bei48482_FM

130 Chapter Four

Lyman R   n2, 3, 4, (4.7)

In the infrared, three spectral series have been found whose lines have the wavelengths

specified by the formulas

Paschen R   n4, 5, 6, (4.8)

Brackett R   n5, 6, 7, (4.9)

Pfund R   n6, 7, 8, (4.10)

These spectral series of hydrogen are plotted in terms of wavelength in Fig. 4.11; the

Brackett series evidently overlaps the Paschen and Pfund series. The value of Ris the

same in Eqs. (4.6) to (4.10).

These observed regularities in the hydrogen spectrum, together with similar regu-

larities in the spectra of more complex elements, pose a definitive test for any theory

of atomic structure.

4.4 THE BOHR ATOM

Electron waves in the atom

The first theory of the atom to meet with any success was put forward in 1913 by Niels

Bohr. The concept of matter waves leads in a natural way to this theory, as de Broglie

found, and this is the route that will be followed here. Bohr himself used a different

approach, since de Broglie’s work came a decade later, which makes his achievement

all the more remarkable. The results are exactly the same, however.

We start by examining the wave behavior of an electron in orbit around a hydro-

gen nucleus. (In this chapter, since the electron velocities are much smaller than c, we

will assume that 1 and for simplicity omit from the various equations.) The de

Broglie wavelength of this electron is



where the electron velocity is that given by Eq. (4.4):



Hence

  (4.11)

4  0 r



m

h



e

Orbital electron

wavelength

e



 4  0 mr

h



m

1



n^2

1



52

1





1



n^2

1



42

1





1



n^2

1



32

1





1



n^2

1



12

1





Figure 4.11The spectral series of

hydrogen. The wavelengths in

each series are related by simple

formulas.

Pfund series

Brackett series

Paschen series

Balmer

series

5000

2000

1000

500

250

200

150

125

100

Lyman

series

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