Q's regarding atomic energy levels (1&2) and orbitals (1)

[bentzy]

I'm currently working on a paper dealing with aspects of Franck-Hertz experiment, and encountered some puzzling descriptions and symbols in an article published in the past, as follows:

1. The article includes a simplified energy level scheme of mercury. This scheme includes also 7th & 8th levels, despite the fact that the outermost level in Hg is n=6. Any reason or explanation to this 'odd' diagram ?

2. It's claimed in this article that when a triplet appears it means that the electronic configuration consists of 2 electrons in 6s6p orbitals "giving a total P state where the spins are coupled to a total spin with quantum number S=1". How this 6s6p configuration came to be so ? what's the meaning of the quoted phrase ? - I'm familiar with spin physics, but the quoted phrase is seemingly unclear. It'll great to elaborate on these.

3. d orbital isn't distributed equally probable along x, y & z axes. As it's shown in various textbooks, and Wikipedia isn't excluded, there is a kind of a spatial preference: x & y are populated first, and the 'leftovers' go to z. What's the reason for this spatial asymmetry ?

Thanks to all participants,
Bentzy cohen.

 

[DrDu]

1. The 7th and 8th level are not populated in the ground state of the atom but may be in excited states, eventually they only form resonances. In Hydrogen you also can calculate the energy of shells with n=2,3, etc.
2. A single s and p electron will always make up for a P, independent of spin (l=0 + l=1 => L=1). That S=1 is the definition of a triplett.
3. Pure convention. In molecules like e.g. quadratic copper complexes you usually chose the z-axis along the highest symmetry axis, so there is some link to another convention. However, this is not relevant For the FC experiment.

 

[bentzy]

New questions regarding F-H experiment

First, thank you for you previous answers - they were helpful.

Second, the 3rd question wasn't supposed to be related to F-H experiment - you can
realize that from the title.

Third, I've two more points to raise, following further study of the subject:
a. It turns out that what level is excited depends on the mean free path traversed by the electrons, which is inversely dependent on the collision cross section. However, the sublevel that is mainly excited is 63P1 (4.89 eV), which belongs to a triplet, while the other two have smaller cross section. Now, this isn't understood: how can the cross section differ for the same specific atom encountered by the electron ? In terms of the mean free path, it's even less understood, since it is related to the average distance between collisions.
b. later.

Cheers, BC.

 

[DrDu]

Cross sections are energy dependent. But the energy gained by an electron during acceleration in an electric field between collisions depends on the time between collisisions or - what ammounts to the same - the inverse of the mean free path length.

 

[bentzy]

I'm afraid my question wasn't clear.

I know the cross section is energy dependent. That's well known, since more energy means more possibility, or probabilty, to 'find' an atom.
I think I have to sharpen my question: the cross section for 6³P₁ is much much greater than those of its neighbors: 6³P₀ & 6³P₂, thus can't be explained by the slight differences between their energies.

In terms of the previous version of my question, I tried to say that considering a given atom encountered by an electron, the very same atom serves very different cross sections !, depending on the sublevel within the above mentioned triplet.
That's what I've been trying to settle, from two points of view.

I hope the problem I've tried to describe is clearer.

Thanks.

 

[ZapperZ]

Please note that whenever you are using a particular source and asking us about things you found in that source, you must make a full citation of it. Simply indicating that "... I'm currently working on a paper... " is insufficient.

Zz.

 

[bentzy]

I'm aware to that, and myself participate in discussions, mainly from the replying side.

I thought I had done it, since I already said in my original question the context within which my questions come from. I see that I had to do more than that. I apologize, anyway.

My previous question has to do with "what really happens in Franck-Hertz experiment ?", and it was based mainly on the following: "Whenever the kinetic energy reaches 4.67eV excitation of the 6³P₀ is possible, but only a few electrons give up 4.67eV of kinetic energy by exciting the 6³P₀ state due to its small cross section with the result that the electrons have a large mean free path. Those remaining continue to gain kinetic energy and reach 4.9eV or more where many of these electrons excite the 6³P₁ state as it has a high cross section above 4.9eV" (the underlines are mine).

The point is that despite the minute difference in energy, the ratio between the corresponding cross sections (manifested in the # of interacting electrons, as quoted) is huge !

Looking forward,
BC

 

[DrDu]

The point is that these states have different total angular momentum and this angular momentum difference has to be provided by the impacting and scattered electron.

 

[bentzy]

Yes, that's what I had in mind (in terms of different wavefunctions, at least), but I don't see the relation between the cross section and the angular momentum, so to speak.

Thanks, again.