for uncertainty analysis.

Teach to this depth — Distinguish temperature, heat, and internal energy precisely — three quantities that are frequently confused. Define specific heat capacity and apply Q = mcΔT. Define specific latent heat and apply Q = mL. Understand energy transfer mechanisms at the mechanism level: conduction (phonon/electron transfer), convection (bulk fluid motion), and radiation (photon emission). Apply Newton’s law of cooling qualitatively.

Connects to — Internal energy is defined here and used in the first law (Phase E); radiation at the mechanism level previews Stefan–Boltzmann and Wien’s law; specific heat appears in thermodynamic cycle analysis.

IA & investigative angle — Measuring specific heat capacity of a material — a well-defined IA with a clear method, uncertainty analysis, and comparison to an accepted value. A cooling-curve investigation is equally productive.

Teach to this depth — State and apply Boyle’s, Charles’s, and Gay-Lussac’s gas laws, then unify as the ideal gas law pV = nRT. Derive the kinetic theory expression p = ⅓ρ⟨c²⟩ from Newton’s laws and statistical reasoning. Define the root-mean-square speed. Derive that average translational KE = (3/2)kT. Understand the assumptions of the ideal gas model and discuss conditions under which real gases deviate.

Connects to — Thermodynamic processes involve the ideal gas law at every step; the Boltzmann constant k links microscopic energy to macroscopic temperature; the Maxwell–Boltzmann speed distribution (qualitative) appears in nuclear reaction context in Phase F.

IA & investigative angle — Tier 2 practice: derive the rms speed of gas molecules at a given temperature; explain using kinetic theory why pressure increases when a gas is heated at constant volume.

Teach to this depth — State the first law ΔU = Q − W with the sign convention explicitly defined. Define and analyse isothermal, adiabatic, isobaric, and isochoric processes on p–V diagrams. Calculate work done as the area under a p–V graph. Apply the first law to each process type. Understand that for an ideal gas ΔU depends only on temperature. Distinguish heat added to the system from work done by the system.

Connects to — The second law and heat engine efficiency (next topic) require all four process types to be understood; the area under a p–V cycle gives the net work output per cycle.

IA & investigative angle — Tier 2 practice: given a p–V diagram of a cycle, calculate the net work done, the heat absorbed, and the heat rejected. Apply the first law to each process type in the cycle.

Teach to this depth — Define a heat engine and its efficiency η = W/Q_H. Derive the Carnot efficiency η_max = 1 − T_C/T_H and understand why it is an upper bound — no engine can exceed it. Introduce entropy as a state function: ΔS = Q/T for a reversible process. State the second law: the total entropy of an isolated system never decreases. Apply to irreversible processes qualitatively and discuss the thermodynamic arrow of time.

Connects to — The Carnot cycle uses all four thermodynamic processes; entropy connects to statistical mechanics (qualitative); the second law is invoked in nuclear and stellar physics when discussing energy degradation.

IA & investigative angle — Tier 2 practice: calculate the Carnot efficiency for given source and sink temperatures; explain why the efficiency of a real heat engine is always less than the Carnot value.

Teach to this depth — Apply the Stefan–Boltzmann law L = σAT⁴. Apply Wien’s displacement law λ_max T = 2.9 × 10⁻³ m K. Define albedo and emissivity. Derive the effective temperature of Earth from solar flux and albedo. Understand the greenhouse effect at the mechanism level — absorption and re-emission of IR by greenhouse gas molecules. Discuss climate feedback mechanisms qualitatively.

Connects to — The identical radiation laws (Stefan–Boltzmann and Wien) are used in Phase F stellar physics to determine stellar temperatures, luminosities, and radii — the same equations applied at astronomical scale.

IA & investigative angle — Tier 2 practice: calculate the effective temperature of a planet given its albedo and distance from the Sun; estimate the surface temperature change from a given change in albedo.

Teach to this depth — Describe Rutherford’s scattering experiment and what it reveals about the nuclear atom. Distinguish emission and absorption spectra physically. Understand that discrete spectra require quantised energy levels — this is the experimental result that demands quantum theory. Describe the Bohr model of hydrogen: electrons in fixed orbits, only certain radii are allowed. Calculate photon energy from frequency E = hf and wavelength E = hc/λ.

Connects to — The photoelectric effect (next topic) is explained using the photon model established here; Bohr model energy levels feed nuclear energy calculations; stellar spectroscopy (Phase F astrophysics) uses these same spectral lines to determine stellar composition and temperature.

IA & investigative angle — Tier 2 practice: identify the transition responsible for a given spectral line; calculate the wavelength of a photon emitted in a specified Bohr-model transition.

Teach to this depth — Describe the photoelectric effect and list its experimental observations: threshold frequency exists; maximum KE of emitted electrons depends on frequency not intensity; emission is instantaneous. Explain why the classical wave model fails to account for each observation. Apply Einstein’s photoelectric equation E_k(max) = hf − φ. Define the work function φ. Analyse a stopping-voltage experiment to determine Planck’s constant experimentally.

Connects to — The photon model established here is extended in Compton scattering; the de Broglie wavelength applies the wave–particle duality in the opposite direction (particles as waves); the stopping-voltage method connects to electric potential from Phase D.

IA & investigative angle — Stopping-voltage experiment — plotting V_stop vs f and extracting h from the gradient. A classic, historically significant experiment with excellent IA potential. Tier 2 practice must include explaining why each observation is inconsistent with the wave model.

Teach to this depth — State the de Broglie hypothesis λ = h/p. Apply to electrons and other particles. Describe the electron diffraction experiment and what it demonstrates — particles exhibit wave behaviour when the wavelength is comparable to the slit/crystal spacing. Understand that which behaviour is observed depends on how the experiment is designed. Introduce the probability interpretation of the wave.

Connects to — Electron diffraction directly confirms the de Broglie hypothesis; Compton scattering (next topic) treats photons as particles with momentum; the probability wave is the conceptual foundation for quantum uncertainty.

IA & investigative angle — Tier 2 practice: calculate the de Broglie wavelength of an electron accelerated through a given voltage; explain why we do not observe wave behaviour for macroscopic objects such as a football.

Teach to this depth — Apply the Bohr model to hydrogen: quantised angular momentum, allowed orbital radii, and the energy level formula E_n = −13.6/n² eV. Calculate the wavelength of photons emitted in transitions between levels. Use energy-level diagrams to identify emission series (Lyman, Balmer, Paschen). Understand the limitations of the Bohr model — it works for hydrogen but fails for multi-electron atoms, requiring a full quantum-mechanical treatment.

Connects to — The Bohr model is the bridge between classical and quantum mechanics; nuclear energy levels (Phase F) use the same quantised-energy concept; laser action depends on population inversion between energy levels.

IA & investigative angle — Tier 2 practice: calculate the wavelength of the first line of the Balmer series; explain why the Bohr model cannot be applied to the helium atom.

Teach to this depth — Describe alpha, beta-minus, beta-plus, and gamma decay — nature, penetration, and ionising power. Write and balance nuclear decay equations using conservation of nucleon number and proton number. Define activity A, decay constant λ, and half-life t_½ = ln 2/λ. Derive and apply the radioactive decay law N = N₀e^−λt. Determine half-life from experimental activity data. Understand background radiation and its significance for measurements.

Connects to — The exponential decay law is mathematically identical to capacitor discharge (Phase D) — the cross-topic connection should be made explicit; fission and fusion (next topic) also involve nuclear equations; radiocarbon dating applies the decay law to archaeology.

IA & investigative angle — Half-life determination from a decay curve — plotting ln A vs t and extracting λ from the gradient. Dice-model simulation as a Tier 1 activity. Tier 2 practice must include background correction and half-life determination from a data table.

Teach to this depth — Apply E = mc² to calculate energy released in nuclear reactions. Define mass defect. Distinguish fission (splitting heavy nuclei) from fusion (joining light nuclei) and the conditions required for each. Calculate Q-values from nuclear mass tables. Understand the chain reaction — critical mass, moderator (slow neutrons), control rods (absorb neutrons), and coolant in a nuclear fission reactor. Describe the conditions for sustained fusion and the technical challenges of thermonuclear energy generation.

Connects to — Binding energy (next topic) explains why fission and fusion release energy; stellar physics uses fusion reactions as the stellar energy source; nuclear waste management invokes the radioactive decay law.

IA & investigative angle — Tier 2 practice: calculate the energy released in a given fission or fusion reaction from mass data; explain the role of each component of a nuclear reactor and the safety implications.

Teach to this depth — Define binding energy as the energy required to completely separate all nucleons. Plot and interpret the binding energy per nucleon (BE/A) vs mass number curve — the peak near iron (A ≈ 56) explains why fission of heavy nuclei and fusion of light nuclei both release energy. Understand the competition between the strong nuclear force and electrostatic repulsion in determining nuclear stability. Discuss the N–Z stability curve qualitatively.

Connects to — The BE/A curve connects directly to Topics 38 and 39 (decay modes and reaction energies); the nuclear force is introduced here and echoed in stellar core conditions in Phase F astrophysics.

IA & investigative angle — Tier 2 practice: use the BE/A curve to explain why iron-56 is the most stable nucleus; calculate the binding energy per nucleon for a given isotope from its atomic mass.

Teach to this depth — Derive the Compton scattering formula Δλ = (h/m_ec)(1 − cos θ) from conservation of energy and momentum applied to a photon–electron collision, treating the photon as a relativistic particle with momentum p = h/λ. Apply the Heisenberg uncertainty principle ΔxΔp ≥ h/4π and ΔEΔt ≥ h/4π. Understand the uncertainty principle as a fundamental property of quantum systems, not an experimental limitation.

Connects to — Compton scattering synthesises the photon model (Topic 35), de Broglie (Topic 36), and relativistic energy–momentum (Topic 42); the uncertainty principle underlies the zero-point energy concept in quantum mechanics.

IA & investigative angle — Tier 2 practice: calculate the Compton wavelength shift for a given scattering angle; use the uncertainty principle to estimate the minimum kinetic energy of an electron confined to a nucleus.

Teach to this depth — State the two postulates of special relativity. Derive time dilation Δt = γΔt₀ and length contraction L = L₀/γ, where γ = 1/√(1 − v²/c²). Apply the Lorentz transformations x′ = γ(x − vt) and t′ = γ(t − vx/c²). Analyse the relativity of simultaneity — events simultaneous in one frame are not in another. Define the spacetime interval s² = c²t² − x² and show it is invariant. Apply relativistic momentum p = γmv and total energy E = γmc², including E² = p²c² + m²c⁴. Analyse the muon lifetime experiment as experimental confirmation of time dilation.

Connects to — Special relativity requires classical kinematics (Topic 5) to be fully secure; the relativistic energy equation connects to E = mc² (Topics 39–40); astrophysics uses relativistic effects near compact objects; Compton scattering uses relativistic photon momentum.

IA & investigative angle — Tier 2 practice: calculate the time measured on a spacecraft’s clock for a given journey at a relativistic speed; determine whether two events in one frame are simultaneous in another frame using the Lorentz transformation.

Teach to this depth — Describe gravitational collapse and the conditions for star formation. Explain why hydrogen fusion begins at ~10⁷ K. Describe the proton–proton chain fusion reaction. Apply the Stefan–Boltzmann law and Wien’s law to real stars to determine surface temperature and radius from luminosity and spectral peak. Define luminosity L and apparent brightness b; apply the inverse-square law b = L/4πd². Define and use stellar parallax for nearby stars.

Connects to — The radiation laws (Stefan–Boltzmann and Wien) were introduced in Topic 33 for Earth; they are now applied at stellar scale — the same equations, different context; nuclear fusion processes mirror those covered in Topic 39.

IA & investigative angle — Tier 2 practice: given the luminosity and surface temperature of a star, calculate its radius using the Stefan–Boltzmann law; convert between parsecs and light-years.

Teach to this depth — Construct and interpret the Hertzsprung–Russell diagram with both axes correctly defined (L vs T_surface, or absolute magnitude vs spectral class). Identify the main sequence, red giant branch, supergiant region, and white dwarf region. Trace the life cycle of both low-mass and high-mass stars, explaining the physical processes at each stage. Understand the end states: white dwarf, neutron star, and black hole. Introduce dark matter and dark energy qualitatively as evidence for a non-luminous universe. Describe the Big Bang evidence: CMB radiation, galactic recession, and primordial nucleosynthesis ratios.

Connects to — The HR diagram synthesises emission spectra (Topic 34), Stefan–Boltzmann law (Topics 33, 43), nuclear energy (Topic 39), and binding energy (Topic 40) — it is a true synthesis topic.

IA & investigative angle — Tier 2 practice: describe the evolutionary track of a star of given mass on the HR diagram; explain what the position of a white dwarf on the diagram tells you about its temperature and radius.

Teach to this depth — Apply the cosmic distance ladder: parallax → spectroscopic parallax → Cepheid variable period–luminosity relation → Type Ia supernovae as standard candles. Define parsec and light-year and convert between them and metres. Apply Hubble’s law v = H₀d and understand its cosmological significance as evidence for universal expansion. Estimate the age of the universe from t ≈ 1/H₀. Discuss the uncertainty in H₀ and its implications for cosmological models.

Connects to — Hubble’s law uses the Doppler shift (Topic 17) at cosmological scale; the age estimate connects to Big Bang cosmology (Topic 44); Cepheid variables use the period–luminosity relation which relies on photometry and the Stefan–Boltzmann law.

IA & investigative angle — Tier 2 practice: calculate the recession velocity of a galaxy from its redshift; estimate the distance to a galaxy using Hubble’s law; explain why Type Ia supernovae are preferred as standard candles over Cepheid variables at large distances.