The Foundations of Chemistry

Let us use a familiar kind of wave, that on the surface of water (Figure 5-11), to illustrate

these terms. The significant feature of wave motion is its repetitive nature. The wave-

length,, is the distance between any two adjacent identical points of the wave, for

instance, two adjacent crests. The frequencyis the number of wave crests passing a given

point per unit time; it is represented by the symbol (Greek letter “nu”) and is usually

expressed in cycles per second or, more commonly, simply as 1/s or s
^1 with “cycles”

understood. For a wave that is “traveling” at some speed, the wavelength and the frequency

are related to each other by

   speed of propagation of the wave or   c

Thus, wavelength and frequency are inversely proportional to each other; for the same

wave speed, shorter wavelengths correspond to higher frequencies.

For water waves, it is the surface of the water that changes repetitively; for a vibrating

violin string, it is the displacement of any point on the string. Electromagnetic radiation

is a form of energy that consists of electric and magnetic fields that vary repetitively. The

electromagnetic radiation most obvious to us is visible light. It has wavelengths ranging

from about 4.0 10 
^7 m (violet) to about 7.5 10 
^7 m (red). Expressed in frequencies,

this range is about 7.5 1014 Hz (violet) to about 4.0 1014 Hz (red).

Isaac Newton (1642–1727) first recorded the separation of sunlight into its component

colors by allowing it to pass through a prism. Because sunlight (white light) contains all

wavelengths of visible light, it gives the continuous spectrumobserved in a rainbow (Figure

5-12a). Visible light represents only a tiny segment of the electromagnetic radiation spec-

trum (Figure 5-12b). In addition to all wavelengths of visible light, sunlight also contains

shorter wavelength (ultraviolet) radiation as well as longer wavelength (infrared) radia-

tion. Neither of these can be detected by the human eye. Both may be detected and

recorded photographically or by detectors designed for that purpose. Many other familiar

kinds of radiation are simply electromagnetic radiation of longer or shorter wavelengths.

In a vacuum, the speed of electromagnetic radiation, c, is the same for all wavelengths,

2.99792458 108 m/s. The relationship between the wavelength and frequency of elec-

tromagnetic radiation, with crounded to three significant figures, is

   c3.00 108 m/s

Figure 5-11 Illustrations of the
wavelength and frequency of water
waves. The distance between any
two identical points, such as crests, is
the wavelength, . We could
measure the frequency, , of the
wave by observing how often the
level rises and falls at a fixed point in
its path—for instance, at the post—
or how often crests hit the post. (a)
and (b) represent two waves that are
traveling at the same speed. In (a)
the wave has long wavelength and
low frequency; in (b) the wave has
shorter wavelength and higher
frequency.

One cycle per second is also called one
hertz(Hz), after Heinrich Hertz
(1857–1894). In 1887, Hertz
discovered electromagnetic radiation
outside the visible range and measured
its speed and wavelengths.

The diffraction of white light by the
closely spaced grooves of a compact
disk spreads the light into its
component colors. Diffraction is
described as the constructive and
destructive interference of light
waves.

(a)

(b)