Key Experimental Observations
The photoelectric effect is the emission of electrons from a metal surface when light shines on it. At first glance this seems unremarkable — light carries energy, energy knocks electrons out, done. But the devil is in the details. When physicists in the late 19th and early 20th centuries measured exactly how the emitted electrons depended on the light's properties, the results were deeply strange and completely impossible to explain with classical wave theory. Those experimental surprises were the first clear crack in classical physics, and understanding them is the gateway to quantum mechanics. The key puzzle can be summarised in two shocks. First, whether electrons are emitted at all depends entirely on the frequency (colour) of the light, not its brightness. You can blast a metal with an incredibly intense beam of red light and get zero electrons. Switch to a dim violet beam and electrons fly out instantly. Second, the maximum kinetic energy of the emitted electrons depends on frequency but not on intensity. Intensity only controls the number of electrons emitted per second (the photocurrent), not how fast they move. Classical wave physics predicts exactly the opposite: brighter waves should shake electrons out more energetically, and any frequency given long enough should eventually eject electrons. Both predictions are wrong. Albert Einstein explained these results in 1905 by proposing that light is quantised — it comes in discrete packets called photons, each carrying energy E = hf, where h is Planck's constant and f is frequency. A single photon interacts with a single electron in an all-or-nothing transaction: if the photon has enough energy to overcome the metal's binding energy (the work function φ), the electron escapes; if not, it doesn't matter how many photons arrive. This photon model perfectly accounts for every observed feature, earning Einstein the 1921 Nobel Prize in Physics.
- Observation 1 — Threshold Frequency
- Observation 2 — Instantaneous Emission
- Observation 3 — Maximum Kinetic Energy Depends on Frequency, Not Intensity
- Observation 4 — Photocurrent is Proportional to Intensity
Observation 1 — Threshold Frequency
For every metal there exists a minimum frequency f₀, called the threshold frequency (or cut-off frequency), below which no photoelectrons are emitted regardless of light intensity or exposure time. For example, sodium has f₀ ≈ 5.5 × 10¹⁴ Hz (green light), so red light (f ≈ 4.3 × 10¹⁴ Hz) never ejects electrons from sodium no matter how bright it is. This is inexplicable classically: a very bright, long-duration wave should accumulate enough energy to eject any electron eventually. The photon model explains it immediately — each photon must have energy hf ≥ φ (the work function) for ejection to be possible. Below threshold, every individual photon simply lacks the energy for the job.
Observation 2 — Instantaneous Emission
Even when light intensity is extremely low, electrons are emitted within nanoseconds of light arriving — there is no measurable delay. Classical wave theory predicts that a faint wave must slowly accumulate energy in the metal over seconds or minutes before an electron absorbs enough to escape. Experimentally, no such delay is ever observed. In the photon model this is natural: the very first photon that arrives can immediately transfer its entire energy hf to one electron. If hf > φ, that electron escapes instantly. Intensity just determines how frequently photons arrive, not whether each one can do the job.
Observation 3 — Maximum Kinetic Energy Depends on Frequency, Not Intensity
The maximum kinetic energy KE_max of emitted electrons increases linearly with the frequency of light, and is completely independent of intensity. Doubling the intensity doubles the number of electrons ejected per second but does not increase their speed. Doubling the frequency (for light above threshold) produces faster electrons. This is measured using a 'stopping voltage' experiment: a reverse voltage V_s is applied until the photocurrent drops to zero. At that point eV_s = KE_max, so the stopping voltage directly measures maximum kinetic energy. Plotting V_s against f yields a straight line with slope h/e — a beautiful direct measurement of Planck's constant.
Observation 4 — Photocurrent is Proportional to Intensity
Once the frequency is above the threshold, the number of electrons emitted per second (measured as photocurrent I) is directly proportional to the intensity of the light. This is the one observation that feels 'classical' — more light, more electrons. But it, too, fits the photon model perfectly: greater intensity means more photons per second, and each photon can eject one electron, so more photons mean more ejected electrons. The energy of each individual electron (set by frequency) is unchanged. Think of photons as individual bullets: more bullets hit more targets, but each bullet carries the same punch regardless of how many are fired.
The Key Equation
- KE_{\max} — Maximum kinetic energy (J (joules)): The greatest kinetic energy a photoelectron can have, achieved when it comes from the surface layer and loses no energy to collisions inside the metal.
- h — Planck's constant (J·s): The fundamental quantum of action, h = 6.626 × 10⁻³⁴ J·s. It sets the scale of all quantum phenomena.
- f — Frequency of incident light (Hz (s⁻¹)): The number of wave cycles per second for the incoming photon. Higher frequency means higher photon energy.
- \phi — Work function (J or eV): The minimum energy needed to free one electron from the metal surface. It is a fixed property of each material (e.g., φ = 2.3 eV for potassium).
- f_0 — Threshold frequency (Hz): The minimum frequency at which emission occurs, defined by hf₀ = φ. Below this frequency, KE_max would be negative, meaning no emission.
Worked Example
Problem. Ultraviolet light of frequency f = 1.20 × 10¹⁵ Hz strikes a zinc surface whose work function is φ = 4.33 eV. (a) Find the maximum kinetic energy of the emitted electrons in eV. (b) Find the stopping voltage needed to halt the fastest electrons. (c) What is the threshold frequency for zinc?
Answer. Maximum kinetic energy ≈ 0.63 eV; stopping voltage ≈ 0.63 V; threshold frequency ≈ 1.05 × 10¹⁵ Hz.
Origins · 1 minAlbert Einstein and how this was discovered
In his 'miracle year' of 1905, Einstein published his explanation of the photoelectric effect, proposing that light energy is quantised into photons of energy E = hf. This explained all the experimental observations that classical wave theory could not, and established the photon as a fundamental particle. It was this work — not relativity — that won him the 1921 Nobel Prize in Physics. Einstein was deeply uncomfortable with the probabilistic nature of quantum mechanics he helped create. He famously said 'God does not play dice with the universe' — yet his own photon hypothesis was one of quantum theory's founding ideas.
Related Concepts
- Work Function and Electron Binding Energy — The work function φ is the central material property in the photoelectric equation; understanding it explains why different metals have different threshold frequencies.
- Planck's Quantum Hypothesis — Planck's constant h appears directly in the photoelectric equation. Planck introduced quantisation to explain blackbody radiation just five years before Einstein applied the idea to light itself.
- The Electromagnetic Spectrum — Threshold frequencies for common metals typically lie in the ultraviolet range. Knowing how frequency relates to colour and photon energy helps predict which parts of the spectrum cause photoemission.
- Wave-Particle Duality of Light — The photoelectric effect provides the clearest evidence that light behaves as particles (photons), complementing experiments like diffraction that show it behaves as waves.