Section 14.2: Exploring Atomic Spectra
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In addition to the extension to hydrogenic atoms, one can also extend the Coulomb model to include effects that add finer structure to the atomic energy levels. These corrections include:
- The proton does not have infinite mass, μp≠ ∞ . Therefore we should replace the electron's mass, μe, with the reduced mass, μ = μeμp/ (μp + μe).
- From the electron's point of view, the proton is moving. Moving electric charges create magnetic fields.
- The electron has spin angular momentum, an intrinsic magnetic moment. This, combined with the magnetic field that the electron experiences gives rise to the so-called spin-orbit correction to the energy.
- The electron, for large enough Z, is probably relativistic.
- The proton also has spin angular momentum.
Combining the spin-orbit interaction with the relativistic effects gives the so-called fine-structure correction which yields the energy levels:
Enjl = −|En| [1 + (Z2α2/4n2)(4n/(j + 1/2) − 3) ], (14.5)
where j = l ± 1/2 and α = 1/137 is the fine-structure constant. While these corrections are small, they do help to remove some of the degeneracies that occur in hydrogenic atom. A few corrections are shown in the following table.
|State||Correction in Z2|En|||j|
|1s||4.439945 × 10−6||1/2|
|2p||−7.769904 × 10−6||1/2|
|2s||−7.769904 × 10−6||1/2|
|2p||−6.659917 × 10−7||3/2|
|3p||−7.399908 × 10−6||1/2|
|3s||−7.399908 × 10−6||1/2|
|3d||−2.663967 × 10−6||3/2|
|3p||−2.663967 × 10−6||3/2|
|3d||−6.342778 × 10−7||5/2|
|4p||−6.382421 × 10−6||1/2|
|4s||−6.382421 × 10−6||1/2|
|4d||−2.830465 × 10−6||3/2|
|4p||−2.830465 × 10−6||3/2|
|4f||−1.308198 × 10−6||5/2|
|4d||−1.308198 × 10−6||5/2|
|4f||−4.624943 × 10−7||7/2|
The electron-proton spin interaction, due to the flipping of the electron's z component of spin, is manifest in the the 21-cm line from radio astronomy and is called the hyperfine-structure correction. There are also other effects from relativistic quantum mechanics and quantum field theory such as the Lamb shift.
In the animation, the atomic spectra for the first 99 elements are shown. Click on an element to see its line spectra. The lines in the ultraviolet and infrared area has been given an artificial color to make them visible. Wavelengths are separated into three regions: ultraviolet light (100 - 400 nm), visible light (400 - 700 nm), and infrared light (700 - 47000 nm). You can measure the wavelength of the lines by putting the mouse over the spectra (some rounding errors will occur). To update changes you must click on an element once more.
The line broadening indicates the broadness of the spectral lines drawn. This parameter should normally be set to 2. When zooming you should decrease it to 1.
There is a big difference in the intensity of the lines in the atomic spectra. This means, that some lines under normal circumstances are barely visible. By increasing the contrast you can give the weak lines an artificial boost. In the absorption spectra the contrast must be default 100.
Often laboratory observations of spectral lines occurs with background light present. If the apparatus is shielded from background light, this effect can be minimized. The "background" effect in the animation, simulates real-world measurements of spectral lines with an amount of background light present. If you don't like this background effect, simply turn it off by setting the continuum value to 0.00. In the absorption spectra the continuum value must be default 0.88.
Credits: Morten Brydensholt