In 1905 — his miraculous year — Albert Einstein published a paper explaining the photoelectric effect using a radical idea: light comes in discrete energy packets. This insight connects to both wave-particle duality and the broader electromagnetic spectrum. This paper, not relativity, won Einstein the Nobel Prize in Physics in 1921. It was the moment quantum physics became unavoidable. The classical picture of light as a continuous wave could not explain why shining light on a metal sometimes ejected electrons and sometimes did not — no matter how bright the light. Einstein's photon theory explained everything, and in doing so, fundamentally changed our understanding of the nature of light and matter.
The photoelectric effect is the emission of electrons from a metal surface when electromagnetic radiation (typically UV or visible light) of sufficient frequency is incident on it. The key equation:
KE_max = hf − φ
where KE_max is the maximum kinetic energy of ejected electrons (J), h = 6.626 × 10⁻³⁴ J·s is Planck's constant, f is the frequency of the incident light (Hz), and φ (phi) is the work function of the metal (J) — the minimum energy needed to release an electron.
What the Classical Wave Theory Predicted (and Got Wrong)
Before Einstein, physicists assumed light was a continuous electromagnetic wave. The classical prediction for the photoelectric effect was:
• Brighter light (higher intensity, more energy per second) → electrons should be ejected faster (more kinetic energy).
• Any frequency of light should eject electrons, given enough time to accumulate energy.
• There should be a measurable time delay between shining light and electrons being emitted.
None of these predictions matched experiment. What was actually observed:
• Below a threshold frequency f₀, no electrons are emitted — regardless of intensity. A very bright red light ejects no electrons from zinc; a dim UV light ejects electrons immediately.
• Above f₀, electrons are ejected instantly — no time delay, even at very low intensities.
• Intensity affects the number of ejected electrons, not their kinetic energy. Brighter light → more electrons, but each electron has the same maximum KE.
• Maximum KE of ejected electrons depends only on frequency — higher frequency → more energetic electrons.
Einstein's Explanation: Photons
Einstein proposed that light consists of discrete energy packets — photons — each carrying energy:
When a photon hits the metal surface, it gives all its energy to a single electron in an all-or-nothing interaction. If the photon energy hf is less than the work function φ of the metal, the electron cannot escape — regardless of how many photons arrive. If hf > φ, the electron escapes with kinetic energy equal to the photon energy minus the work function:
This explains every observation:
• Threshold frequency: hf₀ = φ → f₀ = φ/h. Below f₀, each photon has insufficient energy regardless of how many there are.
• No time delay: a single photon delivers its energy instantly to a single electron.
• Intensity → number of photons → number of ejected electrons (not their energy).
• Higher frequency → higher photon energy → more KE for ejected electrons.
The Work Function
The work function φ is the minimum energy required to liberate an electron from the metal surface. It is a property of the metal — essentially the energy needed to overcome the attractive forces binding surface electrons.
| Metal | Work function φ (eV) | Threshold frequency (Hz) |
|---|---|---|
| Caesium (Cs) | 2.1 eV | 5.1 × 10¹⁴ Hz (visible light) |
| Sodium (Na) | 2.3 eV | 5.6 × 10¹⁴ Hz (visible) |
| Zinc (Zn) | 4.3 eV | 1.0 × 10¹⁵ Hz (UV only) |
| Platinum (Pt) | 5.7 eV | 1.4 × 10¹⁵ Hz (UV only) |
| Gold (Au) | 5.1 eV | 1.2 × 10¹⁵ Hz (UV only) |
Metals with low work functions (caesium, sodium, potassium) can be ejected by visible light and are used in photocells and image sensors. High work function metals (platinum, gold) require UV. This is why ordinary visible light does not damage metals by knocking out electrons — their work functions are too high.
Worked Examples
Example 1: Maximum kinetic energy of photoelectrons
UV light of frequency 1.5 × 10¹⁵ Hz hits a zinc surface (φ = 4.3 eV = 6.89 × 10⁻¹⁹ J).
Example 2: Threshold frequency
Find the threshold frequency for caesium (φ = 2.1 eV = 3.36 × 10⁻¹⁹ J).
This is in the visible green/yellow range — confirming that visible light ejects electrons from caesium.
Example 3: Stopping potential
In a photoelectric experiment, a stopping potential V_s is applied to halt the fastest electrons. Since KE_max = eV_s:
A graph of V_s vs f is a straight line with slope h/e — the method Millikan used in 1916 to measure Planck's constant with high precision.
Significance: The Birth of the Photon
The photoelectric effect established three revolutionary ideas:
1. Light energy is quantised — it comes in packets (photons) of energy E = hf, not as a continuous flow.
2. Quantum processes are discrete — a photon interacts with a single electron in a single event.
3. The energy of a photon depends on frequency, not amplitude — this broke the classical intuition that brighter (higher amplitude) light is always more energetic per interaction.
Together with Planck's blackbody radiation formula (1900) and Bohr's hydrogen atom model (1913), the photoelectric effect was one of three pillars that made the quantum revolution inevitable. By 1925, Heisenberg, Schrödinger, and Dirac would build quantum mechanics — the most precisely tested physical theory ever devised.
Applications of the Photoelectric Effect
Solar cells: photovoltaic cells use the photoelectric effect to convert sunlight to electrical current. Photons above the bandgap energy of the semiconductor (typically silicon, Eg ≈ 1.1 eV) generate electron-hole pairs that are swept apart by an internal electric field, producing a current.
CCD sensors: digital cameras and telescopes use charge-coupled devices where photons liberate electrons in each pixel — the number of electrons is proportional to light intensity. This is the photoelectric effect in semiconductor form.
Photomultiplier tubes: in particle physics and medical PET scanners, a single photon ejects an electron that is accelerated and amplified by successive dynodes, producing a measurable electrical pulse from a single photon event.
Frequently Asked Questions
What is the photoelectric effect?
The photoelectric effect is the emission of electrons from a metal surface when light of sufficient frequency is incident on it. Key equation: KE_max = hf − φ. It proved that light consists of discrete photons of energy hf, not a continuous wave — a cornerstone result that founded quantum physics.
Why did Einstein win the Nobel Prize for the photoelectric effect?
Einstein's 1905 explanation of the photoelectric effect — proposing that light consists of quantised photons of energy hf — resolved experimental observations that classical wave theory could not explain. The Nobel committee in 1921 recognised this as a discovery of fundamental physical law, not merely a clever formula. Relativity was considered too theoretical and speculative at the time.
What is the work function?
The work function φ (in joules or electron-volts) is the minimum energy needed to liberate an electron from a metal surface. It depends on the metal: caesium φ = 2.1 eV (ejected by visible light); zinc φ = 4.3 eV (requires UV). The threshold frequency f₀ = φ/h — below this, no electrons are emitted regardless of intensity.
Why does intensity affect number of electrons but not their energy?
Intensity measures the number of photons per second. Each photon interacts with a single electron and transfers exactly hf of energy. More photons → more electrons ejected, but each electron still receives the same hf minus the work function. Doubling intensity doubles the photocurrent but does not change the maximum kinetic energy of ejected electrons.
What is the threshold frequency?
The threshold frequency f₀ is the minimum light frequency that can eject electrons from a metal: f₀ = φ/h. Below f₀, photon energy hf < φ — insufficient to overcome the work function. No electrons are ejected. Above f₀, electrons are ejected with KE_max = hf − φ. This frequency depends on the metal, not the light source.
Share this article
Written by
Dr. Marcus WebbTheoretical physicist and science communicator with a PhD from Caltech. Research background in classical mechanics and gravitational physics. Passionate about making advanced physics accessible to all learners.
View all articles by this author →
