# Frequency in units of inverse length?

1. Jul 17, 2007

### GammaMacht

Hi, when someone gives me an angular frequency in units of inverse length (i.e., 520.5 cm^-1) how do I convert that to a frequency and and energy (say, in eV?). Thanks for the help!

2. Jul 17, 2007

### GammaMacht

Ahh nevermind, it was just a typo in my calculator. I thought I was going crazy

3. Jul 17, 2007

### xez

You have a wavenumber of N/cm indicating the number
of waves per unit length.

Wave length is related to
Wave frequency and Wave speed by
Wave length [cm] = Wave speed [cm/s] / Wave freq [1/s]

so the (inverse Wave length) = 1/cm =
Wave number per cm =
Wave frequency [1/s] / wave speed [cm/s]

To get Wave frequency:
Wave frequency [1/s] =
Wave number [1/cm] * Wave speed [cm/s]

The speed of light in a vacuum is:
c=2.9979*10^10 cm/s

so in a vacuum Wave frequency [1/s] =
c [cm/s] * Wave number [1/cm].

Photon energy increases with frequency i.e.
energy is proportional to reciprocal wavelength.

Planck's constant = hbar = 6.6260755*10^-34 [J*s]

One eV = 1.60217733*10^-19 J = [J/eV]
So [eV/J] = 1/1.60217733*10^-19 = 6.24150636*10^18.

We can relate the dimensional units as:
Joules = hbar [Js] * Wave Frequency [1/s]
eV = Joules * eV/J = eV/J * hbar [Js] * Wave Frequency [1/s]

photon energy [J] = hbar [Js] * Photon Vacuum Freq. [1/s]

photon energy [eV] = eV/J * hbar [Js] * Photon Vacuum Freq. [1/s]

photon energy [eV] = 6.24150636*10^18 [eV/J] * 6.6260755*10^-34 [hbar Js] * Photon Vacuum Freq. [1/s]

photon energy [eV] = 6.24150636*10^18 [eV/J] * 6.6260755*10^-34 [hbar Js] * Photon Vacuum Freq. [1/s]

photon energy [eV] = 4.13566924*10^-15 [eV/s] * Photon Vacuum Freq. [1/s]

photon energy [eV] = 4.13566924*10^-15 [eV/s] * c [cm/s] * Photon Vacuum Wave Number [1/cm] =

photon energy [eV] = Photon Vacuum Wave Number [1/cm] / 8065.60706

At 100 nanometer vacuum wavelength = 10^5 wavenumber [1/cm] : eV = 10^5/8065.60706 = 12.398eV
At 01 micrometer vacuum wavelength = 10^4 wavenumber [1/cm] : eV = 10^4/8065.60706 = 1.2398 eV
At 10 micrometer vacuum wavelength = 10^3 wavenumber [1/cm] : eV = 10^3/8065.60706 = 0.12398 eV

The vacuum frequency of a photon relates to the material (non vacuum) number
depending on the refractive index of the medium of propagation.

The wave is slowed in the medium by:
speed_of_light_in_medium = speed_of_light_in_vacuum / n
where n is the refractive index of the medium.

The wavelength is shorter in the medium than it would be in free space by:
wavelength_in_medium = wavelength_in_vacuum / n
where n is the refractive index of the medium.

If you know the permittivity and permeability figures for the medium at the wavelength of interest,
you can also calculate the light propagation speed in the medium via:
speed_of_light_in_medium = 1/sqrt(e0*er*u0*ur)
where:
e0 = permittivity of free space = 8.854187817*10^-12 [F/m]
u0 = permeability of free space = 4 * Pi * 10^-7
er = relative permittivity of material over free space permittivity
ur = relative permeability of material over free space permeability

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook