HSC Exam Practice

Sample response. A photon is a discrete quantum (packet) of electromagnetic energy. Its energy is given by E = hf, where E is in joules (J), h = Planck’s constant (6.63 × 10⁻³⁴ J·s), and f is frequency in hertz (Hz). The work function (φ) is the minimum energy required to liberate one electron from the surface of a metal; it is measured in joules (J) or electron-volts (eV).

Marking notes. 1 mark for correct definition of photon as a discrete quantum of EM energy; 1 mark for stating E = hf with symbols defined and units; 1 mark for correct definition of work function (minimum energy to liberate an electron from metal surface).

Sample response. (1) The existence of a threshold frequency: the wave model predicts any frequency should eventually eject electrons (energy builds up); observation shows that below f₀, no electrons are ever ejected — inconsistent. (2) K_max depends on frequency, not intensity: the wave model predicts higher intensity (bigger wave amplitude) should give faster electrons; observation shows K_max = hf − φ (frequency-dependent only) — inconsistent. (3) Instantaneous ejection: the wave model predicts a time lag while energy accumulates; electrons are ejected immediately (within 10⁻⁹ s) — inconsistent.

Marking notes. 1 mark per correctly stated observation with “inconsistent with wave model” label. Accept any three of: threshold frequency, K_max independent of intensity, instantaneous ejection, Compton wavelength shift.

Sample response. Young’s double slit experiment produces alternating bright and dark fringes (an interference pattern) on a screen. This pattern arises from constructive and destructive superposition of waves from the two slits, which is a property unique to waves [1]. A particle model would predict only two bright patches on the screen (one behind each slit), with no dark bands in between — the particle model fails to explain the fringes [1]. The photoelectric effect shows that light must deliver energy in discrete quanta (photons). Below the threshold frequency, no electrons are ejected no matter how intense the light — a wave model cannot explain this threshold because waves deliver energy continuously [1]. If light were only waves, intense low-frequency light should eventually eject electrons (energy accumulates); this is never observed — the photon model explains this perfectly (each photon’s energy is fixed at hf) [1].

Marking notes. 1 mark for explaining why the interference fringe pattern is evidence for waves; 1 mark for stating what the particle model incorrectly predicts for the double slit; 1 mark for explaining why the threshold frequency is evidence for photons; 1 mark for stating what the wave model incorrectly predicts for the photoelectric effect.

Sample response (a). Threshold frequency: f₀ = φ/h = 3.10 / (4.14 × 10⁻¹⁵) = 7.49 × 10¹⁴ Hz [1].

Sample response (b). Photon energy at λ = 280 nm: E = hc/λ = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) / (280 × 10⁻⁹) = 7.10 × 10⁻¹⁹ J [1]. Work function in joules: φ = 3.10 × 1.60 × 10⁻¹⁹ = 4.96 × 10⁻¹⁹ J [1]. K_max = E − φ = 7.10 × 10⁻¹⁹ − 4.96 × 10⁻¹⁹ = 2.14 × 10⁻¹⁹ J [1].

Marking notes. 1 mark for correct threshold frequency (accept 7.48–7.50 × 10¹⁴ Hz); 1 mark for correct photon energy in J; 1 mark for correct conversion of work function to J; 1 mark for correct K_max (accept 2.12–2.16 × 10⁻¹⁹ J). Students may work entirely in eV (K_max = hc/λ − φ = 4.46 − 3.10 = 1.36 eV, then convert; accept this approach).

Sample response. The student is incorrect. Increasing the brightness (intensity) of green light increases the number of photons arriving per second, which increases the number of electrons ejected per second (the photocurrent) [1]. However, each individual photon still has the same energy hf, since the frequency of green light is unchanged. Therefore K_max = hf − φ remains unchanged — each ejected electron still has the same maximum kinetic energy regardless of how bright the light is [1]. The maximum kinetic energy of ejected electrons is determined solely by the frequency of the incident photons (and the work function of the metal) [1].

Marking notes. 1 mark for correctly identifying that increasing intensity increases photocurrent (number of electrons), not K_max; 1 mark for explaining that K_max is unchanged because photon energy hf is unchanged; 1 mark for clearly stating that frequency (not intensity) determines K_max.

Sample response. The ultraviolet catastrophe was the failure of classical electromagnetic wave theory to correctly predict the spectrum of black-body radiation. Classical theory predicted that a hot object should emit infinite energy at short (ultraviolet) wavelengths, which was absurd and contradicted experimental observations showing a peak in the emission spectrum [1]. In 1900, Max Planck resolved this by proposing that electromagnetic energy is emitted in discrete packets (quanta) of energy E = nhf, where n is an integer. This quantisation cuts off the high-frequency emission, matching the observed spectrum [1]. Planck introduced the constant h (Planck’s constant) = 6.63 × 10⁻³⁴ J·s [1].

Marking notes. 1 mark for correctly describing the UV catastrophe (classical prediction of infinite UV emission vs observed finite peak); 1 mark for Planck’s resolution (quantised energy emission, E = hf); 1 mark for naming Planck’s constant and giving its value (6.63 × 10⁻³⁴ J·s; accept 6.60–6.65 × 10⁻³⁴).

Sample response (a) — table completion (4 marks). Using E = hc/λ with hc = 1242 eV·nm: Orange (610 nm): E = 2.04 eV < 2.10 eV; no ejection; K_max = N/A. Green (514 nm): E = 2.42 eV; K_max = 2.42 − 2.10 = 0.32 eV ≈ V_s = 0.31 V (✓). Blue (450 nm): E = 2.76 eV; K_max = 0.66 eV ≈ V_s = 0.66 V (✓). UV (310 nm): E = 4.01 eV; K_max = 1.91 eV ≈ V_s = 1.91 V (✓). Sample calculation shown for one source. V_s = 0.00 V for orange LED because the photon energy (2.04 eV) is less than the work function (2.10 eV); no electron has sufficient energy to escape, so no current flows and no stopping voltage is needed. Award 3 marks for correct table completion (1 per correct row — skip orange); 1 mark for sample calculation; 1 mark for correct explanation of V_s = 0 for orange LED.

Sample response (b) — same intensity, different V_s (3 marks). Both sources have the same intensity (50 W/m²), so the same amount of energy arrives per second [1]. However, the blue LED has a shorter wavelength (higher frequency) than the green laser. Each blue photon carries more energy (2.76 eV vs 2.42 eV), so K_max = hf − φ is larger for blue light — hence the higher stopping voltage [1]. The wave model would incorrectly predict equal stopping voltages for equal intensities (since it links energy delivery rate to wave amplitude, not frequency); the observation that V_s depends on frequency and not intensity directly falsifies the wave model [1].

Sample response (c) — lower intensity, higher V_s (2 marks). There is no contradiction because stopping voltage (and K_max) depends only on photon frequency (via K_max = hf − φ), not on intensity. The UV lamp photons have much higher frequency (shorter wavelength, 310 nm) than the orange LED (610 nm), so each UV photon delivers more energy to each electron [1]. When the intensity of the UV lamp is reduced, the quantity that changes is the number of electrons ejected per second (the photocurrent decreases), while K_max and V_s remain the same [1].

Marking notes. Part (a): 1 mark each for green, blue, UV photon energies and K_max values (3 marks); 1 mark for sample calculation with formula shown. Orange: 1 mark for correct explanation (photon energy < work function). Part (b): 1 mark for noting same intensity but different frequency; 1 mark for correct photon model explanation; 1 mark for stating wave model prediction and why it fails. Part (c): 1 mark for explaining V_s depends on frequency not intensity; 1 mark for identifying photocurrent as the quantity that changes with intensity.

Sample response. By the late 19th century, the wave model of light had overwhelming experimental support. Young’s double slit experiment (1801) produced alternating bright and dark fringes that can only be explained by wave superposition — a particle model predicts only two patches of light. Polarisation of light (demonstrated by Malus and others) proved that light is a transverse wave, since only transverse waves can be restricted to a single plane of oscillation. Maxwell’s electromagnetic theory (1865) provided a mathematical framework: light is a transverse electromagnetic wave propagating at c = 1/√(μ₀ε₀), confirmed by Hertz’s discovery of radio waves (1887). The wave model thus appeared complete and internally consistent.

However, three phenomena could not be explained by the wave model. First, the photoelectric effect (Hertz 1887; Einstein 1905): light below a threshold frequency never ejects electrons regardless of intensity, and K_max depends on frequency not intensity — impossible for a continuous wave. Einstein introduced photons (E = hf), explaining all observations. Second, black-body radiation: classical wave theory predicted infinite UV emission (the ultraviolet catastrophe); Planck (1900) resolved this with quantised emission (E = nhf). Third, the Compton effect (1923): X-rays scattered by electrons change wavelength in a way consistent only with particle-like momentum transfer (p = h/λ); the wave model predicts no wavelength change. Each phenomenon required treating light as having particle-like properties.

The concept of wave–particle duality — that light exhibits both wave and particle properties depending on the type of experiment — fundamentally changed our understanding of nature. Light is not simply “a wave” or “a particle”; it is a quantum entity described by quantum mechanics. Experiments that test for interference (double slit) reveal wave behaviour; experiments that test for energy exchange (photoelectric effect, Compton) reveal particle behaviour. This duality is not a contradiction but a deeper truth: both models are incomplete descriptions of the same underlying quantum reality. The wave model remains extremely useful for optics (diffraction, interference, polarisation) while the photon model is essential for understanding light–matter interactions at the atomic scale.

Marking criteria (7 marks). 1 = correctly explains the evidence for the wave model with reference to at least two named experiments (Young’s double slit, polarisation, Maxwell/Hertz; any two). 1 = correctly explains the evidence for the photon model with reference to at least one named experiment (photoelectric effect, Compton effect). 1 = names and correctly describes a second phenomenon supporting photons (accept Compton effect, black-body radiation / UV catastrophe). 1 = explains specifically how the wave model fails for at least one named phenomenon (e.g. threshold frequency cannot be explained by wave energy buildup). 1 = explains what wave–particle duality means: light exhibits both properties depending on the experiment; neither model alone is complete. 1 = discusses the significance for our understanding (quantum mechanics needed; neither classical model is the full picture; both remain useful in appropriate contexts). 1 = reaches an explicit evaluative judgement: both models are incomplete but complementary; the photon model extended (rather than replaced) the wave model for understanding light–matter interactions.