wavenumber

wavenumber, a unit of frequency, often used in atomic, molecular, and nuclear spectroscopy, equal to the true frequency divided by the speed of the wave and thus equal to the number of waves in a unit distance. In the case of light, the frequency, symbolized by the Greek letter nu (ν), of any wave equals the speed of light, c, divided by the wavelength λ: thus ν = c/λ. A typical spectral line in the visible region of the spectrum has a wavelength of 5.8 × 10⁻⁵ cm; this wavelength corresponds to a frequency (ν) of 5.17 × 10¹⁴ Hz (hertz equals one cycle per second) obtained from the equation. Because this frequency and others like it are so extremely large, it is convenient to divide the number by the speed of light and hence reduce its size. Frequency divided by the speed of light is ν/c, which from the above equation is 1/λ. When wavelength is measured in metres, 1/λ represents the number of waves of the wave train to be found in a length of one metre or, if measured in centimetres, the number in one centimetre. This number is called the wavenumber of the spectrum line. Wavenumbers are usually measured in units of reciprocal metres (1/m, or m⁻¹) or reciprocal centimetres (1/cm, or cm⁻¹). The angular wavenumber k = 2π/λ expresses the number of radians in a unit of distance.