This HL-only mini-lesson covers Theme E.2 — Quantum physics: the photoelectric effect and photons, wave–particle duality, the de Broglie wavelength and matter waves, and atomic energy levels.
Work through each screen, answer the questions as you go (some are reasoning, some are calculations) and collect ⭐ stars. Watch for the HL flag on higher-level extensions. Press Start when you're ready.
E.2 · photons
Photons & the photoelectric effect
Light comes in quanta called photons, each carrying energy proportional to frequency. Shining light on a metal can eject electrons (the photoelectric effect) — but only if the frequency exceeds a threshold set by the work function φ:
E = hf · hf = φ + E_maxh = 6.63 × 10⁻³⁴ J s; E_max = max KE of the ejected electron
Increasing the intensity below the threshold frequency still ejects NO electrons — a fatal problem for the wave model and the evidence that light is quantised.
Quick check
Quick check
?Dim blue light ejects electrons from a metal, but intense red light does not. What does this show?
Calculate
Calculate
#Find the energy of a photon of frequency 5.0 × 10¹⁴ Hz, in units of 10⁻¹⁹ J. (h = 6.63 × 10⁻³⁴ J s.)
#A metal with work function 2.0 × 10⁻¹⁹ J is lit with photons of energy 3.315 × 10⁻¹⁹ J. Find the maximum kinetic energy of the ejected electrons, in units of 10⁻¹⁹ J.
If waves can act as particles, particles can act as waves. Every moving particle has a de Broglie wavelength:
λ = h ÷ p = h ÷ mvconfirmed by electron diffraction through crystals
The wavelength is tiny for everyday objects (huge momentum), which is why we never see a cricket ball diffract — but it is measurable for electrons.
Calculate
Calculate
#An electron has momentum 3.3 × 10⁻²⁴ kg m s⁻¹. Find its de Broglie wavelength, in units of 10⁻¹⁰ m. (h = 6.63 × 10⁻³⁴ J s.)
× 10⁻¹⁰ m
Hint: λ = h ÷ p = 6.63e-34 ÷ 3.3e-24 = 2.0e-10 m → 2.0.
E.2 · energy levels
Atomic energy levels
Electrons in atoms occupy discrete energy levels. When an electron drops from a higher level E₂ to a lower E₁, a photon is emitted whose frequency is fixed by the energy gap:
hf = E₂ − E₁this produces the sharp lines of atomic emission spectra
Because the levels are quantised, only specific photon energies appear — the "barcode" line spectrum that identifies each element.
Calculate
Calculate
#An electron drops between two levels 3.0 eV apart (1 eV = 1.6 × 10⁻¹⁹ J). Find the emitted photon's frequency, in units of 10¹⁴ Hz.