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.

This Bohr model picture of the orbits has some usefulness for visualization so long as it is realized that the "orbits" and the "orbit radius" just represent the most probable values of a considerable range of values. If the radial probabilities for the states are used to make sure you understand the distributions of the probability, then the Bohr picture can be superimposed on that as a kind of conceptual skeleton.

Energy level plot

Energies in eV

Hydrogen spectrum

Electron energy level diagrams
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Hydrogen Energy Level Plot

The basic structure of the hydrogen energy levels can be calculated from the Schrodinger equation. The energy levels agree with the earlier Bohr model, and agree with experiment within a small fraction of an electron volt.


If you look at the hydrogen energy levels at extremely high resolution, you do find evidence of some other small effects on the energy. The 2p level is split into a pair of lines by the spin-orbit effect. The 2s and 2p states are found to differ a small amount in what is called the Lamb shift. And even the 1s ground state is split by the interaction of electron spin and nuclear spin in what is called hyperfine structure.

Electron level calculation

Energies in eV

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Hydrogen Spectrum


Further splitting of hydrogen energy levels

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 λ = nm

and quantum energy hν = eV

At left is a hydrogen spectral tube excited by a 5000 volt transformer. The three prominent hydrogen lines are shown at the right of the image through a 600 lines/mm diffraction grating.

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)

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

Bohr model

Measured hydrogen spectrum

Other spectra

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Measured Hydrogen Spectrum

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

Wavelength
(nm)
Relative
Intensity
Transition
Color
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
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Hydrogen Energy Levels


Active illustration: click for more detail

Illustration of transitions
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