### Hydrogen Spectrum

The following table presents calculated spectral lines from the Rydberg equation, corrected for the finite mass of the hydrogen atom:

$\frac{1}{\lambda }=\mu R_{\infty }\left [ \frac{1}{N_{final}^{2}}-\frac{1}{N_{initial}^{2}} \right ]$

$R_{\infty }=\frac{\alpha ^{2}}{2\lambda _{C}}=10973731.568661m^{-1}$

$\mu =\frac{M_{n}}{M_{n}+m_{e}}=0.999456$

Wavelengths are in nanometers.

Observed spectral lines are in parentheses.  The Balmer and Paschen wavelengths were corrected for the index of refraction of air which was assumed to be 1.000276.  The Lymann wavelengths were measured in a vacuum, and the Brackett and Pfund wavelengths were not corrected due to the uncertainty of the refractive index of air at these wavelengths.

For Balmer and Paschen wavelengths:

$\lambda _{vac}=1.000276\lambda _{obs}$

N(initial)>
N(final) V
10

9

8

7

6

5

4

3

2

9

38870.0 - - - - - - - -
8

16209.2 27803.5 - - - - - - -
7

8760.1 11308.7 19062.0 - - - - - -
6

5128.7 5908.2 7502.5 12371.9 - - - - -
5

3039.2 3297.0 3740.6 4653.8 7459.9
(7400)
- - - - (Pfund Series)
4

1736.7 1817.9 1945.1 2166.1 2625.9
(2630)
4052.3
(4050)
- - - (Brackett Series)
3

901.7 923.2 954.87
(954.88)
1005.22
(1005.26)
1094.1
(1094.1)
1282.2
(1282.2)
1875.6
(1880)
- - (Paschen Series)
2

379.9 383.65
(383.64)
389.02
(389.01)
397.12
(397.12)
410.293
(410.294)
434.173
(434.173)
486.274
(486.274)
656.469
(656.453)
(656.466)
- (Balmer Series)
1

92.1 92.3 92.6 93.1 93.781
(93.782)
94.975
(94.976)
97.255
(97.254)
102.573
(102.583)
121.568
(121.566)
(Lymann Series)