Caption: The electromagnetic spectrum.

Wave Specification: Frequency, Wavelength, Photon Energy, Wavenumber:

Periodic waves can be specified (or characterized) by either wavelength λ or frequency f since they are reciprocals of each other aside from a constant as shown by the generic phase velocity formula fλ=v_phase where v_phase is the phase velocity, the velocity at which a waveform propagates. The 2 specifications have the same information content.

Electromagnetic radiation (EMR) waves are a special case since they can be specified in 4 related ways with the same information content: by wavelength λ, frequency f = c/λ, photon energy E = hf = hc/λ = 1.2398419739(75) eV-μ/λ_μ and wavenumber k = 1/λ, where vacuum light speed c = 2.99792458*10**8 m/s (exact by definition) ≅ 3*10**8 m/s = 3*10**5 km/s ≅ 1 ft/ns, Planck constant h = 6.62607015*10**(-34) J·s = (4.135667696 ...)*10**(-15) eV-s (exact by definition), and the electron-volt (eV) = 1.602176634*10**(-19) J (exact by definition).

Note the most familiar wave specification formula for EMR

  fλ=c 

Which wave specification you use depends on convenience or convention.

To explicate conventional uses:

1. wavelength is conventionally used for the:
   1. ultraviolet band (fiducial range 0.01--0.4 μm).
   2. visible band (fiducial range 0.4--0.7 μm).
   3. infrared band (fiducial range 0.7 μm -- 0.1 cm).
   The units used are usually any of:
   1. angstrom (Å) = 0.1 nm = 10**(-10) m.
   2. nanometer (nm) = 10**(-9) m.
   3. micron (μm) = 10**(-6) m.
2. frequency is conventionally used for the radio band (fiducial range 3 Hz -- 300 GHz = 0.3 THz, 0.1 cm -- 10**5 km) usually using as convenient any of the units:
   1. kilohertz (kHz) = 10**3 Hz.
   2. megahertz (MHz) = 10**6 Hz.
   3. gigahertz (GHz) = 10**9 Hz.
   4. terahertz (THz) = 10**12 Hz.
3. photon energy E = hf = hc/λ = 1.2398419739(75) eV-μ/λ_μ (where the formulae are the de Broglie relations and the electron-volt (eV) = 1.602176634*10**(-19) J (exact by definition)) is conventionally used for the:
   1. X-ray band (fiducial range 0.1240--124.0 keV, 0.1--100 Å)
   2. gamma ray band (fiducial range 1 keV--∞ = 0.001--∞ MeV).
   Note the fiducial ranges for the X-ray band and the gamma ray band overlap. In fact, there is NOT a sharp division (unless one is defined) between the 2 electromagnetic spectrum bands since the physical processes most associated with the production of what are deemed X-rays and what are deemed gamma rays overlap in their ranges of produced photon energies. Yours truly thinks that photon energy should be used for all electromagnetic spectrum bands both for uniformity and because photon energy is often the physically most relevant information about EMR.
4. wavenumber k = 1/λ is also conventionally used for the ultraviolet band (fiducial range 0.01--0.4 μm), visible band (fiducial range 0.4--0.7 μm), and infrared band (fiducial range 0.7 μm -- 0.1 cm) with the common unit being inverse centimeters (cm**(-1)). Wavenumber by the just-given definition is often used in spectroscopy and chemistry. However, there is an alternate definition used in theoretical physics: wavenumber k = 2π/λ (see Wikipedia: Wavenumber: Definition).

Credit/Permission: © Philip Ronan (AKA User:Sakurambo, 2007 / Creative Commons CC BY-SA 3.0.
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