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Light and other forms of electromagnetic radiation move through a vacuum with a constant speed, c, of 2.998 ×  10 m/s. This radiation shows wavelike behavior, which can be characterized by a frequency, ν, and a wavelength, λ, such that c = λν. Light is an example of a traveling wave. Other important wave phenomena include standing waves, periodic oscillations, and vibrations. Standing waves exhibit quantization, since their wavelengths are limited to discrete integer multiples of some characteristic lengths. Electromagnetic radiation that passes through two closely spaced narrow slits having dimensions roughly similar to the wavelength will show an interference pattern that is a result of constructive and destructive interference of the waves. Electromagnetic radiation also demonstrates properties of particles called photons. The energy of a photon is related to the frequency of the radiation as E = hν , where h is Planck's constant. That light demonstrates both wavelike and particle-like behavior is known as wave-particle duality, which has superseded the classical view. All forms of electromagnetic radiation share these properties, although various forms including X-rays, visible light, microwaves, and radio waves interact differently with matter and have very different practical applications.

Early in the nineteenth century, Thomas Young demonstrated that light passing through narrow, closely spaced slits produced interference patterns that could not be explained in terms of Newtonian particles but could be easily explained in terms of waves. Later in the nineteenth century, after James Clerk Maxwell developed his theory of electromagnetic radiation and showed that light was the visible part of a vast spectrum of electromagnetic waves, the particle view of light became thoroughly discredited. By the end of the nineteenth century, scientists viewed the physical universe as roughly comprising two separate domains: matter composed of particles moving according to Newton's laws of motion, and electromagnetic radiation consisting of waves governed by Maxwell's equations. Today, these domains are referred to as classical mechanics and classical electrodynamics . Although there were a few physical phenomena that could not be explained within this framework, scientists at that time were so confident of the overall soundness of this framework that they viewed these aberrations as puzzling paradoxes that would ultimately be resolved somehow within this framework. As we shall see, these paradoxes led to a contemporary framework that intimately connects particles and waves at a fundamental level called wave-particle duality, which has superseded the classical view.

Visible light and other forms of electromagnetic radiation play important roles in chemistry, since they can be used to infer the energies of electrons within atoms and molecules. Much of modern technology is based on electromagnetic radiation. For example, radio waves from a mobile phone, X-rays used by dentists, the energy used to cook food in your microwave, the radiant heat from red-hot objects, and the light from your television screen are forms of electromagnetic radiation that all exhibit wavelike behavior. Waves need not be restricted to travel through matter. As Maxwell showed, electromagnetic waves consist of an electric field oscillating in step with a perpendicular magnetic field, both of which are perpendicular to the direction of travel. These waves can travel through a vacuum at a constant speed of 2.998 Ã — 10 m/s, the speed of light .

All waves, including forms of electromagnetic radiation, are characterized by, a wavelength, a frequency, and an amplitude. The product of a wave's wavelength and its frequency , c = λν, is the speed of the wave. Thus, for electromagnetic radiation in a vacuum, speed is equal to the fundamental constant, c:

Wavelength and frequency are inversely proportional: As the wavelength increases, the frequency decreases. The inverse proportionality is illustrated in Figure 7.2. This figure also shows the electromagnetic spectrum, the range of all types of electromagnetic radiation. Each of the various colors of visible light has specific frequencies and wavelengths associated with them, and you can see that visible light makes up only a small portion of the electromagnetic spectrum. Because the technologies developed to work in various parts of the electromagnetic spectrum are different, for reasons of convenience and historical legacies, different units are typically used for different parts of the spectrum. For example, radio waves are usually specified as frequencies , while the visible region is usually specified in wavelengths .

One particularly characteristic phenomenon of waves results when two or more waves come into contact: They interfere with each other. Figure 7.5 shows the interference patterns that arise when light passes through narrow slits closely spaced about a wavelength apart. The fringe patterns produced depend on the wavelength, with the fringes being more closely spaced for shorter wavelength light passing through a given set of slits. When the light passes through the two slits, each slit effectively acts as a new source, resulting in two closely spaced waves coming into contact at the detector . The dark regions in Figure 7.5 correspond to regions where the peaks for the wave from one slit happen to coincide with the troughs for the wave from the other slit, while the brightest regions correspond to regions where the peaks for both waves happen to coincide. Likewise, when two stones are tossed close together, they can create an interference pattern on a surface, such as a drum, that is visible as a result of constructive and destructive interference of the waves.

Not all waves exhibit wavelike behavior. Standing waves, which remain constrained within some region of space, also exhibit quantization. For example, when a vibrating string is divided into two parts that are close together but not touching, the resulting standing wave pattern can be seen as a series of nodes and antinodes. Similarly, when light passes through two closely spaced narrow slits, an interference pattern results from the constructive and destructive interference of the waves.

In conclusion, light and other forms of electromagnetic radiation exhibit wavelike behavior, which can be characterized by their wavelength, frequency, and amplitude. The speed of these waves is a fundamental constant, c. Waves can also exhibit standing wave patterns, which are constrained within some region of space and exhibit quantization. These phenomena have led to the development of contemporary frameworks that intimately connect particles and waves at a fundamental level, known as wave-particle duality.