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# Photon Frequency and Energy

Light is composed of particles, called photons, that carry an electric and magnetic field. When a large enough number of photons travel together—for instance, in a radio wave—the individual photons blend together, and we see a large-scale electric and magnetic field without seeing the individual photons. Because photons always travel at the speed of light relative to any object with mass, the electric and magnetic fields, which vary in time and space, pass by as a wave traveling at the speed of light. The electric field is perpendicular to the direction of motion of the photon, and the magnetic field is perpendicular to both the direction of motion and the electric field. At any point in the wave, the magnitude of the magnetic field equals the magnitude of the electric field.

One property of a wave is that it can be described as a collection of sine waves of various frequencies; the frequency measures the number of oscillations a sine wave makes per second as measured at a fixed point. In the case of light, the frequency ν measures the oscillation of the electric and magnetic fields.

In addition to a frequency, a wave is described by a set of wavelengths that describe the variation of a wave in space at any given time. For light, the variation is again in the electromagnetic field of the wave. For a pure sine wave, the wave length λ measures the distance between points where the electric fields are pointing in the same direction with the same magnitude. The wavelength of a sine wave is related to the frequency through the speed of light, so that ν λ = c.

Any wave can be decomposed into a set of sine waves. When decomposed in this way, the result is a spectrum, which shows the contribution of each sine wave frequency to the overall wave. For light, the spectrum is normally expressed as a flux of energy, given in units of power per unit area per unit frequency.

An interesting property of photons is that the energy each photon carries is related to the set of frequencies that describes its electromagnetic field. For a photon whose field varies as a pure sine wave, the energy is proportional to the frequency. This is given by

E = h ν ,

where E is the energy of the photon and h = 6.626×10−27 ergs s is Planck's constant.

These relationships between energy, frequency, and wavelength mean that any of these measures can be used to describe the spectrum of an electromagnetic wave. In practice, different observing communities use different units. To some extend this reflects the nature of the detector. The radio astronomy community always speaks in terms of frequency rather than energy, because they observe radio waves as a continuum electromagnetic field rather than as a collection of photons. The x-ray and gamma-ray astronomy communities, in contrast, always express their observations in terms of photon energy, because they detect individual photons rather than a collective electromagnetic field, and a photon interact with the detector by dumping part or all of its energy into the detector.

My own preference for photon energy is units of electron rest mass energy, but I'm a theorist, and theorists are notorious for wanting to set as many physical constants as possible to unity. Field theorists are the extreme example of this, setting the speed of light, the Planck constant, and the gravitational constant all to unity. So as not to burden you, I will stick to the units used by observers.

In general, in the far infrared and below, a spectrum is described in terms of frequency, which is given in units of Hertz (Hz), which is the number of cycles per second, or some multiple of Hertz, such as kilohertz (1kHz = 1,000 Hz), megahertz (1 MHz = 106 Hz), or gigahertz (1 GHz = 109 Hz). This community also uses wavelength, measuring the wavelength in meters or centimeters. The infrared, optical, and ultraviolet communities generally speak in terms of wavelength, using as their measure the centimeter, the micron (10−7 cm), or the angstrom (10−8 cm). The far infrared, x-ray, and gamma-ray communities speak in terms of photon energy, and their favorite unit of measure is the electron volt, which is normally expressed in units of kilo-electron volt (1 keV = 1,000 eV), mega-electron volt (MeV = 106 eV), giga-electron volt (GeV = 109 eV ) and the tera-electron volt (TeV = 1012 eV). The high energy community also likes to express the photon flux as counts (which is what detectors register) or photons (which has an energy that is deduced from a knowledge of detector physics) per unit time per unit area per unit photon energy.

The table that follows relates the different energies.

## Units of Photon Frequency and Energy

 1 cm 2.99792458×1010 Hz 1 Å (Angstrom) 2.99792458×1018 Hz 1 eV 2.417898940(21)×1014 Hz 1 keV 2.417898940(21)×1017 Hz 1 MeV 2.417898940(21)×1020 Hz