Photons & the Photoelectric Effect

You’ll be able to

Relate a photon’s energy to the frequency of light
Explain the photoelectric effect and the role of the work function
Distinguish the effect of increasing light intensity from increasing frequency

Light comes in packets

Quantum physics says light is not a smooth stream but a hail of energy packets called photons. Each photon carries an energy fixed by its frequency: E = hf, where h = 6.63 × 10⁻³⁴ J·s is Planck’s constant. Higher-frequency light (blue, ultraviolet) has more energetic photons than lower-frequency light (red, infrared). Brightness is just the number of photons per second — a dim blue beam still delivers more energetic photons than a bright red one. Photon energies are often quoted in electron-volts (1 eV = 1.6 × 10⁻¹⁹ J).

The photoelectric effect

Shine light on a metal and it can eject electrons — the photoelectric effect. But there is a catch that classical waves cannot explain: below a certain threshold frequency, no electrons come out no matter how bright the light, while above it electrons appear instantly even for dim light. Einstein’s explanation: one photon gives all its energy to one electron. The electron needs a minimum energy, the work function φ, to escape the metal; whatever is left over becomes the electron’s kinetic energy. KE_max = hf − φ.

Photon energy & the photoelectric equation

E = h · f · KE_max = h · f − φ

φ is the work function — the minimum energy to free an electron from the metal. Electrons are emitted only when hf ≥ φ; the excess energy becomes the electron’s maximum kinetic energy.

Worked example

Light whose photons carry 5.0 eV of energy strikes a metal with a work function of 2.0 eV. Find the maximum kinetic energy of the ejected electrons.

1.Use the photoelectric equation: KE_max = hf − φ, where hf = 5.0 eV is the photon energy.
2.Substitute: KE_max = 5.0 eV − 2.0 eV.
3.Subtract: 5.0 − 2.0 = 3.0 eV.

Answer: KE_max = 3.0 eV. (Because the 5.0 eV photon energy exceeds the 2.0 eV work function, electrons are indeed ejected.)

Checkpoint

A metal has a work function of 2.0 eV. Light whose photons carry 5.0 eV strikes it. What is the maximum kinetic energy of the ejected electrons?

Watch out

Whether electrons are emitted depends on the light’s frequency (photon energy), not its brightness. A blindingly bright red light below threshold ejects nothing, while a faint ultraviolet source above threshold works instantly. This is the classic result no wave theory could explain.

Checkpoint

For a photoelectric setup already above threshold, increasing the intensity of the light (same frequency) increases:

On the exam

Separate the two knobs: frequency controls each electron’s energy (KE_max = hf − φ), while intensity controls the number of electrons. Exam questions constantly test whether you know that brighter light does not make faster electrons.

Answer the 2 checkpoints as you read.