The Photon Model

Photon — a quantum of electromagnetic radiation: a discrete packet of energy, not a continuous flow.

Photon energy —

E = hf

and since c = fλ,

E = hc / λ

where h is the Planck constant, 6.63 × 10⁻³⁴ J s.

What "quantised" means — energy arrives in whole packets or not at all. A source cannot emit half a photon, and an electron cannot absorb a fraction of one. This is the central break with classical physics, where energy could be transferred in any amount however small.

Example: a photon of frequency 5.0 × 10¹⁴ Hz carries E = (6.63 × 10⁻³⁴)(5.0 × 10¹⁴) = 3.3 × 10⁻¹⁹ J. That is a very small number in joules, which is why atomic physics usually uses electronvolts instead.

Energy and wavelength are inversely related — from E = hc/λ, a shorter wavelength means a more energetic photon. Gamma photons carry millions of times the energy of radio photons, which is why the hazard rises along the spectrum.

Intensity versus photon energy — this distinction does most of the work in this topic. The intensity of a beam depends on how many photons arrive per second. The energy of each photon depends only on the frequency. A very bright red lamp delivers enormous numbers of low-energy photons; a dim ultraviolet source delivers few high-energy ones.

The electronvolt — the energy transferred when an electron moves through a potential difference of one volt:

1 eV = 1.60 × 10⁻¹⁹ J

Convert to joules by multiplying by the electronic charge, and back by dividing.

Estimating h with LEDs — an LED emits photons of energy roughly equal to the work done moving one electron across it, so eV ≈ hc/λ at the threshold voltage where it just lights. Measuring V for LEDs of several known wavelengths and plotting V against 1/λ gives a straight line of gradient hc/e, from which h follows.