How to Calculate a Wavenumber
- 1). Divide one by the wavelength to calculate the wavenumber.
Wavenumber= 1/wavelength
For example, calculate the if the wavelength is 5.5E-5 meters then
Wavenumber=1/5.5E-5=18182 m^-1. - 2). Divide the wavenumber value in m^-1 by 100 to obtain it in inverse centimeters.
Wavenumber=18182 m^-1/100=181.82 cm^-1. - 3). Using the links in resources obtain the values of the fundamental physical constants (speed of light and Planck constants) .
Speed of light (c) =299,792,458 m/s.
Planck constant (h) =4.13566733E'15 eV s (1E-15 denotes "ten in power -15"). - 4). Divide energy by the product of the physical constants (Step 3) calculate the wavenumber.
Wavenumber (in m^-1)= Energy/h x c= Energy/ 299,792,458 m/s x 4.13566733E'15 eV s/ = Energy/1.23984187E-6. Note that energy has to be expressed in "electron volt (eV)" units.
Example: if energy is 0.25 eV then
Wavenumber=0.25/1.23984187E-6=201638 m^-1 or 2016.38 cm^-1 (see Step 2). - 5). Divide frequency by the speed of light to obtain the wavenumber.
wavenumber (m^-1)= frequency/c = frequency (Hz)/299,792,458 (m/s). Note that frequency is measured in Hertz (Hz).
As example, calculate the wavenumber for the frequency of 5E13 Hz.
Wavenumber=5E13 Hz/299,792,458 (m/s)=166782 m^-1=1667.82 cm^-1.