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Mathematics for Physics

80 Photon Momentum

The momentum carried by a photon, equal to Planck’s constant divided by its wavelength, that is used to compute the momentum of a light quantum from its wavelength.

(\(p = h/\lambda\)).

definition [d] (Photon Momentum) From Emam: quantum mechanics teaches us that the momentum of the photon is

  • \(p_{\mathrm{ph}} = \dfrac{h}{\lambda}\) ,

where \(h = 6.626 \times 10^{-34}\,\mathrm{J\cdot s}\) is Planck’s constant and \(\lambda\) is the photon’s wavelength.

where

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

80.1 Elementary Example

80.1.1 Simple

A photon with \(\lambda = 500\,\mathrm{nm}\) has momentum \(p = h/\lambda\).

\[ \lambda = 5.00 \times 10^{-7}\,\mathrm{m} \]

\[ p = \dfrac{6.626 \times 10^{-34}}{5.00 \times 10^{-7}} = 1.325 \times 10^{-27}\,\mathrm{kg\cdot m/s} \]

where

  • \(p\) is the photon momentum.

80.1.2 General

Shorter wavelengths carry larger photon momentum.

\[ \lambda_{1} = 400\,\mathrm{nm},\quad \lambda_{2} = 500\,\mathrm{nm},\quad \lambda_{3} = 600\,\mathrm{nm} \]

\[ p_{i} = \dfrac{h}{\lambda_{i}} \]

where

  • each \(p_{i}\) is the momentum of a photon of wavelength \(\lambda_{i}\).