Photoelectric Effect: Light Ejecting Electrons Explained

Shine light on a clean metal surface and electrons can fly off it instantly — but only if the light's frequency is high enough. Dim blue light ejects electrons while the brightest red light does nothing. This is the photoelectric effect, and it proved that light arrives in packets of energy called photons.

It matters because no wave theory of light can explain it: waves should deliver more energy when brighter, regardless of colour. Einstein's 1905 photon explanation earned him the Nobel Prize and became one of the founding experiments of quantum physics. The same principle runs the light sensors in cameras and solar panels.

Key Concepts

• Photon: a packet of light energy, E = hν = hc/λ. Symbol ν (nu) is frequency in hertz, λ wavelength in metres, c = 3.00 × 10⁸ m/s, h = 6.626 × 10⁻³⁴ J·s.
• Work function (φ): the minimum energy needed to pull an electron out of a particular metal, in joules or electronvolts. Each metal has its own value.
• Threshold frequency (ν₀): the minimum light frequency that can eject electrons, ν₀ = φ/h. Light below this frequency ejects nothing, however bright.
• Kinetic energy of ejected electrons: KEmax = hν − φ. Extra photon energy beyond the work function becomes the electron's motion.
• Instantaneous emission: electrons are ejected the moment light hits — there is no waiting time for energy to "build up".
• Intensity effect: brighter light ejects more electrons per second, but does not make any single electron faster.

Formulas

• Einstein's photoelectric equation: KEmax = hν − φ = hc/λ − φ. Units: joules throughout (1 eV = 1.602 × 10⁻¹⁹ J).
• Threshold condition: electron ejection needs hν ≥ φ, i.e. ν ≥ ν₀ = φ/h.
• Electron speed: from KE = ½mv², vmax = √(2·KEmax/m), with electron mass m = 9.109 × 10⁻³¹ kg.

A handy constant: hc = 1240 eV·nm, so a photon's energy in eV is 1240 divided by its wavelength in nanometres.

Worked Example

Light of wavelength 400 nm falls on a metal with work function 2.0 eV. Find the maximum kinetic energy and speed of the ejected electrons.

1. Photon energy: E = 1240 eV·nm / 400 nm = 3.10 eV.
2. Subtract the work function: KEmax = 3.10 − 2.0 = 1.10 eV.
3. Convert to joules: 1.10 × 1.602 × 10⁻¹⁹ = 1.76 × 10⁻¹⁹ J.
4. Speed: v = √(2 × 1.76 × 10⁻¹⁹ / 9.109 × 10⁻³¹) = √(3.86 × 10¹¹).
5. Compute: √3.86 × 10⁵·⁵ ≈ 1.965 × 3.162 × 10⁵ = 6.21 × 10⁵ m/s.

KEmax = 1.10 eV and vmax = 6.21 × 10⁵ m/s.

Common Misconceptions

• Brighter light makes faster electrons. Brightness (intensity) only increases the number of photons, so more electrons are ejected — each with the same maximum energy, which depends only on frequency.
• Any light works if you wait long enough. Below the threshold frequency, no electrons are ever ejected, even after hours — one photon interacts with one electron, and a weak photon simply cannot pay the work-function price.
• The effect only works with visible light. Ultraviolet ejects electrons from most metals, and X-rays eject even tightly bound inner electrons (the basis of X-ray photoelectron spectroscopy).

Real-World Applications

• Solar cells convert photons to electric current using the same photon-electron energy transfer.
• Photomultiplier tubes and camera light meters detect light via electron ejection.
• Automatic doors and burglar alarms use photoelectric sensors interrupted by a beam.
• Night-vision devices amplify tiny numbers of photo-ejected electrons.
• X-ray photoelectron spectroscopy identifies elements by the energies of ejected electrons.

Light comes in photons of energy hν, each photon gives all its energy to one electron, and the electron escapes only if hν beats the metal's work function. Frequency decides whether and how fast; brightness decides how many.