bei48482_FM

Quantum Theory of the Hydrogen Atom 225

Figure 6.17In the normal Zeeman effect a spectral line of frequency  0 is split into three components

when the radiating atoms are in a magnetic field of magnitude B. One component is  0 and the others

are less than and greater than  0 byeB     4 m. There are only three components because of the selec-

tion rule ml 0, 1.

Magnetic field present

Spectrum with magnetic

field present

Spectrum without

magnetic field

l = 1

ml = 1

ml = 0

ml = – 1

No magnetic field

l = 2

 0

(h 0 – e B 2 hm (

ml = 2

ml = 1

ml = 0

ml = – 1

ml = – 2

( (

h 0

∆ml = +1 ∆ml = – 1

∆ml = 0

h 0 +e Bh

2 m

( 0 – 4 eBπm ( 0 ( 0 + 4 eBπm (

h 0

leads to a “splitting” of individual spectral lines into separate lines when atoms radiate

in a magnetic field. The spacing of the lines depends on the magnitude of the field.

The splitting of spectral lines by a magnetic field is called the Zeeman effectafter

the Dutch physicist Pieter Zeeman, who first observed it in 1896. The Zeeman effect

is a vivid confirmation of space quantization.

Because mlcan have the 2l1 values of lthrough 0 to l, a state of given orbital

quantum number lis split into 2l1 substates that differ in energy by (^) BBwhen
the atom is in a magnetic field. However, because changes in mlare restricted to
ml0, 1, we expect a spectral line from a transition between two states of differ-
ent lto be split into only three components, as shown in Fig. 6.17. The normal Zeeman
effectconsists of the splitting of a spectral line of frequency  0 into three components
whose frequencies are
 1  0  (^) B  0  B
 2  0 (6.43)
 3  0  (^) B  0  B
In Chap. 7 we will see that this is not the whole story of the Zeeman effect.
e

4 m
B

h
Normal Zeeman
effect
e

4 m
B

h
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