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The electromagnetic spectrumFrom Physclips: Physics with animations and film.

Electromagnetic waves fill a spectrum with wavelengths from thousands of kilometres long down to

wavelengths more than 1020 times smaller. They may be detected using a range of quite different

instruments. As the graphic shows, visible light comprises only a tiny fraction of this spectrum: less than

an octave. Photon energies also vary over this huge range: in the radio band we collect huge numbers

of photons, each having only a tiny energy. The phase of the photons in a radio transmission is not

random: it is such that their fields add together, and we can therefore observe their combined electric

and magnetic fields as they oscillate in time and space. For gamma rays, we may observe the effects of

many charged particles, all created by a single photon.

This page discusses the uses and properties of the different bands, and several of the important

concepts associated with electromagnetic waves.

Radio: standard names, frequencies and wavelengths

Infrared, visible, ultraviolet, Xrays, gamma rays

Common names for radio bands

MeasurementPhotons: wave vs particle vocabularies for EM radiation

Temperature and colour

Photons and chemistry

EntropyInformation

Standard names for radio bands

In one classification system, the waves used for radio communication (and other purposes) are neatlydivided up in decades, ie divided into bands whose wavelengths and frequencies vary over a factor of

10. In wavelength, the bands begin and end on metres times a power of ten. Because the speed of light

is close to 3 10 8m/s, when these bands are expressed in frequencies, their limits are 3 times a power

of 10 Hz. eg for 3 GHz, λ = c/f = 10 cm. The names of the bands are:

Sources in the Super Low and Extra Low Frequency bands (SLF and ELF) are

mainly accidental or natural. For instance, electricity authorities have very long antennae, calledpower lines, that radiate at 50 or 60 Hz. This signal is picked up as 'hum' and is cursed by

electrical engineers everywhere. A large natural source is the interaction of the solar wind with

the ionosphere that produces low frequency currents (telluric currents) in the earth and oceans,

and these are studied by geophysicists to deduce, inter alia, the presence of ore bodies whose

electrical conductance differs from that of the surrounding crust. Like ULF, these bands may be

used for communication with submarines, with low information rates.

300 Hz - 3 kHz. Ultra Low Frequency (ULF). Electromagnetic waves in this rangeare not strongly absorbed by water or the earth. They may therefore be used to communicate

with submarines and with mines. One disadvantage is that, with such low frequency, one can

only modulate their amplitude or frequency very slowly (eg with morse code) so they cannot

carry much information. This is not a disadvantage if only the phase is required, as is the case for

navigation systems. The wavelengths are so long that antennae may be huge.

3 - 30 kHz. Very Low Frequency (VLF). Again, the information carrying capacity islimited. These are used in navigation systems.

30 - 300 kHz. Low Frequency (LF). This band has the advantage that it can propagate

around the Earth, by refraction and reflection at the ionisphere or the surface of the Earth itself.

Indeed, these two conductors form a waveguide for waves in this range, which can therefore be

used to communicate across the oceans and around the world.

The electromagnetic spectrum

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300 kHz - 3 MHz. Medium Frequency (MF). (This includes the AM radio band: see

below). These waves are not so well reflected/refracted by the ionosphere, but at night there is

enough reflection that one can pick up radio stations hundreds or thousands of km away. This is

not possible with the much shorter waves used for FM radio or television: for these you need an

unobstructed path to the transmitter that is not much different from a straight line.

3 - 30 MHz. High Frequency (HF). This is also known as the Short Wave band. Itincludes the CB band (see below) and the channels used for radio control. As the frequency of

the carrier wave increases, it becomes possible to encode more information and to crowd

channels (proportionately) closer together.

30 - 300 MHz. Very High Frequency (VHF). (includes FM radio and television).

Antennae are often made to be about one quarter or one half wavelength long.

300 MHz - 3 GHz. Ultra High Frequency (UHF). (GHz = 109 Hz). This includes

some television and mobile phones: see below. Many channels are available.

3 - 30 GHz. Super High Frequency (SHF). (roughly corresponds to microwaveband) Used for communication with satellites.

30 - 300 GHz. Extra High Frequency (EHF). Not much used for radio

communication (yet), because of the technological difficulty of encoding and decoding amplitude

and frequency modulation at such high frequencies.

Here ends the radio band. Hereafter, wavelengths are used almost exclusively, partly for traditional

reasons, and partly because frequencies in the THz range (THz = 1012 Hz) are difficult to measure

directly. (They can be measured by heterodyning: observing the difference frequencies they make with

reference signals.)

Infrared, visible, ultraviolet, X and gamma rays

Infrared: wavelengths longer than visible and up to about 1 mm (often measured in microns ormicrometres, symbol μm). Infrared radiation can be felt as radiant heat: eg when you stand in

front of a fire. Some snakes have IR sensors. The military uses IR binoculars for the samereason as snakes do: to find mammals, who are usually warmer than our surroundings.

Visible: Wavelengths are about 400 nm (violet light) to 700 nm (red light). A nanometre,

symbol nm, is 10-9 m. The sun radiates most strongly in this range, and our atmosphere does not

absorb it (Los Angeles excepted). This is not a coincidence: we have evolved on this planet inthis atmosphere, so of course we have evolved sensors that use the available radiation. (Pace

Drs Pangloss, Liebniz and certain other naifs. Any readers interested in teleology should followthis link.) Visible light can cause chemical reactions (eg vision and photosynthesis) but usuallydoes not. The diodes used in solar cells work at a potential difference of about 0.6 volts, so

every visible photon has enough energy to shift one electron across the interface. See theintroductory page on the photovoltaic effect.

Ultraviolet: wavelengths shorter than visible, down to about 10 nanometres. UV is more

useful in chemistry, because each photon has energy comparable with that of a chemicalreaction. It is dangerous for the same reason: a UV photon has enough energy to damage DNA

molecules in your cells (so remember to wear sunscreen and a hat). If objects are hotter than thesun (eg some massive young stars), they radiate in the UV. Bees can see in the near UV and so

flowers have UV colours to attract them. (Bees can also see the polarisation of light, which theyuse to navigate, but that's another story.) When the energy of photon is high enough, it is oftenexpressed in electron volts: an ultraviolet photon with 10 eV or more has enough energy to

ionise an atom if its outer electron is held at an electric potential of 10 Volts. This is typical of thebinding energies of atoms, which is why UV is chemically potent.

X rays: wavelengths from several nm to 10 pm (a picometre is 10-12 m). Xrays with

wavelengths comparable to atom dimensions are used to determine the structure of crystals, in atechnique developed by the Australian physicists, William and Lawrence Bragg, for which theyreceived the Nobel prize in 1915. X rays are divided informally into 'soft' X rays with long

wavelengths and 'hard' X rays with shorter wavelengths and higher energies. Their energies areenough to ionise atoms and to destroy chemical bonds. They are produced naturally by some

radioactive sources, or by very hot objects like neutron stars. They are also produced by

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smashing high energy electrons into metal targets: X rays thus produced are used to treat

cancers including breast cancer. Soft X rays are stopped by (enough) air. Hard X rays can

penetrate deeply into tissue.

Gamma rays: wavelengths less than about 10 pm. They have very high energy, and oftencome from deep space, sometimes in bursts from cataclysmic cosmic events, such as the

collapse or collision of stars. A 10 GeV cosmic ray has the same energy as an electron wouldhave it were accelerated through 10 billion volts. This is enough energy to cause a chain reaction

of ionisation events in the Earth's atmosphere, leading to a shower of charged particles.

Common names for radio bands. For practical purposes, other divisions of the radio part of the spectrum are used, including those bandsallotted for specific types of communication. So for instance people talk of the AM radio band, of the CB band etc. Here are some examples:

AM radio: 535 - 1,700 kHz (0.535 - 1.7 MHz) Have a look at the dial on your radio and check the frequency of your favourite AMstation. Then divide this into the speed of light to get the wavelength. Fortunately, you do not need an antenna that has a comparable length,

although the strength of the signal will increase as you increase the antenna length.

Short wave - several different bands in the range 5.9 - 26.1 MHz

Citizens band (CB) radio - Several bands around 27 MHz.

FM radio: 88 - 108 MHz. If the announcer says 102.5 FM, she is telling you the frequency of her station. The wavelength are about 3

metres, so simple antennae should be about 1/4 or 1/2 this length. To get an idea of how crowded the EM spectrum is, have a look at thisscan (click on the yellow graphic) provided by Balint Seeber, a rather special physics student at UNSW.

Television - several different bands between 54 and 220 MHz. (Television carries more information than radio does--pictures plus

sound-- and so needs broader bands for each channel)

Mobile phones: 824 - 849 MHz

Global Positioning System: 1.2 -1.6 GHz

The microwave band is used less formally for wavelengths of cm down to mm, or frequencies up to 10s or 100s of GHz. Themicrowave band is used for radar and long distance trunk telephone communications. Domestically, it is also used in microwave ovens.

* A FAQ about microwave radiation is whether that produced by a portable telephone can do damage to the brain to which it may be rather close. The evidence onthis is still not clear. A discussion is at given in "Microwave Radiation and Leakage of Albumin from Blood to Brain", James C Lin, IEEE Microwave Magazine,September 2004.

Measurement

Measurement techniques, as well as the uses, vary considerably over the range. At long wavelengths and low frequencies, we can observeprecisely how the electric and magnetic field vary with time. At the lowest frequencies, we can measure the time per cycle: at high frequencies, the

number of cycles per unit time. In high GHz or Thz regime, we can no longer measure frequency directly, although we can calculate it from thewavelength and the speed, or measure it using indirection means such as heterodyning. Wavelenths are usually measured using spectrometers,which use the phenomenon of interference. For X rays, the diffraction gratings in the spectrometers are crystals. For gamma rays, whose

wavelengths are rather smaller than atomic dimesions, all we can measure is the energy.

Wave vs particle vocabularies for EM radiation

The different limitations involved in measurements have implications for our choice to use phrases from the wave vocabulary or the particlevocabulary to describe radiation. For instance, if we are talking about a transmitted radio wave in the medium wave band, then huge numbers ofphotons would combine to make an electric and a magnetic field whose amplitude we could measure fairly accurately. The intensity of this wavewould be proportional to the square of the amplitude of the electric field (or the square of the amplitude of the magnetic field). We would not talk

about photons, because it is virtually impossible to measure them individually: they each have less energy than the kinetic energy of atoms andelectrons due to their thermal motion. We could not distinguish photon capture from the random thermal motion of electrons in our detector. Evenif we cool a detector down to microKelvin temperature (see graphic) to try to measure photons one at a time, their energy is so small that it is adifficult task. (Measuring the energy in radio waves is like measuring water by volume: the molecules of water are there, but there are very manymolecules in every drop so we think of water as a continuum.)

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This radio wave is also different from from ordinary light because it it is polarised, and because it has a very long coherence length: that is we canrelate the phase predictably over regions of the wave separated by many km. Further, it is possible to measure and to display the electromagneticfields (or rather the voltages they produce in an antenna) as a function of time. These measurement possibilities dispose us to use the vocabulary ofwaves to describe the phenomena.

Light

On the other hand, for light or for waves with shorter waves, we cannot measure or display E(t): the fields oscillate too fast. Instead, with light, we'catch photons': a single photon interacts with a photoreceptor molecule in your eye, a crystal in a film, an electron in a photocell/photomultiplier

tube etc. Because this is localised in space and time, we are using the particle vocabulary. In this vocabulary, the intensity of the wave is the energyper photon times the number of photons per unit area.

Notice that the choice to use wave or particle vocabulary has been made according to what we can measure (or sometimes what is convenient to

discuss). (It is the opinion of this author that little insight is gained from talking about wave-particle 'duality' or whether EM radiation 'is' a wave ora collection of particles. Such talk may, however, help sell popular science books.)

Temperature and colour

When photons with a given energy equilibrate with matter, the thermalenergy of the atoms (or electrons, etc) is comparable with that of thephotons. A body in equilibrium with its radiation is called a black body, and

the wavelength at which a black body with (absolute) temperature T has itsgreatest radiant power is given by Wien's displacement law:

λmax = (2.9 x 10-3 m.K)/T.

(See Black body radiation for more details. There is also a page on thermalradiation and why clothes work.) Thus the sun, whose surface approximatesa black body with temperature 5,700 K, has maximum radiation at about500 nm, in the middle of the visible range. It also emits wavelengths on either

side, and this combination is what we call white light. A hotter star (or awelding spark) emits proportionately more shorter wavelengths and soappears blue. A cooler star (or a normal fire) emits mainly longerwavelengths, and so appears red.

So, if the sun has peak radiation in the green, why doesn't it look green? The answer has to do with bandwidth (which is defined as the differencebetween the frequencies that have half the power of the maximum, one on either side). The whole visual bandwidth is less than an octave: fromviolet to visible red the wavelength change is less than 100%. The bandwidth of each of our photo receptor types (formally named L for long, M

for medium and S for shorb, but more commonly known as R, G and B) is about 20%. The wavelengths of maximum sensitivity for the three typesof photo receptor are 440, 545 an 565 nm, and the plot shows black body radiancy for these temperatures.

As the plot of black body radiation shows, the bandwidth (frequency range between points of half maximum power) of a hot body is rather more

than 100%. Looking at this curve, you will see that a star (or other simple hot body) with maximum radiation in the green emits very strongly inred, green and blue. In the case or the sun, or most 5700 K bodies that are close to us, the intensity is great enough that it will saturate all threecolour receptor types, so that we see white. So how can we see red and blue stars? The edges of the peaks in the curve are steep. When we seea blue star, its maximum is in the UV, and red and orange stars have theirs in the IR. (again, have a look at the curve). One star with a maximum inthe green is the sun. Now you're not supposed to look at the sun when it is overhead, but I did (very briefly) and it is white, due to saturation of all

photoreceptors. (The other colours it has near sunrise and sunset are due to atmospheric scattering or, in the case of the green flash, due toscattering plus dispersion.)

The background radiation of the universe has a temperature of a 3 K (or -270°C), and so its spectrum is mainly in the microwave range. Because

we can't see microwaves, it therefore looks 'black' or invisible to us: it is the radiation coming from the night sky where there are no stars. Thisradiation has been travelling through space ever since the universe was a few hundred thousand years old, when it first became electromagneticallytransparent. The universe was much hotter then, but because it has expanded a lot, its radiation has expanded too (wavelengths have becomelonger) and become much cooler.

Photons and chemistry

Ultraviolet light causes sunburn but visible does not. Why so? Many chemical reactions may be activated by electromagnetic radiation. In thesimplest case, one photon interacts with one molecule to initiate the reaction. Each photon has an energy hf, where h is Planck's constant,

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6.63 X 10−34 J.s = 4.14 X 10−15 eV.s.

A hydrogen atom has an ionisation energy of about 13 eV so, looking at the spectrum table above, a photon with a wavelength not much shorterthan 100 nm (well out in the ultraviolet) has enough energy to ionise a hydrogen atom. Familiar chemical reactions have reaction energies of tens of

kJ per mol. Let's take 50 kJ.mol−1 as a reaction energy, divide it by Avagadro's number (6 X 1023 to obtain a value per molecule, and use

1.6 X 10−19 eV per joule to obtain about 0.5 eV per molecule as a reaction energy. So, if it were just a question of getting from initial to final state,a photon in the infrared could supply the energy. Usually, however, there is an actived state with a rather higher energy, so more energy is needed.

Visible light can cause some reactions – such as the photochemistry in our eyes, or on photographic film. Photosynthesis is another (rathercomplicated) example. Ultraviolet light has more energy available, so UV can cause sunburn, while visible light does not. Hard UV can breakcarbon-carbon bonds and have serious biochemical effects for people.

Entropy

The (change in) entropy is defined as the heat added reversibly to a system, divided by its temperature. Usually, heat and radiation go from lowentropy (high T) to high entropy (low T). For example, in a kitchen grill, infrared radiation at several hundred K (and some weak red light) is

transmitted to food at lower temperature (a few hundred K).

This may seem to raise a paradox: microwaves have energies of meV, yet in a microwave oven they are used to heat food whose moleculesalready have thermal energies of ~0.1 eV. The point here is that the intensity of the radiation produced by the magnetron or klystron in the

microwave oven is much greater than that of its thermal radiation. Putting your food in interstellar space, where the microwave radiation is weak,would not cook it: it would simply cool to about 3 K. Further, the radiation produced by a magnetron (or by a radio transmitter) is not random,whereas thermal radiation is random. Transmitters usually produce photons that all have nearly the same phase. For example, a sufficiently intensebut low frequency electric field could produce an electric field of magnitude 100 MV/m, which is enough to ionise atoms, even though one photon

might not have nearly enough energy for ionisation. The field is strong because all of the photons are in phase and we have a low entropy source.This brings us to the relation between entropy and information.

Information

Just like the waves produced by a microwave oven, the radio waves used for communication consist of huge numbers of photons, all very nearly inphase. This gives them a much lower entropy than that of a similar number of photons with random phase. We can then vary the photon phase

(usually in the very slight ways associated with amplitude and frequency modulation) so as to carry useful information.

Sources whose photons have random phase carry information in other ways. Astronomers use waves from radio to gamma rays to make imagesof the sky. To do this, a minimum of several photons (and usually many more) must be averaged for each pixel in the image. Under optimal, dark

adapted conditions, a single human photoreceptor must capture several photons in a tenth of a second to be excited and to give us the sensation ofa weak flash of light. Our eyes are at best about 10% efficient, so this requires us to receive at the cornea several dozen photons focussed ontoone point in the retina. Charged Coupled Detectors are used in cameras and they are considerably more efficient than our eyes, especially CCDsoperating at very low temperatures.

History

This page is a distillation of the work of many people who have worked to understand electromagnetism, light and heat. Thinking about light isan essay by physics teacher Russell Downie on the history of our understanding of light.

Joe Wolfe © 2002. Modified May 03 J.Wolfe@unsw.edu.au, phone 61- 2-9385 4954 (UT + 10,

+11 Oct-Mar).School of Physics, University of New South Wales, Sydney, Australia.

There are pages on related material at

RC filters, integrators and differentiatorsLC oscillationspower, RMS values and three-phase circuits

TransformersMotors, generators, alternators and loudspeakersDrift velocity and Ohm's lawElectricity and magnetism in Einstein's relativity

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