4.5QuantumStretch

The Photoelectric Effect

Shine light on a metal surface and electrons can be knocked clean off it — but only if the light’s colour is right. Brightness turns out to be irrelevant to whether this happens at all, a fact that stumped physicists until Einstein proposed treating light as a stream of particles rather than a continuous wave.

40 min Video by Physics with Ms. Beenish Module 4.5 Quantum physics

Photoelectric Effect | A Level Physics | Threshold Frequency & Work FunctionWatch the full walkthrough before the notes below.

Open on YouTube

What you'll be able to do

Describe the key experimental observations of the photoelectric effect
Explain why the wave model of light cannot account for these observations
Define work function and threshold frequency
Use Einstein’s photoelectric equation

The photoelectric effect

When electromagnetic radiation above a certain frequency strikes a metal surface, electrons — $photoelectrons$ — are emitted. Three key observations define the effect: emission is (effectively) instantaneous; below a $threshold frequency$ , no electrons are emitted at all, however intense the light; and above the threshold, increasing intensity increases the NUMBER of photoelectrons per second, but never their maximum kinetic energy.

A wave model of light cannot explain this: it predicts energy should accumulate continuously regardless of frequency, so a dim light of any frequency should eventually free an electron given enough time. Experimentally, below the threshold frequency, no amount of waiting or brightening ever produces emission.

Tip — Learn the three key observations as a set — instant emission, a sharp threshold frequency, and intensity affecting only the RATE (never the maximum energy) of emission.

Einstein’s explanation

Einstein explained the effect by treating light as photons, each carrying energy $E = h f$ . A photoelectron is emitted when a single photon transfers its entire energy to a single electron at once — explaining the instantaneous emission. Freeing an electron costs a minimum energy, the $work function$ , $ϕ$ , unique to each metal; a photon below this energy can never free an electron, no matter how many arrive, which defines the threshold frequency.

ϕ = h f_{0}

Work function = Planck constant × threshold frequency.

1Rearrange

ϕ = h f_{0}

f_{0} = \frac{ϕ}{h}

f_{0} = \frac{4.0 \times 1 0 ^{- 19}}{6.63 \times 1 0 ^{- 34}}

Answer

f_{0} \approx 6.03 \times 1 0^{14}

Einstein’s photoelectric equation

Any surplus photon energy beyond the work function becomes kinetic energy of the emitted electron. The MAXIMUM kinetic energy corresponds to the least tightly bound electrons at the surface.

h f = ϕ + E_{k (m a x)}

Einstein's photoelectric equation.

1Photon energy:

E = h f = 6.63 \times 1 0^{- 34} \times 8.5 \times 1 0^{14} = 5.64 \times 1 0^{- 19}

2Rearrange:

E_{k (m a x)} = h f - ϕ = 5.64 \times 1 0^{- 19} - 3.5 \times 1 0^{- 19}

Answer

E_{k (m a x)} \approx 2.14 \times 1 0^{- 19}

Tip — If the calculated hf comes out less than φ, no photoelectrons are emitted at all — don’t report a negative kinetic energy; report zero emission.

Equation recap

ϕ = h f_{0}

Work function from threshold frequency.

h f = ϕ + E_{k (m a x)}

Einstein's photoelectric equation.

Common mistakes to avoid

Believing more intense light can free electrons below the threshold frequency.

Intensity only changes the NUMBER of photons per second — below f₀, every individual photon still has too little energy, however many arrive.

Assuming all photoelectrons leave with the maximum possible kinetic energy.

Only the least tightly bound (surface) electrons achieve Ek(max) — more tightly bound electrons need more energy to escape and leave with less kinetic energy.

Forgetting to check hf ≥ φ before calculating Ek(max).

If hf < φ, no photoelectrons are emitted at all — always check this before calculating a kinetic energy.

Key takeaways

Instant emission, a sharp threshold frequency, and intensity affecting only rate (not maximum energy) cannot be explained by a wave model of light.
Einstein’s photon model: each photon transfers all its energy hf to one electron at once.
Work function φ = hf₀ is the minimum energy needed to free an electron.
Einstein's equation: hf = φ + Ek(max).

Test yourself

Ready to lock in The Photoelectric Effect? Pick a mode and earn XP & Dobloons.

The Photoelectric Effect

40 min Video by Physics with Ms. Beenish Module 4.5 Quantum physics