# Difference between revisions of "Wavenumber"

Mark Widmer (Talk | contribs) (Clarified that wavenumber is reciprocal of wavelength, and that wavevector (sometimes also called wavenumber) is different than wavenumber.) |
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− | In science, the '''wavenumber''' indicates the number of wavelengths that would fit in a unit of length. | + | In science, the '''wavenumber''' indicates the number of wavelengths that would fit in a unit of length, and is numerically equal to the reciprocal of the wavelength. The normal units for wavenumbers are inverse centimeters cm<sup>-1</sup>. A different name for this unit is kayser (after [[Heinrich Kayser]]). Light with a wavelength of 500 nm (green) has a wavenumber of 20,000 cm<sup>-1</sup> or 20 kK. Photon energy and frequency are proportional to wavenumber: 10 kK corresponds to 1.24 eV. |

Historically, wavenumbers were introduced by [[Janne Rydberg]] in the 1880's in his analyses of atomic spectra. | Historically, wavenumbers were introduced by [[Janne Rydberg]] in the 1880's in his analyses of atomic spectra. | ||

− | + | The wavevector(<math>k</math>), wavelength (<math>\lambda</math>), and frequency (<math>f</math>) are related: | |

− | :<math>k = \frac{2 \pi}{\lambda}, \qquad k = \frac{2 \pi f}{v}</math> | + | :<math>k = \frac{2 \pi}{\lambda}, \qquad k = \frac{2 \pi f}{v},</math> |

+ | |||

+ | where <math>v</math> is the speed of the wave. | ||

+ | |||

+ | Sometimes (<math>k</math>) is also referred to as wavenumber, but is greater by a factor of <math>2 \pi</math> than the wavenumber described earlier as the reciprocal (<math>1/\lambda</math>) of the wavelength. |

## Revision as of 03:08, 24 October 2020

In science, the **wavenumber** indicates the number of wavelengths that would fit in a unit of length, and is numerically equal to the reciprocal of the wavelength. The normal units for wavenumbers are inverse centimeters cm^{-1}. A different name for this unit is kayser (after Heinrich Kayser). Light with a wavelength of 500 nm (green) has a wavenumber of 20,000 cm^{-1} or 20 kK. Photon energy and frequency are proportional to wavenumber: 10 kK corresponds to 1.24 eV.

Historically, wavenumbers were introduced by Janne Rydberg in the 1880's in his analyses of atomic spectra.

The wavevector(), wavelength (), and frequency () are related:

where is the speed of the wave.

Sometimes () is also referred to as wavenumber, but is greater by a factor of than the wavenumber described earlier as the reciprocal () of the wavelength.