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Mathematics for Physics

131 Photon Momentum

A momentum carried by a photon that is used to compute the momentum of a light quantum from its wavelength, where a photon is a discrete packet of light.

The de Broglie momentum of a photon. The momentum of a photon is Planck’s constant divided by its wavelength. This principle is used to compute radiation pressure and Compton scattering.

The photon momentum is

\[ p_{\mathrm{ph}} = \dfrac{h}{\lambda} \]

where

  • \(p_{\mathrm{ph}}\) is the photon momentum.
  • \(h\) is Planck’s constant.
  • \(\lambda\) is the photon wavelength.

The relation \(p=E/c\). The same momentum is the photon energy divided by the speed of light. This principle is used to write \(p = E/c\) for a massless quantum.

The energy-momentum relation of a photon is

\[ p = \dfrac{E}{c} = \dfrac{hf}{c} \]

where

  • \(p\) is the photon momentum.
  • \(E\) is the photon energy.
  • \(c\) is the speed of light.
  • \(h\) is Planck’s constant.
  • \(f\) is the frequency.

The inverse relation of momentum to wavelength. Shorter wavelengths carry larger photon momentum. This principle is used to compare ultraviolet, visible, and infrared photons.