Orbital and energy shell transitions

In summary, the conversation discusses the process of electron transitions in atoms, specifically in hydrogen atoms. The questions raised are related to the specifics of these transitions, such as the energy levels and orbitals involved, and the preferred path of the electron. The answer to these questions lies in the understanding of selection rules, which determine the allowed transitions between different eigenstates of a system. These rules can be derived through symmetry considerations and involve matrix elements that determine the probabilities of these transitions.
  • #1
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I've always learned that putting energy-photons into an atom can bump an electron up to a "higher energy state", and that when the electron "falls" back down into a lower energy state, it then emits a photon, and so forth. What I never seem to find, however, in these descriptions are any specifics.

My question, say for a hydrogen atom, is 1) Is this higher energy state an electron gets bumped up to simply a generally higher energy shell? Say n=1 to n=2 or n=4? Or is there some specific orbital within that higher energy shell the electron prefers, like say the Px orbital in n=2 versus the Pz orbital...or, perhaps one of the D orbitals versus a P orbital if the electron is bumped to even a higher energy level. I guess, more specifically, does bumping up an electron in a hydrogen atom actually CREATE one of the p,d,f,etc. orbitals we know are found in larger atoms? Or, alternatively, is it just bumped into some temporary amorphous higher energy "state?"

The second related question is, correspondingly, does the electron have any preferred "path" down to lower energy levels via some orbital hierarchy-cascade? Thanks.
 
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  • #2
I think the answer to your question is the understanding of so-called selection rules.

Think about two eigenstates of a system [itex]|\psi^i\rangle[/itex] and [itex]|\psi^f\rangle[/itex] with i="initial" and f="final" and some additional interaction represented by an operator [itex]\hat{T}[/itex]. In non-rel. QM this could e.g. be an electromagnetic field (instead of a photon b/c we do not want to deal with field quantization which is beyond QM and requires QFT).

The transition between the two states induced by the interaction is described by the matrix elements

[tex]\langle\psi^f|\hat{T}|\psi^f\rangle[/tex]

Now looking at the hydrogen atom states [itex]|nlm\rangle[/itex] and using an electromagnetic wave you get the usual selection rules for different multipoles. Neglecting spin, spin-orbit coupling and other tiny effects one can derive (via symmetry considerations), that an electromagnetic wave representing a dipole results in transitions for which the following rules must hold:

[tex]|n^i\,l^i\,m^i\rangle\;\to\;|n^f\,l^f\,m^f\rangle[/tex]
is allowed for

[tex]|l^f - l^i| = 1[/tex]
[tex]|m^f - m^i| = 0,1[/tex]

The probabilities for these transitions can be calculated from the matrix elements

[tex]\langle n^f\;l\pm 1\;m\pm 1,0|\hat{T}_\text{dipole}|n^i\,l\,m\rangle[/tex]

For all other combinations, i.e. for transitions violating the dipole rules the matrix element is exactly zero and the transition is forbidden.

http://en.wikipedia.org/wiki/Selection_rule
 
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1. What are orbital and energy shell transitions?

Orbital and energy shell transitions refer to the movement of electrons between different energy levels or orbits within an atom. This movement is caused by the absorption or emission of energy in the form of light or heat.

2. How do orbital and energy shell transitions affect the properties of an atom?

The energy levels and arrangement of electrons within an atom determine its chemical and physical properties. Orbital and energy shell transitions can change the number and arrangement of electrons, thereby altering an atom's reactivity, conductivity, and other properties.

3. What causes orbital and energy shell transitions to occur?

Orbital and energy shell transitions occur when an atom absorbs or releases energy in the form of photons. This can happen through various processes such as heat, light, or collisions with other particles.

4. How are orbital and energy shell transitions related to spectroscopy?

Spectroscopy is the study of the interaction between matter and electromagnetic radiation. Orbital and energy shell transitions play a crucial role in spectroscopy, as they are responsible for the absorption and emission of specific wavelengths of light, which can be used to identify elements and study their properties.

5. Can orbital and energy shell transitions occur in molecules?

Yes, orbital and energy shell transitions can also occur in molecules. However, the process is more complex due to the multiple atoms and energy levels involved. The energy levels in molecules are also influenced by the bonds between atoms, which can affect the nature and frequency of transitions.

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