Power lines, AM radio, Wi-Fi, body heat, rainbows, sunburn, X-rays and gamma rays are one kind of wave at different frequencies. This chapter walks the whole range band by band and shows why frequency alone decides what each band can do.
Common mix-up: radio and light are not different kinds of thing, and “radiation” does not mean “radioactive.” Every band on this page is electromagnetic radiation: the same electric and magnetic ripple, moving at the same speed. What changes is frequency, and with it the energy each photon carries. Only the top end, from far ultraviolet upward, carries enough per photon to ionize atoms.
Every band in this chapter is the same thing: a self-sustaining ripple of electric and magnetic field, the wave that Maxwell’s equations predict and that Chapter 04 shows being born from a shaken charge. In vacuum it always moves at 299,792,458 meters per second. The only thing that changes from band to band is how fast the field flips.
That one number, frequency, fixes two others. Wavelength is the speed of light divided by frequency, so a 60 Hz wave is 5,000 km long and a green-light wave is about half a micrometer. And each photon, the smallest lump of energy the wave can hand over (that’s Chapter 06), carries energy equal to Planck’s constant times frequency.
Those two quantities decide everything practical. Wavelength sets the size of antenna you need and what the wave can slip around: a wave largely ignores obstacles much smaller than itself and is blocked by ones much bigger. Photon energy sets what the wave can do to a single atom or molecule: push its electrons around, twist it, shake its bonds, lift an electron to a higher step, or tear one off.
The band names are human conventions, not physics. Nothing happens at 300 GHz, where “microwave” turns into “far infrared,” except that the technology for making and catching the waves changes. The boundaries that matter are set by matter itself: where photon energy matches a molecule’s rotation, a bond’s vibration, an electron’s step, or the energy levels of a nucleus.
Radio engineers slice the spectrum by powers of ten. The International Telecommunication Union names each decade: ELF 3–30 Hz, SLF 30–300 Hz, ULF 300–3,000 Hz, VLF 3–30 kHz, LF 30–300 kHz, MF 300–3,000 kHz, HF 3–30 MHz, VHF 30–300 MHz, UHF 300–3,000 MHz, SHF 3–30 GHz, EHF 30–300 GHz and THF 300–3,000 GHz.
Each name spans one decade of wavelength too: HF is 10–100 m, UHF is 10 cm to 1 m, EHF is 1–10 mm, which is why EHF is also called “millimeter wave.” Everyday usage is looser: “ELF” often means anything under 3 kHz, including the 60 Hz in your walls, which the ITU strictly files under SLF.
For light, a handy shortcut: photon energy in electron volts ≈ 1,239.84 ÷ wavelength in nanometers. Red light at 620 nm carries 2.00 eV; a 124 nm ultraviolet photon carries 10 eV.
At the bottom sit waves so long they barely act like waves at human scale. The 60 Hz current in North American wiring (50 Hz in most of the world) has a wavelength of 5,000 km. A power line is a hopeless antenna at that wavelength: an efficient antenna is around half a wavelength long, and a city block is a few millionths of one. So almost all of a power line’s field stays bound close to the wire as a near field, rising and falling in place, and almost none radiates away.
Navies use the long waves anyway, for one reason: seawater. Salt water conducts, and a conductor kills a wave within a skin depth that shrinks as frequency rises. The US Navy’s Project ELF transmitted at 76 Hz from antennas in Wisconsin and Michigan until 2004. At 76 Hz the skin depth in seawater is about 29 m, so a submarine cruising deep could still hear it. The price was bandwidth: a few characters per minute, mostly amounting to “come up and call in.”
Very low frequency (3–30 kHz) is the everyday compromise. Station NAA in Cutler, Maine, broadcasts at 24 kHz (12.5 km waves); there the skin depth is only about 1.6 m, so submarines must come up to within roughly 10–20 m of the surface, but they get hundreds of bits per second at best rather than characters per minute. These waves travel in the gap between the ground and the ionosphere as if in a planet-sized waveguide, wrapping around the globe.
Low frequency carries the WWVB time signal at 60 kHz from Fort Collins, Colorado, which quietly sets “atomic” wall clocks across the US. Medium wave holds AM radio, 530–1,700 kHz in the Americas, with waves 180–570 m long. By day these travel as a ground wave: vertically polarized waves cling to the Earth and follow its curve well past the horizon, farther over wet soil and salt water, which conduct better. At night the ionosphere’s lowest layer, which soaks up medium waves in daylight, fades away; the waves bounce off higher layers instead, and a big station like 1010 WINS in New York can be heard hundreds of kilometers away.
For seawater take μ ≈ μ₀ = 1.2566 × 10⁻⁶ N/A² and σ ≈ 4 S/m. At 76 Hz, ω = 477.5 rad/s, so ωμσ = 2.40 × 10⁻³ and δ = √(833) ≈ 28.9 m. At 24 kHz the same sum gives δ ≈ 1.6 m.
Each skin depth costs a factor of e in amplitude, which is 8.7 dB. A submarine 20 m down listening at 24 kHz sits about 12 skin depths deep and loses roughly 107 dB, a factor of 50 billion in power. That is why VLF transmitters run at hundreds of kilowatts to megawatts and why their antennas are arrays of towers spread over hundreds of acres.
The ELF case is worse at the transmitting end. Half a wavelength at 76 Hz is about 2,000 km. The Navy’s antennas were tens of kilometers of overhead wire grounded at each end, a tiny fraction of a wavelength, so only a small part of the electrical power fed in left as radio; most warmed the ground. (The formula above is the good-conductor approximation, which seawater satisfies easily below about 1 MHz.)
Shortwave, 3–30 MHz with waves 10–100 m long, is the band that bounces. Ultraviolet and X-rays from the Sun strip electrons off gas molecules high in the atmosphere, from about 60 km up to several hundred, leaving the ionosphere: a thin soup of free electrons. A layer of free electrons acts as a mirror for any wave below its plasma frequency and is see-through above it.
A shortwave signal sent up at a slant comes back down hundreds or thousands of kilometers away, can bounce off the ground and go up again. That’s skip, and it is why a radio amateur with 100 W on the 14 MHz band can talk to another continent with no satellite involved. The mirror depends on the Sun, though: electron density rises by day and over the 11-year sunspot cycle, so the highest usable frequency drifts by the hour.
Above roughly 30 MHz the ionosphere is effectively transparent, which is also why radio astronomers can see through it. VHF and UHF therefore travel in straight lines and stop at the horizon. FM radio (88–108 MHz, waves about 3 m long) and broadcast TV rely on tall towers: the radio horizon is about 4.12 √h kilometers for an antenna h meters up, so a 300 m mast covers roughly 71 km.
Here the wavelengths are human-sized, 10 cm to 10 m. The waves bend around buildings and pass through walls and bodies with modest losses, and antennas fit in a hand. That is the sweet spot for mobile phones, which mostly live between about 600 MHz and 3.8 GHz.
GPS lives here too. Satellites 20,200 km up broadcast the L1 signal at 1575.42 MHz (λ = 19.03 cm). By the time it reaches you it has spread so thin that about 10⁻¹⁶ W lands on your phone’s antenna, weaker than the background thermal noise. Receivers recover it anyway by correlating against the known code each satellite sends, which lets them pull a signal out from under the noise.
Sent straight up, a wave comes back only if it is below the layer’s peak plasma frequency, called the critical frequency fc. Sent at an angle θ from vertical, it can reflect up to about fc / cos θ, the “secant law,” because only the vertical part of its motion has to be turned around. Grazing paths can therefore use frequencies about three times fc (Earth’s curvature caps the angle). That ceiling is the maximum usable frequency radio amateurs watch.
The lowest layer, the D layer at 60–90 km, doesn’t reflect much; it absorbs, because its electrons collide with dense air and turn wave energy into heat. Absorption falls roughly as 1/f², so it hurts medium wave far more than shortwave. The D layer needs sunlight to exist and fades within an hour or so of sunset. That is why AM stations travel so much farther at night.
Microwaves (roughly 300 MHz to 300 GHz, 1 m down to 1 mm) are short enough to aim. A dish a few dozen wavelengths across makes a tight beam, and that is the whole trick behind radar, satellite TV and point-to-point links. A Ku-band satellite TV signal near 12 GHz has a 2.5 cm wavelength, so a 60 cm dish is 24 wavelengths wide. US weather radar (NEXRAD) uses 2.7–3.0 GHz and measures rain by timing the echoes off falling drops.
This is also where molecules start to respond as whole objects. A polar molecule like water has a lopsided charge, so an alternating field twists it back and forth. In a gas, molecules can only spin at certain rates, and each step between rates is a sharp absorption line: water vapor at 22.235 GHz and 183.3 GHz, oxygen in a cluster near 60 GHz and at 118.75 GHz, carbon monoxide at 115.27 GHz, the line radio astronomers use to map cold gas between the stars.
Microwave ovens run at 2.45 GHz, but that is not a resonance of water. Liquid water can’t spin freely; its molecules are jammed together, so instead of sharp lines it has one broad absorption hump peaking near 20 GHz at room temperature. 2.45 GHz was chosen because it is an unlicensed band and because food absorbs it gently enough for the waves to reach a centimeter or two inside. (The 2.4 GHz chapter covers the neighbors it shares that band with.)
Above 24 GHz is millimeter wave. 5G mmWave uses bands around 24–47 GHz; at 28 GHz the wave is 10.7 mm long, and a hand, a leaf or a pane of low-E glass can block it. In exchange there are gigahertz of empty spectrum for data. Car radar at 76–81 GHz (λ ≈ 3.9 mm) sweeps up to 4 GHz of bandwidth, enough to tell apart two objects 3.75 cm apart in range. Near 60 GHz, oxygen absorbs about 15 dB per kilometer, so signals there die quickly, which is useful for short links that shouldn’t interfere with the neighbors.
The universe glows here too. The cosmic microwave background, the cooled afterglow of the Big Bang at 2.725 K, peaks at about 160 GHz. Above that lies the terahertz gap, roughly 0.1–10 THz: too fast for ordinary transistors to follow, yet too low in photon energy for the LEDs and lasers that make light. A 1 THz photon carries 4.1 meV, less than the 26 meV of thermal jiggling at room temperature, so detectors drown in their own heat unless they are cooled.
Water’s microwave absorption is dielectric relaxation, not a resonance. Each molecule tries to line its dipole up with the field, but it is hydrogen-bonded to its neighbors and takes about 10 picoseconds to reorient. Fields much slower than that are followed easily with little loss; fields much faster are ignored. The loss peaks when the field period roughly matches the relaxation time, near 20 GHz for room-temperature water.
An oven at 20 GHz would cook only the outer millimeters and leave the middle raw. 2.45 GHz sits well below the peak, so absorption is weaker and the waves reach deeper. Ice relaxes far more slowly than liquid water and so absorbs far less, which is why defrosting is uneven: thawed patches absorb strongly, heat faster, and thaw their neighbors last.
Molecular rotation lines in gases are different: those are true quantum steps. A molecule’s rotational energy comes in levels set by its moment of inertia, and light molecules with small moments have widely spaced levels, so their lines fall at higher frequencies. That is why water’s lines sit in the microwave while heavy molecules’ lines crowd at lower frequencies.
Infrared runs from about 300 GHz to 400 THz, wavelengths from 1 mm down to 750 nm. It is the band of molecular vibration. Chemical bonds act like springs, and each way a molecule can flex has a natural frequency in the infrared: CO₂ bends at 15 µm and stretches lopsidedly at 4.3 µm. Those two absorptions are the core of the greenhouse effect. Earth’s surface, at about 288 K, glows most strongly near 10 µm, and CO₂ and water vapor catch part of that glow on its way out.
Everything warm emits infrared. Your body at 310 K peaks at about 9.4 µm, and thermal cameras look in the 8–14 µm range, which happens to be a gap in the atmosphere’s absorption. Toward the visible end, infrared is about electrons again. TV remotes flash 940 nm LEDs (1.32 eV photons), invisible to you but easy for a cheap silicon photodiode. Long-haul fiber carries data at 1,550 nm (193 THz, 0.80 eV) because silica glass is clearest there: about 0.2 dB per kilometer, so 1% of the light is still left after 100 km, when an optical amplifier boosts it again.
Visible light, 380–750 nm (789–400 THz), is the narrow band where photon energy, 1.65 to 3.26 eV, matches the steps outer electrons can take in molecules. Pigments, chlorophyll and the retinal molecule in your eye all absorb light by lifting an electron one step; that is where color, photosynthesis and vision come from. It is also roughly where chemical bonds sit, around 2–5 eV, which is why light can drive chemistry at all. Eyes evolved for this band because the Sun pours out light here and because water, which eyes are mostly made of, is transparent here and strongly absorbing through much of the infrared.
Ultraviolet runs from 400 nm down to about 10 nm. Sunscreen labels split the near end into three: UV-A, 315–400 nm, which tans and ages skin and passes through window glass; UV-B, 280–315 nm, which burns and makes vitamin D; and UV-C, 100–280 nm, which shreds DNA and is used in 254 nm germicidal lamps. Ozone 15–35 km up absorbs all of the Sun’s UV-C and most of its UV-B. Past about 10 eV, below 124 nm, a photon can rip an electron straight off most atoms. Air absorbs these so strongly that the band is called “vacuum ultraviolet”; you can only work with it in a vacuum.
A two-atom bond vibrates like two masses on a spring: f = (1/2π) √(k/μ), where k is the bond’s stiffness and μ the reduced mass m₁m₂/(m₁+m₂). Light atoms on stiff bonds vibrate fastest. The O–H stretch sits near 3,600 cm⁻¹ (chemists count waves per centimeter), which is λ = 2.78 µm and f = 108 THz. The heavier, softer C=O stretch sits near 1,700 cm⁻¹, λ = 5.9 µm.
Because each functional group has its own vibration frequencies, an infrared absorption spectrum works as a molecular fingerprint, which is how a lab identifies an unknown compound or a gas analyzer measures CO₂ in a room.
Electronic steps are bigger because electrons are so much lighter than nuclei and are confined to atom-sized regions: squeeze a light particle into a small space and its energy levels spread far apart. That is the quantum reason visible and UV come from electrons while infrared comes from whole atoms moving.
X-ray photons span roughly 100 eV to 100 keV and beyond, wavelengths from 10 nm down to 10 pm, and they come from electrons hitting hard. In an X-ray tube, electrons accelerated through tens of kilovolts slam into a metal target. As they decelerate they throw off a smooth spread of photons called bremsstrahlung, German for “braking radiation,” cut off sharply at the tube voltage: a 100 kV tube can’t make a photon above 100 keV.
Some of those electrons knock an innermost electron clean out of a target atom. When an outer electron falls into the hole, it emits a photon at a sharp, element-specific energy: a characteristic line. Copper’s Kα line at 8.05 keV is the workhorse of laboratory X-ray crystallography, the method that maps where atoms sit in crystals, from salt to proteins.
X-ray photons are far too energetic for the chemistry-scale steps that absorb light, so they pass through light atoms easily. They are stopped mainly by photoelectric absorption, which rises steeply with atomic number (roughly as Z³ to Z⁴) and falls steeply with photon energy (roughly as 1/E³). Calcium (Z = 20) in bone stops far more than the carbon, hydrogen and oxygen of soft tissue. That contrast is the X-ray image.
Gamma rays come from the nucleus. A nucleus left excited after a decay sheds the extra energy as a photon: cobalt-60 emits 1.17 and 1.33 MeV, cesium-137 emits 662 keV, and technetium-99m, the most-used medical tracer, emits 140 keV. When a positron meets an electron, both vanish into two 511 keV photons flying apart, and a PET scanner locates them by catching the pair. Strictly, “X-ray” versus “gamma” names the origin, not the energy, and the ranges overlap: a 140 keV gamma ray is softer than the hardest X-rays from a 150 kV tube.
The sky goes much higher. NASA’s Fermi telescope maps gamma rays above 1 GeV, and ground telescopes catch TeV photons (10²⁶ Hz and up) indirectly, through the faint blue flashes of the particle showers they set off in the upper atmosphere.
In hydrogen, an electron falling from level 2 to level 1 releases 13.6 eV × (1 − ¼) = 10.2 eV. In a heavy atom, an electron dropping into a hole in the innermost shell feels nearly the whole nuclear charge, minus one unit screened by the remaining inner electron, so the energy scales as 10.2 eV × (Z − 1)².
Henry Moseley measured these lines across the elements in 1913 and found they lined up with atomic number, not atomic mass. That settled what the periodic table is actually ordered by and exposed gaps at Z = 43, 61, 72 and 75, elements not yet discovered. Moseley was killed at Gallipoli in 1915, aged 27.
The formula is approximate: it drifts for heavy elements, where the inner electrons move fast enough that relativity matters. For tungsten (Z = 74) it gives 54 keV against a measured 59.3 keV.
Drag to pan, scroll or pinch to zoom, and tap any spot to bring it to the center line. The readouts describe the frequency under the center line. Every labeled source sits at its true frequency, and more labels appear as you zoom in. The bottom strip shows how much of each band from space reaches the ground.
Look at the bottom strip. From the ground, the sky is open in two wide windows. The optical window runs from about 300 nm to about 1 µm, with scattered gaps further into the infrared. The radio window runs from about 10 MHz to a few hundred gigahertz, with oxygen and water-vapor lines carving into its top end.
Everything else is stopped. The air above each square meter of ground weighs about 10.3 tonnes (atmospheric pressure, 101,325 Pa, divided by g), as much shielding as a 10 m column of water. X-rays and gamma rays are absorbed high in the atmosphere, and ozone takes out UV-C 15–35 km up. That is why X-ray astronomy began only with rockets (the first cosmic X-ray source, Scorpius X-1, turned up on a 1962 flight) and why Chandra (1999) and Fermi (2008) fly in orbit. It is also why life on land is possible: the shielding that blinds X-ray astronomers protects your DNA.
Infrared is blocked mainly by water vapor, so infrared telescopes go high and dry, like Mauna Kea at 4,207 m, or leave entirely, like the James Webb Space Telescope (launched 2021). And radio below about 10 MHz bounces off the ionosphere from above just as it does from below, so the longest cosmic radio waves never reach the ground either.
Slide the temperature from the cold of deep space to a hot blue star and watch Planck’s curve slide across the spectrum. Each curve is scaled to its own peak; the readouts give the true numbers. Use the presets for real objects.
Every object above absolute zero radiates, because its charges jiggle thermally and jiggling charges radiate. An idealized perfect absorber, a blackbody, emits a spectrum that depends on nothing but its temperature. Max Planck found the formula for it in 1900, and in doing so started quantum physics.
Two rules fall out of it. Wien’s law: the peak wavelength is 2.898 mm·K divided by the temperature. The Stefan–Boltzmann law: total power per square meter is σT⁴, with σ = 5.670 × 10⁻⁸ W/(m²·K⁴), so doubling the temperature multiplies the glow sixteen-fold.
You, at 310 K, peak at about 9.4 µm and radiate about 520 W from each square meter of skin, mostly balanced by what the walls radiate back at you. A stove element at about 1,000 K peaks at 2.9 µm; only the short-wavelength tail of its curve reaches the visible, which is why it glows dull red. Objects start to glow visibly in the dark at around 800 K, the Draper point. The Sun’s surface, 5,772 K, peaks near 502 nm. A blue star at 20,000 K peaks at 145 nm, in the ultraviolet, and looks blue-white because its visible tail tilts toward the blue.
And at 2.725 K, the cosmic microwave background peaks at 1.06 mm. Arno Penzias and Robert Wilson found it in 1965 as a stubborn hiss in a horn antenna in Holmdel, New Jersey, that no amount of cleaning would remove.
Planck’s law for spectral radiance per unit wavelength is Bλ(T) = (2hc² / λ⁵) · 1 / (ehc/λkBT − 1), with kB = 1.381 × 10⁻²³ J/K. Setting its slope to zero gives hc/λkBT = 4.965, which is Wien’s law.
Bin the same spectrum per unit frequency instead and the peak moves: it sits at ν = 58.79 GHz/K × T. For the cosmic background that is 160 GHz, which corresponds to 1.87 mm, not 1.06 mm. Neither number is wrong. A “peak” depends on whether you chop the spectrum into equal wavelength steps or equal frequency steps, because those steps aren’t the same size across the spectrum. The instrument reports both.
At long wavelengths Planck’s formula reduces to the classical Rayleigh–Jeans law, Bλ ≈ 2ckBT/λ⁴. At short wavelengths the classical law blows up to infinity; Planck’s doesn’t, because energy comes in lumps of hf. Chapter 06 picks up the story there.
| Band | Frequency | Wavelength | Photon energy | Made by | Meets matter by | Used for |
|---|---|---|---|---|---|---|
| ELF · VLF | 3 Hz–30 kHz | 100,000–10 km | < 1.2 × 10⁻¹⁰ eV | AC currents in huge antennas | Induces currents; reaches meters into seawater | Power grid, submarine broadcasts |
| LF · MF | 30 kHz–3 MHz | 10 km–100 m | 10⁻¹⁰–10⁻⁸ eV | Oscillating circuits, tall masts | Ground wave hugs Earth; D layer absorbs by day | AM radio, time signals |
| HF | 3–30 MHz | 100–10 m | ~10⁻⁸–10⁻⁷ eV | Circuits, wire antennas | Reflected by the ionosphere (skip) | Shortwave, ham radio |
| VHF · UHF | 30 MHz–3 GHz | 10 m–10 cm | 10⁻⁷–10⁻⁵ eV | Circuits, compact antennas | Line of sight; passes walls, bends round corners | FM, TV, phones, GPS |
| Microwave | 3–300 GHz | 10 cm–1 mm | 10⁻⁵–10⁻³ eV | Magnetrons, transistors; molecular rotation | Twists polar molecules; sharp gas lines | Radar, satellites, ovens, 5G |
| Terahertz | 0.3–10 THz | 1 mm–30 µm | 1–41 meV | Rotations, lattice vibrations; hard to make | Absorbed strongly by water vapor | Spectroscopy, astronomy, scanners |
| Infrared | 10–400 THz | 30 µm–750 nm | 0.04–1.65 eV | Molecular vibration; thermal glow | Shakes bonds; absorbed by CO₂, H₂O | Thermal cameras, remotes, fiber |
| Visible | 400–789 THz | 750–380 nm | 1.65–3.26 eV | Outer-electron steps; hot objects | Lifts electrons in molecules: color, vision | Seeing, photosynthesis |
| Ultraviolet | 0.79–30 PHz | 380–10 nm | 3.3–124 eV | Electron steps, arcs, hot plasma | Breaks bonds; far UV ionizes | Sterilizing, chipmaking |
| X-ray | 30 PHz–30 EHz | 10 nm–10 pm | 124 eV–124 keV | Braking electrons, inner-shell holes | Photoelectric absorption (rises with Z) | Imaging, crystallography |
| Gamma | above ~10¹⁹ Hz | below ~30 pm | above ~100 keV | Nuclei, annihilation, cosmic engines | Compton scattering, pair production | Radiotherapy, PET |