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3.10 Hydrogen Spectral Series

Pre-Lecture Reading 3.10

Video Lecture

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Hydrogen Spectral Series (14:21)

Supplementary Notes

Why Hydrogen?

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Hydrogen is the most abundant element in the universe, by far.
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Hydrogen is also the simplest element.

Lyman Series

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See Lyman Series.
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Consider transparent, hydrogen gas. If cooler than about 10,000 K, most of its electrons will be in the ground state.
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A continuum of light passing through this gas will consequently result in Lyman series absorption.

Figure 1

Lyman series transitions

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Lyman alpha (Lyα)
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  Ground state ↔ 1^st excited state
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  10.2-eV or 121.6-nm photon
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Lyman beta (Lyβ)
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  Ground state ↔ 2^ndexcited state
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  12.1-eV or 102.6-nm photon
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Lyman gamma (Lyγ)
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  Ground state ↔ 3^rd excited state
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  12.8-eV or 97.3-nm photon
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...
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Lyman limit
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  Ground state ↔ ionization
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  13.6-eV or 91.2-nm photon

These are all ultraviolet photons.

Balmer Series

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Consider hotter, transparent, hydrogen gas. If about 10,000 K, most of its electrons will be in the 1^st excited state.
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A continuum of light passing through this gas will consequently result in Balmer series absorption.

Balmer series transitions

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Balmer alpha (Hα)
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  1^st excited state ↔ 2^nd excited state
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  1.9-eV or 656.5-nm photon
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Balmer beta (Hβ)
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  1^st excited state ↔ 3^rd excited state
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  2.6-eV or 486.3-nm photon
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Balmer gamma (Hγ)
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  1^st excited state ↔ 4^th excited state
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  2.9-eV or 434.2-nm photon
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...
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Balmer limit
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  1^st excited state ↔ ionization
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  3.4-eV or 364.7-nm photon

These are almost all visible photons.

Paschen Series

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Consider even hotter, transparent, hydrogen gas. If about 25,000 K, most of its electrons will be in the 2^nd excited state.
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A continuum of light passing through this gas will consequently result in Paschen series absorption.

Paschen series transitions

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Paschen alpha (Paα)
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  2^nd excited state ↔ 3^rd excited state
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  0.7-eV or 1875.6-nm photon
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Paschen beta (Paβ)
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  2^nd excited state ↔ 4^th excited state
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  1.0-eV or 1282.2-nm photon
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Paschen gamma (Paγ)
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  2^nd excited state ↔ 5^th excited state
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  1.1-eV or 1094.1-nm photon
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...
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Paschen limit
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  2^nd excited state ↔ ionization
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  1.5-eV or 820.6-nm photon

These are all infrared photons.

Other Series

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Brackett series (3^rd excited state ↔), Pfund series (4^th excited state ↔), Humphreys series (5^th excited state ↔), etc., are all infrared through radio photons.
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Beyond Humphreys, these series are increasingly difficult to measure and do not even have names.

Detection of spectral lines—in absorption or emission—yields not only composition information, but temperature information.

Exercise

Experiment with UNL's Hydrogen Atom Simulator.

Assignment 3

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Do Questions 7 and 8.