the same as in vacuum. This assumption is not valid for condensed phases like
water, glass, or any other transparent medium.
The quantum theory of light, discussed in Chapter 9, provides a relation-
ship between the energy of light and its frequency. Recall that light of a par-
ticular frequency comes in bundles of energy (which we call photons) having
a certain, specific amount given by the formula
Eh (14.5)
Equations 14.4 and 14.5 allow us to convert between energy, wavelength, and
frequency of light.
It is typical to divide the possible values of wavelength/frequency/energy of
light into various regions. Table 14.1 lists the approximate frequencies, wave-
lengths, and energies of the regions, and Figure 14.2 shows a diagram of a con-
tinuous spectrum and how it is divided. Such divisions have historical as well
as practical reasons. For example, one obvious division is visible light,which is
light that we can see. Visible light is electromagnetic radiation having wave-
lengths from about 7700 Å to 4000 Å (or 7.700
10 ^7 m to 4.000
10 ^7 m).
At higher frequencies (and therefore energies) than visible light is ultraviolet
(“higher than violet,” abbreviated UV) radiation, X rays, and gamma radiation.464 CHAPTER 14 Rotational and Vibrational Spectroscopy
Table 14.1 The electromagnetic spectruma
Frequency range Wavelength range Energy range
Region (in s^1 ) (variable units) (kJ/mol of photons)
Gamma rays 3
1017 1 nm 120,000
X rays 3
1017 –3
1016 ~1–10 nm 12,000,000–12,000
Ultraviolet (UV)b 7.5
1016 –7.5
1014 4–400 nm 30,000–300
Visible light 7.5
1014 –3.9
1014 400–770 nm 300–155
Infrared (IR)c 3.9
1014 –3
1011 770 nm–1000 m 155–0.12
Microwaves 3
1011 –3
108 1 mm–1000 mm 0.12–0.00012
Radio waves 3
108 1000 mm 0.00012
aBecause the limits on the ranges are inexact, some of the boundaries may overlap.
bOccasionally separated into UVA (320–400 nm) and UVB (280–320 nm) regions.
cOccasionally separated into near IR (770–2500 nm), middle or mid-IR (2500–50,000 nm), and far IR
(50,000 nm–1000 m) regions. 1 100
(Region limits are approximate)
Microwaves Infrared Ultraviolet
VisibleRadiowaves X rays Gammarays10 ^9 m3 108
770 nm 400 nm1017 s^110 ^8101610 ^7101510 ^6101410 ^5101310 ^4101210 ^3101110 ^2101010 ^1109RedOrangeYellowGreenBlueVioletFigure 14.2 The electromagnetic spectrum. The top numbers are the approximate frequency
boundaries of the regions, and the approximate wavelength boundaries are listed on the bottom.
The visible portion of the spectrum, shown expanded, is actually a small part of the complete
electromagnetic spectrum.