PHYC10004 Chap.10 Photons: Blackbody, Photoelectric and Compton Effects
Photons: Blackbody, Photoelectric and Compton Effects
Week 8 begins the quantum block with the experiments that forced physics to treat light as particles.
Blackbody radiation follows Wien's law for its peak wavelength and the Stefan-Boltzmann law for its total power, but classical theory predicted an ultraviolet catastrophe; Planck resolved it by quantising energy in steps of hf.
Einstein's photon explains the photoelectric effect: one photon of energy hf ejects one electron, whose maximum kinetic energy is hf − φ, so a threshold frequency exists and brighter light raises the current without changing the stopping voltage.
The laboratory measures Planck's constant from exactly this relation. X-ray tubes produce a continuous spectrum with a sharp short-wavelength cutoff plus characteristic lines, and Compton scattering shows that photons carry momentum p = h/λ: scattered X-rays emerge with longer wavelength by an amount that depends only on the scattering angle.
The chapter works in electronvolts with hc ≈ 1240 eV nm, and switches to joules for photon counts.
What this chapter covers
- 01
Blackbody Radiation
- 02
Wien and Stefan-Boltzmann Laws
- 03
The Ultraviolet Catastrophe
- 04
Photon Energy and Momentum
- 05
The Photoelectric Effect
- 06
Work Function and Stopping Voltage
- 07
X-ray Production
- 08
Compton Scattering
- 09
Photon Counting
Worked example · free
Count the photons leaving a laser pointer
- 1Photon energy: E = hc/λ = 1240 eV nm/650 nm = 1.91 eV.
- 1Convert to joules for use with a power: 1.91 × 1.6022 × 10⁻¹⁹ = 3.06 × 10⁻¹⁹ J.
- 1Photon rate: n = P/E = 5.0 × 10⁻³/3.06 × 10⁻¹⁹ = 1.6 × 10¹⁶ photons per second.
Key terms
- Blackbody
- A blackbody is an ideal absorber and emitter whose radiated spectrum depends only on its temperature.
- Wien's Law
- Wien's law states that a blackbody's peak wavelength is inversely proportional to its temperature, λ_max T = 2898 μm K.
- Photon
- A photon is a quantum of electromagnetic radiation with energy E = hf and momentum p = h/λ.
- Work Function
- The work function is the minimum energy needed to free an electron from a metal surface, typically a few electronvolts.
- Stopping Voltage
- The stopping voltage is the reverse voltage that just halts the most energetic photoelectrons, so that eV_stop equals their maximum kinetic energy.
- Compton Shift
- The Compton shift is the increase in wavelength of a photon scattered by an electron, Δλ = (h/mc)(1 − cos θ).
Photons: Blackbody, Photoelectric and Compton Effects FAQ
Why does brighter light not give photoelectrons more energy?
Each electron absorbs a single photon, and a photon's energy depends only on the light's frequency. Brighter light delivers more photons per second, so more electrons are ejected and the current rises, but each electron's maximum kinetic energy and the stopping voltage stay the same.
What does the ultraviolet catastrophe refer to?
Classical theory predicted that a blackbody should radiate ever more energy at shorter wavelengths, without limit. Measured spectra instead peak and fall away. Planck removed the contradiction by assuming energy is exchanged only in steps of hf, the first quantum idea.
Do I need to derive the Compton equation?
The lectures say students are not expected to derive it from first principles. You should be able to use it, explain that the photon gives some energy and momentum to a recoiling electron and so leaves with a longer wavelength, and note that the shift depends only on the angle.
Why is no Compton shift noticed for visible light?
The shift is at most a few picometres, set by h/mc for the electron. For X-rays of tens of picometres that is a large fraction, but for visible light of hundreds of nanometres it is far too small a fraction to notice.
Exam move
Build a single energy ledger for this chapter: compute photon energies in electronvolts with hc ≈ 1240 eV nm and convert to joules only for power and photon counts. Practise the blackbody chain of Wien, Stefan-Boltzmann and photon rate on a star, a planet and a room-temperature object.
Rehearse the photoelectric observations against the classical predictions in a table, then work threshold, stopping-voltage and intensity questions. Finish with Compton chains from incident energy through shift and scattered energy to electron kinetic energy.
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