),
wavenumber (k) or energy (hf or E). Once any one of these
quantities is known, all the others may be calculated.In one sense, light is one of the most familiar things in our lives. We see because we have organs (our eyes) that sense the intensity (brightness) and wavelength (color) of light. We experience light (more generally, electromagnetic radiation) in a variety of other ways as well. For example, we sense radiant heat when our skin is near a warm object. This is due to our skin's reaction to infrared radiation.
More generally, we learn almost all of what we know about the world around us from the interaction of the objects in the world with electromagnetic radiation.
Light is a name we give to electromagnetic radiation that we can see with our eyes. Often, the term is used a little more broadly, to include electromagnetic radiation that is just outside the range we can see, in the ultraviolet and infrared. The term electromagnetic radiation refers to a phenomenon that moves energy from one place to another, and carries with it an electric field and a magnetic field. We will explain these concepts in this chapter.
),
wavenumber (k) or energy (hf or E). Once any one of these
quantities is known, all the others may be calculated.Energy is carried from one place to another (e.g., from the Sun to the top of Earth's atmosphere) by electromagnetic radiation. This consists of photons, individual packets of energy, which move through empty space in straight-line paths at the speed of light (c), 2.99793 x 108 m/s; they travel somewhat more slowly through air, water, glass, or other media. Photons have electric and magnetic fields. These fields oscillate as the photon moves through space. If we plot the size of the electric or magnetic field of the photon as a function of time (or of the distance the photon travels) we will trace out a sine wave. The electric and magnetic field waves are related; they oscillate at right angles to each other and at a right angle to the direction of the wave propagation as illustrated in Figure 4.01.
We can choose to call the direction the photon is traveling the x axis. And we can choose to call the direction of the electric field the y axis. So as the photon moves along, the electric field vector traces out a sine wave in the x-y plane. The magnetic field vector is perpendicular to both the direction the photon is moving and the electric field vector. Thus, the magnetic field oscillates in the x-z plane. The amplitudes of the electric field (designated on Figure 4.01 as E) and the magnetic field (B) are proportional to each other. That is, they are related by the formula
These waves, known as electromagnetic waves, are unique because, unlike water waves or sound waves, electromagnetic waves can travel through a vacuum. Whether we describe electromagnetic radiation as a wave or as a particle in any given instance depends solely on which is more useful to explain the particular phenomenon we are discussing.
Radiant energy, originally produced in thermonuclear reactions in the Sun, is carried to Earth by electromagnetic waves. There are several different kinds of waves, but we will discuss the simplest kind, known as plane polarized waves. The electromagnetic wave depicted in Figure 4.02 is an example of a plane polarized wave.
The highest point on a wave is called the crest and the lowest point the trough. The time it takes for one crest (trough) to reach the position of the next crest (trough) is called the period (p) and is measured in seconds (s). The reciprocal of the period is called the frequency (f). The frequency and period are related by the equation
The frequency can be thought of as the number of wave crests or troughs that pass a fixed position in a second and has the units of cycles per second or just s-1. The distance between wave crests or troughs is called the wavelength. With a little math we see that the wavelength can be expressed as
=
c/fwhere c is the speed of the photon.
This equation shows that the higher the frequency of the wave, the shorter the wavelength. We can also describe the length of a wave by its wavenumber (k) through the relationship
/The wavenumber represents the number of waves, measured in
radians, that fit into a given distance, say 1 meter. The higher the
wavenumber the shorter the wavelength. So any photon and its
electromagnetic wave can be characterized by a specific velocity
(c), wavelength ()
or wavenumber (k), and period (p) or frequency
(f).
The energy (E) of a photon is directly proportional to its frequency and thus inversely proportional to the wavelength. We can write the relationship as
where h is a constant called Planck's constant. Once we know the energy, wavelength or frequency of the electromagnetic wave we can calculate the other two quantities. The greater the frequency (or the shorter the wavelength) of the photon's electromagnetic waves, the more energetic the photon. Usually we choose to specify the wavelength and energy, which are easier than frequency to measure experimentally. A summary of the basic quantities that characterize electromagnetic radiation, the formulas relating these quantities, and associated constants and units, is provided in Table 1.
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A photon of electromagnetic radiation may, in principle, have any energy at all: Very small, very large, or anything in between. We call the complete range of possible electromagnetic radiation energies the electromagnetic spectrum. Of course, for any given energy photons will have a definite frequency and a definite wavelength. So we can think of the electromagnetic spectrum as a range of energies, a range of wavelengths, or a range of frequencies, depending on our preference, or on tradition, when discussing specific phenomena. Since the tradition in the study of visible light is to use wavelengths, that is what we shall do here.
There is an infinite number of possible wavelengths electromagnetic radiation can have. It turns out that radiations having similar wavelengths have similar interactions with matter, but usually radiations whose wavelengths are very different (say by a factor 10 or more) have different kinds of interactions with matter. Thus, it is convenient to divide the electromagnetic spectrum into separate wavelength regions, where radiation having wavelengths in a particular region have a certain kind of interaction with matter. See Figure 4.05.
2.3.1 Gamma rays -- The most energetic waves, having the shortest wavelengths (and so the highest frequencies and greatest photon energies), are called gamma rays. Gamma rays are produced in nuclear reactions. When they pass through matter, gamma rays tend to knock electrons completely out of their atoms and molecules, leaving the atoms or molecules as ions afterwards. For this reason, gamma rays are also sometimes referred to as "ionizing radiation." The ions produced by gamma ray exposure are very reactive, and their reactions can prevent them from ever returning to their preexposure configurations. For this reason, exposure of living organisms to ionizing radiation can have derimental effects, caused by irreversible damage to biomolecules. From the human standpoint this can be good, as when gamma ray exposure of food products is used as a means of killing microbes, or it can be bad, as when it happens to us.
2.3.2 X-rays -- The region of next-longer wavelengths (next lower frequencies, next smaller energies) is the X-ray region. X-rays can be produced in nuclear reactions, but are also produced by the bombardment of metal surfaces with very fast moving electrons. They are also known to be produced in the vicinity of storms on the Sun's surface. Figure 4.04 is an image of the Sun as it appears in soft (relatively low energy) X-rays. The bright spots correspond to locations where soft X-rays are produced at the bases of solar prominences, large storms on the Sun's surface. X-rays are also an ionizing radiation, though are somewhat less potent than gamma rays. X-rays can make the electrons in an atom go from having a low energy to having a high energy, but still be bound to the atom. They can also change the energy of an atomic nucleus, though without causing the nucleus to break apart (nuclear fission). X-rays are deflected by electrons and atomic nuclei, which makes them useful both for medical imaging and for investigating the precise structures of molecules (X-ray crystallography). Both X-rays and gamma rays are produced in astrophysical processes in stars and galaxies, and they constitute a part of the "cosmic rays" that constantly bombard Earth.
2.3.3 Ultraviolet radiation -- With smaller energies than X-rays, ultraviolet (uv) radiation both causes, and is produced by, electrons changing their energies within atoms and molecules. It can also be emitted as blackbody radiation from hot bodies such as stars. Ultraviolet radiation can cause molecules to break apart, and it is a mildly ionizing radiation, compared to gamma and X-rays. Through these processes, uv radiation can damage biological organisms. Though the sun puts out a substantial amount of ultraviolet radiation, we are protected from most of it by oxygen and ozone in Earth's atmosphere. We further subdivide the uv region into three subregions (a, b, and c): uva radiation (320 nm to 400 nm) is not absorbed to any great extent by either oxygen or ozone, so much of the uva radiation that falls on the top of the atmosphere propagates through to Earth's surface; uvb radiation (295 nm to 320 nm) is absorbed by ozone, so some of this radiation reaches Earth's surface, depending on how much ozone is in the atmosphere; and uvc radiation is absorbed by ozone and by oxygen. uvc radiation is almost completely filtered out by the atmosphere, so very little reaches the ground.
2.3.4 Visible light -- At slightly longer wavelengths than uv radiation, there is a narrow region of the electromagnetic spectrum where, it just so happens, the radiation has just the right energy to interact with certain pigment molecules in the retina of the eye to give us sight. This is called the visible region of the spectrum. It also just happens to coincide with the wavelengths at which the sun puts out the greatest amount of radiant energy. Visible radiation is not ionizing. Its interactions with atoms and molecules almost all result only in electrons changing from having one energy to having a different energy, but remaining bound to their molecules. The fact that different materials absorb photons having different energies results in our perception of their having different colors. The human eye is sensitive to electromagnetic radiation with wavelengths between about 400 nm to 700 nm. All the colors we see in the rainbow (violet, indigo, blue, green, yellow, orange, and red) are in this wavelength range. The shortest wavelengths (greatest photon energy) are perceived as violet, while the longest (least photon energy) are perceived as red. It is interesting to note that some species can see light with shorter and/or longer wavelengths than can humans. Bees see farther into the ultraviolet than we do, and this helps them both with flower recognition and with navigation; mosquitoes see farther into the infrared, which helps them find warm blooded animals.
2.3.5 Infrared radiation -- At somewhat longer wavelengths than the visible region is the infrared (ir) region of the spectrum. Infrared photons have energies that are too small to change the energies of electrons in molecules. Instead, infrared radiation tends to change the vibrational states of molecules, that is, how fast the atoms in a molecule are shaking back and forth. When the molecules absorb infrared radiation, their atoms move faster, and so the temperature of the molecules increases. Heat lamps work on this principle. The transport of heat by (infrared) electromagnetic radiation is often called "radiant heat."
2.3.6 Radio waves -- At even longer wavelengths are radio waves. As the name suggests, we use this region of the electromagnetic spectrum for radio communications, as well as television and radar. The radio region consists of a wide range of wavelengths, which is commonly subdivided (uhf, vhf, television, radar, microwave, millimeter wave, etc.), according to how they can be used. This is in turn largely determined by the differences in the way these waves propagate through the atmosphere.
To summarize, the electromagnetic spectrum -- the range of all possible wavelengths of electromagnetic radiation -- is customarily divided into a number of ranges. There is no fundamental difference in the kind of electromagnetic radiation one finds in one region and another. The differences are, rather, defined in terms of what those radiations do to matter when they interact with it. We only call visible light visible because, as nature would have it, we can see it. Customarily, we use the term "light" only when referring to electromagnetic radiation that is in the uv, visible, or ir regions of the spectrum. These are the regions where the radiation output from the Sun is the greatest, and where the solar radiation has the greatest impact on Earth and her atmosphere.
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