Wavenumber to Wavelength Conversion

By Sean Lancaster
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The study of electromagnetic radiation covers a large range of wavelengths. It spans from nm or Angstroms for visible light to meters for radio waves. Each region of the spectrum has its own terminology for expressing the wavelength of the radiation. A rather unique unit of measure occurs in the infrared and near infrared region of the spectrum. The wavelengths are measured in wavenumbers (cm^-1). In order to work across a wider range of the spectrum, it is helpful to convert from this odd reference system to a system that is more standard for discussing wavelength.

Wavenumbers are Wavelengths

The typical method of expressing wavelength of radiation is by expressing it as a unit of length like m or nm. Reporting wavelength in units of wavenumbers only occurs in the near infrared and infrared region of the electromagnetic spectrum. It is a measure of length but not in the same format you are used to seeing it. The conversion to other more traditional units of measurement is not complicated but does require your understanding of the relative sizes of the units used.

Wavenumber to Microns

In the infrared and near infrared region, wavelengths on the scale of microns are typical. Converting from wavenumbers to microns is accomplished by utilizing a conversion factor that changes cm^-1 to microns. There are 10,000 microns per cm. To convert wavenumbers to microns, divide 10,000 by the number of wavenumbers to yield the wavelength expressed in microns.

Wavenumbers to Nanometers

The closest wavelength range to the near infrared is the visible spectrum. The human eye can see these wavelengths. Everything that you perceive every day emits or reflects light in the range of approximately 400 to about 700 nm. The conversion of wavenumbers to nm is possible by using a conversion factor of 10,000,000 nm per cm. Divide 10,000,000 by the number of wavenumbers to yield the wavelength in units of nm.

Conversion to Other Spectral Regions

You can convert wavenumbers to any other unit of measurement for wavelength in other regions of the electromagnetic spectrum. The limitation you will reach is that you must understand the relative size of each of the other units of measure to cm. The conversion factor incorporates the relative size difference of the unit of measure to cm. Divide the relative difference by the wavenumbers. The result of this calculation is the wavelength in the new unit of measure.

About the Author

Sean Lancaster has been a freelance writer since 2007. He has written for Writers Research Group, Alexis Writing and the Lebanon Chamber of Commerce. Lancaster holds a Doctor of Philosophy in chemistry from the University of Washington.