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
applies exactly only in vacuum.
Note also photon energy
and wavenumber
are both just proportional to
frequency.
Which wave specification
you use depends on convenience or convention.
To explicate conventional uses:
- wavelength
is conventionally used for the:
- ultraviolet band (fiducial range 0.01--0.4 μm).
- visible band (fiducial range 0.4--0.7 μm).
- infrared band (fiducial range 0.7 μm -- 0.1 cm).
The
units used are usually any of:
- angstrom (Å) = 0.1 nm = 10**(-10) m.
- nanometer (nm) = 10**(-9) m.
- micron (μm) = 10**(-6) m.
- 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:
- kilohertz (kHz) = 10**3 Hz.
- megahertz (MHz) = 10**6 Hz.
- gigahertz (GHz) = 10**9 Hz.
- terahertz (THz) = 10**12 Hz.
- 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:
- X-ray band (fiducial range
0.1240--124.0 keV, 0.1--100 Å)
- 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.
- 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
was conventionally used in spectroscopy,
but is nowadays becoming
obsolete
yours truly thinks.
Credit/Permission: ©
Philip Ronan (AKA User:Sakurambo,
2007 /
Creative Commons
CC BY-SA 3.0.
Image link: Wikipedia:
File:EM spectrum.svg.
Local file: local link: electromagnetic_spectrum_wave_specification.html.
File: Electromagnetic Radiation file:
electromagnetic_spectrum_wave_specification.html.