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Electromagnetic waves

This section will refer to several mathematical models of waves. These are discussed in the Mathematics of Waves section. You might want to review that section before continuing with electromagnetic waves.

EM waves are two waves in one

Electromagnetic waves are periodic disturbances in the electromagnetic field. They don't need a medium like water waves or sound waves, and can propagate through the vacuum of space.

The two figures below illustrate the basic anatomy of an electromagnetic (EM) wave. EM waves consist of a periodic disturbance in the electric field that occurs at right angles to its constant companion wave in the magnetic field.

Speed of light

In a complete vacuum, the speed of light is 2.99792458 × 108 m·s-1, exactly.

We know the speed of light exactly because in 1983 the length of the meter was redefined as

"the length of the path traveled by light in vacuum during a time interval of 1/299,792,458th of a second.

The two components of an electromagnetic wave are shown below in two different ways so that you might have a chance at figuring out the basic geometry. The wave propagates in the z-direction. The electric field wave occurs in one plane (say the x-z plane) and the magnetic field wave in the plane at 90˚ to the first (y-z). If, for example, the electric field wave oscillates up and down, the magnetic field wave will oscillate from side to side. Both waves always share the same nodes (points where they cross the axis), and they're always 90˚ apart.

Basic wave math

The relationship between wavelength and frequency for EM waves is

$$\lambda \cdot \nu = c$$

where $c = 2.99792458 \times 10^8 \; \frac{m}{s}$ is the speed of light in vacuum. For most purposes, $3.0 \times 10^8$ m/s will be fine.

Light does slow down in other media, leading to phenomena like refraction: the bending of light rays as they pass from one medium to another.

The electromagnetic spectrum

Electromagnetic waves comprise all of the electromagnetic radiation you are familiar with, and some with which you may not be. The electromagnetic spectrum is shown schematically below, and you should memorize its basic features, particularly the order of the named regions from left to right.

It's worth staring at the figure for a while. While there are blocks labeled "radio," "microwave," and so on, there is no real cutoff between those regions. Wavelength and frequency (which are related by the equation λ · ν = speed) vary continuously from one end of the spectrum to another. The labels are just what we've tended to call these regions as we've learned about them or used them in various applications.

Approximate wavelengths for the edges of the regions of the spectrum are printed on top.,

While we refer to the wavelength of the light (it's common to refer to all electromagnetic waves as "light," even radio waves and microwaves), in all regions of the spectrum, frequency measurements become too cumbersome to deal with past 1012 Hz, or 1 THz.

Notice, also, that the visible region of the spectrum – the region visible by human eyes – is only a very small segment of all of the possible wavelengths of electromagnetic radiation. Many other living things can sense light outside of this region.

Finally, there is no fixed transition point between UV and X-ray radiation, or between any other region of the spectrum. One section just flows continuously into another.

In the sections below, we'll look at a few of the regions of the spectrum in more detail.

Pro tip: memorizing the EM spectrum

Start by knowing the visible region: ROYGBIV (If you're British, it's "Rogers Of York Gave Battle In Vain."). From there, infra-red is next to red and ultra-violet is next to violet. Then if you can remember that it starts with radio and microwave, and that it ends with x- and gamma rays, you've got it.

Radio waves

The radio wave section of the EM spectrum is expanded below. It spans a few-hundred Hz to about 1 GHz in frequency. The radio- & microwave spectrum is usually referred to in terms of frequency — Hz. I'll leave it to you to calculate the wavelengths.

Radio waves are heavily used in communications, including AM & FM radio, shortwave and other radio transmissions, and broadcast television, though the latter has been replaced by digital & satellite delivery. Radio frequencies are also used for cellular telephone and wireless Internet transmissions, and for radar.

You can see in the diagram below that the entire radio-frequency region has been mapped out and given (somewhat humorous) names like "Tremendously high frequency (THF)."

In the US, different "bands" of the radio spectrum are apportioned for different uses. First responders — police, fire, ambulance — use a frequency band reserved for them. A band is reserved for citizen radio use (CBs), bands are reserved for AM and FM broadcast radio stations, military communications, and so on.

Radio waves are of low frequency, and thus low energy, though the power with which they're broadcast can be quite high. Shortwave radios (HF band) can bounce radio signals between the ground and a layer in the atmosphere called the ionosphere up to 5 times to broadcast and receive signals from around the planet.

In addition to heating your food, microwave frequencies are also used for communications.

Microwave ovens heat food efficiently because the energy of microwaves matches the rotational energy level spacing of water molecules in the liquid. Microwaves cause water molecules to climb the ladder of rotational energy levels, and eventually to collide and convert that energy to faster vibration of O—H bonds, which we experience as heat.

Infrared light

All objects, when heated, emit EM radiation. At lower temperatures, lower-frequency light (lower energy) is emitted. As the temperature increases, light of higher frequencies is emitted. We know that a very hot piece of metal, for example, glows with visible red light, and that if we heat it hot enough, it will glow white.

Before that happens, warm objects emit a lot of infrared light, radiation we normally experience as radiated heat—the heat you can feel when you hold your hand above something hot. Here is a graph of this so-called blackbody radiation at three temperatures from 3000K to 5000K. At each temperature an object emits significant IR radiation, but the peak shifts toward the UV end of the spectrum.

We can take pictures of things, like people, with infrared-sensitive cameras, to get a picture of how bodies radiate heat or how and where houses leak heat to the outside.

The IR spectrum is divided into some loose categories, as shown below.

The energies of far-infrared (FIR) light correspond to the energy of the vibrations and rotations of weak intermolecular bonds like the hydrogen bonds in liquid and gaseous water. In fact, FIR is absorbed strongly by atmospheric water.

IR waves with wavelengths closer to 1 μm have energies closer to the vibrational energies of chemical bonds, such as the O—H bonds of water, which are 100 times stronger than H-bonds between water molecules. Infrared spectroscopy can be used to to excite the vibrations of bonds in all sorts of molecules, and the particular frequencies of those vibrations help us to determine the structures of molecules.

Wavenumbers (cm-1)

The frequencies/wavelengths of IR radiation are often expressed in units of reciprocal centimeters (cm-1), also called "wavenumbers."

Atmospheric carbon dioxide (CO2) molecules absorb IR radiation strongly at frequencies of 2565 cm-1 and 560 cm-1. These are the heat-trapping frequencies most responsible for the early stages of atmospheric warming that are leading to global warming and climate change.

One particular danger of atmospheric CO2 buildup is that warmer land and sea temperatures will lead to increased levels of methane gas (CH4) in the atmosphere. Methane has more IR absorption frequencies and stronger absorptions of IR radiation than CO2, and could lead to a "runaway" effect by producing further warming, more methane, ... and so on.

Ultraviolet light

Ultraviolet light is EM radiation that is "beyond violet," and has wavelengths as low as about 1 nm. Typically light of smaller wavelength is called x-ray radiation.

The energies of ultraviolet rays correspond to the spacings between electronic energy levels of atoms and molecules. Thus, when atoms and molecules are exposed to UV radiation, their electrons can rearrange, or even be ejected from an orbital.

Because of its power to rearrange electrons, and therefore to break and reform bonds, UV light can be both useful and harmful. Perhaps the most obvious example of UV damage to humans is sunburn, which results from direct damage to proteins in the skin. Overexposure to UV light from the sun or other sources can also result in direct damage to the DNA in cells, which, if left unrepaired by the cell, can lead to skin cancers.

UV light can also damage the photoreceptor pigments in the eye, which is why sunglasses are important when it's bright outside.

Earth's atmosphere absorbs a great deal of UV radiation that would otherwise be damaging to biological organisms. This is mostly accomplished in the ozone (O3) layer through the overall photochemical reaction:

O3   +   hν → O   +   O2

where is the energy of the UV photon capable of splitting an ozone molecule, ν (Greek "nu") is the frequency of the light and h = 6.626 × 10-23 is Planck's constant.

When the ozone layer (20-30 Km above the surface) is depleted as a result of pollution — by common refrigerant molecules, for example — this protective layer, with which life on Earth evolved, can no longer protect organisms from damaging UV radiation.

Some exposure to UV radiation, on the other hand, is necessary for humans. Vitamins in the D family, necessary for good health, are found in only a few foods, but are readily synthesized by cells in the skin when exposed to UV light.


The Greek alphabet


Ionizing radiation

X-rays and gamma (γ) rays are often referred to together as ionizing radiation because they pack enough energy to knock electrons — even electrons in "core" orbitals of larger atoms — completely out of an atom or molecule, creating an ion. More importantly, atoms and molecules that have been so ionized can be highly reactive, and often rearrange their bonds to form other — perhaps undesireable — products. This is particularly problematic if we're talking about living organisms.

In nature, x-rays and γ-rays are only formed in nuclear decay reactions, and in the nuclear reactions of stars. These processes involve transitions between energy levels so widely spaced that they emit high-energy x-ray and γ-ray photons when they occur.

We can create x-rays artificially, and of course we do to good effect. You might have needed an x-ray a time or two in your life. Here we trade a low exposure to ionizing radiation damage for the benefit of being able to record an image our insides — to see what's going on in there. X-rays work for this purpose because most x-ray photons simply pass right through our tissues. The fraction that are absorbed is dependent on the type of tissue, and that's how we obtain contrast in an x-ray image.

X-rays are also used in the field of crystallography to determine the detailed 3-D structures of large molecules like proteins and nucleic acids (RNA, DNA). X-rays used for crystallography are often produced by synchrotrons.

Video examples

Three examples

Here are three examples of how to use the wavelenght-frequency-speed relation for electromagnetic waves: λ·ν = c

Minutes of your life: 4:28

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