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Mathematics for Physics

132 Planck Relation

A relation that is used to compute the energy of a light quantum from its frequency, where a light quantum is a discrete packet of electromagnetic energy.

The Planck relation \(E=hf\). The energy of one photon is Planck’s constant times the frequency. This principle is used to convert a measured frequency into a photon energy.

The Planck relation is

\[ E = hf \]

where

  • \(E\) is the energy of one light quantum.
  • \(h\) is Planck’s constant.
  • \(f\) is the frequency of the light.

The angular form \(E=\hbar\omega\). The same energy is \(\hbar\omega\) in angular frequency. Angular frequency is \(2\pi\) times the ordinary frequency. This principle is used to write photon energy in the notation of wave mechanics.

The angular form of the Planck relation is

\[ E = \hbar\omega \]

where

  • \(E\) is the photon energy.
  • \(\hbar\) is the reduced Planck constant.
  • \(\omega\) is the angular frequency.

The linear scaling of energy with frequency. Energy scales linearly with frequency. This principle is used to compare photons across the electromagnetic spectrum.

Note: Also called Planck’s relation. Also called the Einstein light-quantum energy relation.