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IB Diploma Physics HL · Theme E.2 Quantum physics (HL)
Mini-Lesson

Quantum Physics

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.

photons E = hf photoelectric matter waves

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.)
× 10⁻¹⁹ J
Hint: E = hf = 6.63e-34 × 5.0e14 = 3.315e-19 J → 3.32.
Calculate

Calculate

#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.
× 10⁻¹⁹ J
Hint: E_max = hf − φ = 3.315e-19 − 2.0e-19 = 1.315e-19 J → 1.32.
E.2 · matter waves

Wave–particle duality

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.
× 10¹⁴ Hz
Hint: ΔE = 3.0 × 1.6e-19 = 4.8e-19 J; f = ΔE ÷ h = 4.8e-19 ÷ 6.63e-34 = 7.24e14 → 7.24.
Sort it

Which quantum idea?

Tap an item, then tap the group it belongs to.

💡 Photoelectric effect

🌊 Matter waves

🪜 Energy levels

Match it

Match the expression to its name

Tap a statement on the left, then its match on the right.

Statement
Answer
Recap

The big ideas to know

Photons: E = hf; light is quantised

Photoelectric: hf = φ + E_max; needs f above threshold, not just intensity

Duality: λ = h/p; particles diffract like waves

Energy levels: discrete; hf = E₂ − E₁ gives line spectra

Evidence: photoelectric = particle nature of light; diffraction = wave nature of matter

That completes Quantum Physics for IB Diploma Physics HL. Press Finish to see your score.

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