Chemistry - A Molecular Science

Chapter 2 Quantum Theory

Electric field

fs

l=700 nm l=400 nm

0

2800

0

9.33

nm

(a)

(b)

Figure 2.1 Two electromagnetic waves Only the electric field is shown. The magnetic field oscillates perpendicular to the electric field. The red wave would be perceived as visible red light and the violet wave as visible violet light. (a) Snapshot of the electric field over a 2800 nm range as the two waves pass through. (b) The variation of the electric fi

eld at one position during a 9.33 fs

(9.33x10

-15

s) interval of time, the time

required for light to move the

2800 nm used in (a).

2.1

THE NATURE OF LIGHT

Much of what we understand about atoms and molecules is based on the way they interact with light. To understand what those interac

tions tell us about matter, we must first

understand something of the nature of light. Light is

electromagnetic radiation

,

oscillating electric and magnetic fields that travel through space at a speed of 2.998x10

8

m

-1.s

, the

speed of light (c)

. Figure 2.1a represents a ‘snapshot’ of the amplitude of the

electric field in 2800 nm region of space at the moment that two different colors of light, red and violet, are passing through. Although

the two waves pass through the region at the

same speed, the speed of light, they differ in their

wavelength (

λ),

which is the distance

between two adjacent maxima or minima in their electric fields. The top wave in Figure 2.1a has a wavelength of 700 nm

(7x10

-7 m), while the bottom wave has a wavelength of

400 nm. Light with a wavelength near 700 nm

would be perceived as red light by the

human brain, while light with a wavelength close to 400 nm would be seen as violet. All visible light lies between these two wavelengths.

White light

is the sum of all of the

colors that comprise visible light.

The two light waves can also be represented

by showing the variation in their electric

field at some point over a period of time

(Figure 2.1b). The red wave makes four

oscillations during 9.33x10

-15

s, while the violet wave makes seven oscillations. The

number of oscillations of the electric or ma

gnetic field of a light wave during one second

is called its

frequency

(ν,

nu).

= 4 oscillations/9.33x10ν

-15

s = 4.29x10

14 s

-1 for the red

wave and 7.50x10

14 s

-1 for the violet wave. Comparing Figures 2.1a and b, we note that the

shorter the wavelength of a light wave, the higher is its frequency. The relationship between the speed, frequency, and wavelength of a light wave is

given in Equation 2.1.

Color

(^) λ
c
= c/ν
λ
Red 700 nm
† 3.0
x^10
8 m·s
-1 4.3
x^10
14 s
-1^
Violet 400 nm
3.0
x^10
8 m·s
-1 7.5
x^10
14 s
-1^
† 1 nm = 1x10
-9 m
c =
νλ
Eq. 2.1
The table in the margin characterizes th
e two light waves shown in Figure 2.1.
A
spectrum
is a display of the component colors of a light beam, separated by their
wavelengths. Raindrops can sometimes separate
the component colors of white light by
their wavelengths to produce a rainbow, which is a display of the spectrum of white light. This spectrum is produced when each wavelength
(color) of light is bent at a different
angle as it passes through the water droplets. Becau
se the colors all merge into one another
continuously
, the resulting spectrum is called a
continuous spectrum

. A continuous

spectrum can also be obtained by dispersing white light through a prism or from a grating.

© by

North

Carolina

State

University