bei48482_FM

Atomic Structure 137

Balmer nf2:     n3, 4, 5, 

Paschen nf3:     n4, 5, 6, 

Brackett nf4:     n5, 6, 7, 

Pfund nf5:     n6, 7, 8, 

These sequences are identical in form with the empirical spectral series discussed earlier.

The Lyman series corresponds to nf1; the Balmer series corresponds to nf2; the

Paschen series corresponds to nf3; the Brackett series corresponds to nf4; and the

Pfund series corresponds to nf5.

Our final step is to compare the value of the constant term in the above equations with

that of the Rydberg constant in Eqs. (4.6) to (4.10). The value of the constant term is





1.097 107 m^1

(9.109 10 ^31 kg)(1.602 10 ^19 C)^4



(8)(8.854 10 ^12 C^2 /Nm^2 )(2.998 108 m / s)(6.626 10 ^34 Js)^3

me^4



8  02 ch^3

E 1



ch

1



n^2

1



52

E 1



ch

1





1



n^2

1



42

E 1



ch

1





1



n^2

1



32

E 1



ch

1





1



n^2

1



22

E 1



ch

1





Figure 4.16Spectral lines originate in transitions between energy levels. Shown are the spectral series

of hydrogen. When n, the electron is free.

Lyman

series

Balmer

series

Paschen

series

Brackett

series

Series

limit

Series

limit

Energy

n = 1

n = 2

n = 3

n = 4

n = 5

n = ∞ E = 0

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