This physics grades 11-12 lesson on photoelectric effect notes gives the key ideas first, then worked examples and diagrams. After that, practise with the worksheet on photoelectric effect and check yourself with the quiz.
Quick answer: Light comes in photons of energy E = hf. In the photoelectric effect a photon ejects an electron only if hf is at least the work function φ, and the electron then has maximum kinetic energy Kmax = hf − φ. Particles also show wave behaviour, with de Broglie wavelength λ = h/p.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB E.2
Photoelectric effect notes: the key ideas
What is a photon?
Light travels as a wave, yet it is absorbed and emitted in tiny packets. Each packet is a photon, and its energy depends only on the frequency of the light, not on how bright the beam is. Violet photons carry more energy than red ones, and X-ray photons far more.
E = hf = hc / λ
E = photon energy (J), h = Planck constant = 6.63 × 10⁻³⁴ J s, f = frequency (Hz), c = 3.00 × 10⁸ m/s, λ = wavelength (m). Use 1 eV = 1.60 × 10⁻¹⁹ J to convert to electronvolts.
Calculate the energy of a photon of wavelength 450 nm.
E = hc/λ = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) / (450 × 10⁻⁹) = 4.42 × 10⁻¹⁹ J = 4.42 × 10⁻¹⁹ / 1.60 × 10⁻¹⁹ = 2.76 eV.
What is the photoelectric effect?
When light of high enough frequency shines on a clean metal surface, electrons are ejected. A negatively charged zinc plate loses its charge in ultraviolet light, but a bright red lamp has no effect at all. This puzzled physicists because the wave model predicted that any bright light should eventually work.
The work function φ is the minimum energy needed to remove an electron from the surface of a metal. The threshold frequency f₀ is the lowest frequency that can eject electrons: φ = hf₀.
How does Einstein’s equation explain the observations?
Einstein proposed that one photon gives all its energy to one electron. Part pays for escaping the metal and the remainder becomes kinetic energy. The most energetic electrons come from the surface and have the maximum kinetic energy.
hf = φ + Kmax, so Kmax = hf − φ. The stopping potential Vs is the reverse voltage that just stops the fastest electrons: eVs = Kmax.
Sodium has a work function of 2.30 eV. Light of wavelength 400 nm falls on it. Calculate Kmax and the stopping potential.
E = hc/λ = 4.97 × 10⁻¹⁹ J = 3.11 eV. Kmax = 3.11 − 2.30 = 0.81 eV, so Vs = 0.81 V.
| Observation | Wave model | Photon model |
|---|---|---|
| No emission below f₀, however bright | predicts emission if bright enough | one photon is too weak, no matter how many |
| Emission is instant | predicts a delay while energy builds up | one photon gives its energy at once |
| Kmax independent of intensity | predicts larger Kmax for brighter light | brightness changes the number of photons, not their energy |
| Current proportional to intensity | agrees | more photons, more electrons |
What does de Broglie’s equation say about matter?
If light waves behave like particles, perhaps particles behave like waves. Louis de Broglie suggested that a particle of momentum p has a wavelength, and electron diffraction by crystals confirmed it. This is wave-particle duality.
λ = h / p = h / (mv)
λ = de Broglie wavelength (m), p = momentum (kg m/s), m = mass (kg), v = speed (m/s).
Calculate the de Broglie wavelength of an electron moving at 3.0 × 10⁶ m/s.
λ = h/(mv) = 6.63 × 10⁻³⁴ / (9.11 × 10⁻³¹ × 3.0 × 10⁶) = 2.4 × 10⁻¹⁰ m (0.24 nm), similar to the spacing of atoms in a crystal.
Students think brighter light gives faster electrons. A brighter beam gives more electrons per second but not faster ones: speed depends on frequency only.
Always change the photon energy to the same unit as the work function before you subtract. Most work functions are given in eV, so convert hc/λ using 1 eV = 1.60 × 10⁻¹⁹ J.
- Photon energy: E = hf = hc/λ, with h = 6.63 × 10⁻³⁴ J s.
- Einstein: hf = φ + Kmax; threshold frequency f₀ = φ/h.
- Stopping potential: eVs = Kmax.
- Intensity changes the number of photoelectrons, not their maximum energy.
- de Broglie: λ = h/p = h/(mv).
Photon energy, work function and matter waves: frequently asked questions
What is the work function?
The work function φ is the minimum energy needed to free an electron from a metal surface. It is different for every metal and is often quoted in electronvolts.
Why does bright red light not release electrons from zinc?
Each red photon has too little energy to free an electron. Energy is not shared between photons, so more red photons do not help.
What does the gradient of a Kmax against f graph give?
The gradient equals Planck’s constant h, and the intercept on the energy axis is −φ. The frequency axis intercept is the threshold frequency.
What is an electronvolt?
One electronvolt is the energy gained by an electron moving through a potential difference of 1 V, which equals 1.60 × 10⁻¹⁹ J.
How was the wave nature of electrons shown?
Electrons directed at thin crystals produce diffraction patterns like those of waves. The measured wavelength matches λ = h/p.
