Thursday, November 17, 2011

Energy Spectrum

kw: analysis, observations, particle physics

While a number of web sites illustrate the energy spectrum, none covers the entire useful range. This picture shows a chart that I'd have preferred as a table, but this blogging tool does a particularly bad job displaying tables. To see the table more clearly, right click on it and choose "Open Link in New Tab" or "Open Link in New Window".

While this might be called the electromagnetic spectrum, I have specifically included a range of energies very seldom probed by photons, energies higher than a few GeV, which are typically found only in baryons accelerated by synchrotrons and in cosmic rays. At these high energies, the particles are moving close enough to c that the wavelength-energy conversion is a reasonable approximation.

This is an energy spectrum, so the table is based on the energy, in electron-volts (eV) in the first two columns. Column 1 is the lower limit of a decade range shown in scientific notation, and Column 2 (blue) shows more conventional units for each range, from 100 femto-eV (feV) to 1 Zetta-eV (ZeV). The reason I went no further will be explained later on.

The central column, wavelength (λ), ranges downward from tens of thousands of km to the yoctometer (ym) range, and smaller. The ym is the smallest defined length unit, though I suppose I could have expressed these shorter wavelengths in Planck units. The conversion from E to λ is hc, or 1.2398419 eV-μ, which is 1.2398419x10-6 eV-m. Rounding to 1.24 eV-μ introduces only a small error, about 0.01%.

The next column, frequency (f, brown), is proportional to energy, and ranges from a few Hz to many YottaHertz (YHz) and higher. This is the highest frequency we have a defined prefix for. The conversion from λ to f is the speed of light, 299,792,458 m/s. Rounding to 3x108 introduces an error less than 0.1%.

Finally, each range has a descriptive term applied, but we should realize there is quite a bit of overlap between some of the ranges. For example, extreme UV and soft x-rays overlap, and the term used depends on how someone is using them. Now let's take a little tour.

Acoustic Range

We seldom realize it, but we are constantly bathed in a low level of either 50- or 60-Hz "hum" from fluorescent lights, electric motors and other things energized by "wall current". The last time I was in Japan, I noticed that the power in the Tokyo area was 60 Hz, but the rest of the country was still using 50 Hz power. It made a difference in how my electric shaver sounded. By working backward through the conversions, we find that 50 and 60 Hz have wavelengths of 6,000 and 5,000 km, respectively, and photon energies of 2.067x10-13 and 2.48x10-13 eV. In ranges much below 1 eV, photon energy doesn't mean much, because the photoelectric effect or other particle interactions don't operate.

The highest note on a piano is 4,186 Hz (4.186 kHz), based on standard tuning of A=440 Hz. The electromagnetic wavelength of this note is 71.7 km, but the acoustic wavelength in standard, sea-level air is 81mm.

The high squeal of an old, CRT-type TV set is 14.75 kHz, which young people can hear, but oldsters like me cannot. Its EM wavelength is 20.3 km.


I am a radio ham. The lowest frequency hams can use at present is 1.8 MHz, which has a wavelength of 167 m. The band's upper edge is 2 Mhz, with a wavelength of 150 m. The band is called the 160 meter band. There are a large number of amateur and international broadcast short-wave bands in the HF (high frequency) range. The most popular are near 14 MHz, the ham's "20-meter band" (14.0-14.35 MHz, with wavelengths of 21.4-20.0 m) and the broadcasters' "19-meter band" (15.1-15.9 MHz, and 19.9-19.0 m wavelength).

VHF and UHF designate frequencies from 30-300 and 300-3,000 MHz. This very useful range is filled with broadcast TV, point-to-point radio, cellular phone services, and at 2,450 MHz (2.45 GHz), microwave ovens. The microwave oven wavelength is 122 mm. This is a compromise frequency. Firstly, it was a political compromise, as various regulatory bodies had to determine a frequency range that wouldn't interfere with existing communications and control services. But using this frequency rather than one much higher or lower is also a compromise. Microwave ovens don't heat evenly because the way the waves bounce around inside the cavity creates higher- and lower-power spots. A much lower frequency would heat more evenly, but much less efficiently. A very much higher frequency would also heat more evenly, but the heat would not penetrate very deeply into the food, and penetration was considered more important than evenness of heating. Besides, most modern microwave ovens have turntables; just be sure to put the item being heated a little off center, which helps the waves spread around better.

The range of energies considered "radio+microwave" keeps expanding. The current limit is about 100 GHz, with wavelengths near 0.3 mm. Above this is the T-ray or T-wave realm, from 0.1 to 100 THz. These are just beginning to be used in place of backscattered x-rays for screening airport passengers for weapons. They can allow an operator to see weapons that a metal detector would miss. The trouble is, with their sub-millimeter resolution and ability to pass right through most fabrics, they produce a "naked" image of a person, so at least in America, there are huge privacy fights going on about them. Personally, I figure if an operator, whether male or female, gets a few jollies from seeing a T-wave image of me, that's not my problem, it is his or hers.

Near-Visible and Visible Ranges

Wavelengths shorter than about 0.1mm are called extreme infrared (EIR), and the IR ranges through far IR (FIR, but used rarely) to near IR, which ends at 0.7μ, at the red end of visible light. The remote control that runs your TV uses one of two IR wavelengths, either 0.8μ or 1.2μ, both of which are pretty easy to produce and detect. The shorter wavelength is less common, because many Asian people can see it. The frequency of 0.8μ is 375 THz, and of 1.2μ is 250 THz. Here the photoelectric effect gets going well enough that it is worth reporting the energies: 1.55 and 1.03 eV, respectively.

The wavelength of greatest visibility is usually quoted as 555nm (0.555μ), with a frequency of 540 THz and a photon energy of 2.23 eV. The bluest light usually seen is at 400 nm, although people who have had cataracts removed can see near-UV light as "blue" as 360 nm. These limits have frequencies of 750 and 833 THz, respectively, and photon energies of 3.10 and 3.44 eV.

Light bluer than about 300 nm is absorbed by the atmosphere, but shorter wavelengths in the "vacuum UV" range are very useful for chemical identification. They are also useful for astronomy, so far-UV and extreme-UV telescopes have been placed in orbit. The conventional limit of UV astronomy is 91.2 nm, because shorter wavelengths are strongly absorbed by neutral hydrogen in space. This limit's frequency is 3,290 THz or 3.29 PHz. Above the PetaHertz range we seldom mention frequency, because we are in the realm of particle behavior. This limit has a photon energy of 13.6 eV, which is enough to totally ionize a hydrogen atom.


X-rays are defined as electromagnetic radiation produced by accelerated electrons, further delimited as ionizing, so the softest x-rays are the 92.1 nm radiation that ionizes hydrogen.

From this point, particle energy is the key parameter and secondarily, wavelength. The beginning of the soft x-ray range is conventionally 10 nm, with photon energy of 124 eV. X-rays are not very penetrating at energies below about 1 keV, which has a wavelength of 1.24 nm. Your doctor's or dentist's x-ray machine uses a broad-spectrum source with a peak near 60 keV and a wavelength near 0.02 nm or 20 pm. In older literature, this was called 0.2 Angstroms. The hardest x-rays are about twice this energetic, at 120 keV and 10 pm wavelength.

Gamma Radiation

Gamma radiation originates in the atomic nucleus, or by energetic particle interactions such as electron-positron annihilation. The softest gamma rays are about as energetic as soft x-rays, but the typical gamma ray has an energy of one or more MeV. Gamma rays as energetic as 6 MeV are produced by alpha emitters such as Uranium; such a photon has a wavelength of 0.2 pm or 200 fm (femtometers). Gamma ray photons and other particles with such energies are useful probes of the nucleus, which is also measured in fm.

One useful gamma radiation energy is 511 keV, which equals the rest mass of an electron. When an electron and a positron annihilate each other, they produce two gamma rays with this energy (and a 2 pm wavelength). In particle accelerators, protons and antiprotons are produced in copious amounts. Annihilation radiation for proton-antiproton interaction is a pair of gamma ray photons with an energy of 938 MeV. This near-GeV range is the upper limit of useful gamma ray photon energies. There are no natural processes that produce photons above this range, except scattering of lower-energy photons by cosmic rays.

Cosmic Rays

Cosmic rays are not photons, they are matter particles: mostly protons, a few electrons, and even fewer heavier nuclei. They come in energies throughout the energy range, but particles with less than 9 GeV don't make it through the Earth's magnetic field. Some are guided by the field to Earth's poles, where they stimulate aurorae. More energetic particles reach the atmosphere and scatter off atmospheric atoms to create air showers of less energetic particles. Detecting and summing up an air shower allows us to characterize the original particle, at least by its incoming energy.

The spectrum of cosmic rays is scale-free, smoothly descending in numbers with higher energies, to a cutoff near 6x1019 eV. Above this energy, an energetic proton that has traveled more than a hundred million parsecs will have scattered off many photons of the cosmic background radiation, losing energy even while it produces those rare multi-GeV photons. In spite of this, a few huge air showers have been detected that indicate an ultra-high-energy cosmic ray occasionally makes it through to Earth with an energy between 1 and 3x1020 eV. That last represents a proton with the energy of a well thrown baseball, as much as 50 Joules.

It is not known how the most energetic cosmic rays originate. Perhaps a proton-proton collision can give one a "kick" at the expense of the other, near enough to Earth that CMB scattering doesn't bleed off too much energy. I suspect the limit of my scale, at 1021 eV, will never be detected. The air shower would be larger than the largest detector array we can build on the planet's surface!

Tour over. You may now unbuckle your seat belt and disembark.

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