Difference between revisions of "Wavenumber"

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(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. 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&nbsp;kK. Photon energy and frequency are proportional to wavenumber: 10&nbsp;kK corresponds to 1.24 eV.
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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&nbsp;kK. Photon energy and frequency are proportional to wavenumber: 10&nbsp;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.
  
Wavenumbers (<math>k</math>), wavelength (<math>\lambda</math>), and frequency (<math>f</math>) are related:
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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>
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:<math>k = \frac{2 \pi}{\lambda}, \qquad k = \frac{2 \pi f}{v},</math>
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where <math>v</math> is the speed of the wave.
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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.

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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.