Electron Transitions

The Bohr model for an electron transition in hydrogen between quantized energy levels with different quantum numbers n yields a photon by emission with quantum energy:

This is often expressed in terms of the inverse wavelength or "wave number" as follows:

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Hydrogen Energy Levels

The basic hydrogen energy level structure is in agreement with the Bohr model. Common pictures are those of a shell structure with each main shell associated with a value of the principal quantum number n.

Energy level plot

Energies in eV

Hydrogen spectrum

Electron energy level diagrams

Hydrogen concepts
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Electron level calculation

Energies in eV


Hydrogen concepts
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Hydrogen Spectrum

This spectrum was produced by exciting a glass tube of hydrogen gas with about 5000 volts from a transformer. It was viewed through a diffraction grating with 600 lines/mm. The colors cannot be expected to be accurate because of differences in display devices.

For atomic number Z = ,

a transition from n2 = to n1 =

will have wavelength l = nm

and quantum energy hn = eV

Radiation of all the types in the electromagnetic spectrum can come from the atoms of different elements. A rough classification of some of the types of radiation by wavelength is:
Infrared   > 750 nm
Visible   400 - 750 nm
Ultraviolet   10-400 nm
Xrays   < 10 nm
(An approximate classification of spectral colors: Violet (380-435nm), Blue(435-500 nm), Cyan (500-520 nm), Green (520-565 nm), Yellow (565- 590 nm), Orange (590-625 nm), Red (625-740 nm).

Bohr model

Measured hydrogen spectrum

Other spectra


Great experiments of physics

Hydrogen concepts
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Measured Hydrogen Spectrum

The measured lines of the Balmer series of hydrogen in the nominal visible region are:

383.5384 5 9 -> 2 Violet
388.9049 6 8 -> 2 Violet
397.0072 8 7 -> 2 Violet
410.174 15 6 -> 2 Violet
434.047 30 5 -> 2 Violet
486.133 80 4 -> 2 Bluegreen (cyan)
656.272 120 3 -> 2 Red
656.2852 180 3 -> 2 Red
The red line of deuterium is measurably different at 656.1065 ( .1787 nm difference).

Illustration of transitions

Hydrogen fine structure (3->2 transition)
More extensive table of spectral lines

Hydrogen concepts

Atomic spectra
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