[KAJLogic]

I am curious if this is accurate first. Assume this situation an oxygen atom has four electrons, then is introduced to four more. The initial configuration will undoubtedly be 1s2 2s2. Now after the other four to electrons are introduced (which will remove it's charge). I know it should end up being 1s2 2s2 2p4, however the thing that I am interested in is what are the variables involved in these electrons decisions (obviously I use the word "decision" loosely).

These are the variables I assume are involved:

Distance - the columbic attraction between the electron and the proton says that it wants a reduced distance

Orbital Volume - how many electrons the "orbital" it is about to enter can facilitate without causing magnetic force to begin resisting the columbic force.

Amount of electrons in said orbital - has this orbital reached a volume that it can no longer house another electron.

nodes - the amount of mathematical volume this can traverse without crossing the node. ( I still don't understand this so if you can point me in a direction that can clarify these orbital nodes would be GREAT )



Are these the variables involved in an electrons "decisions"?

[magician4]

an electron in the vicinity of a nucleus isn't a point type object anymore, but a standing wave with a respective wavefunction belonging to instead.

one of the consequences of this situation is, that except for very large distances - i.e. a multitude of atom "diameters" at least - an electron simply has the property of "defined place in space and time" no longer, and hence all the physical effects related to "distance, speed, ..." become meaningless.
this, for example , includes Coulomb forces.

Now what?

Well, to deal with this situation you have to pass on working with everything related to a defined "place, distance..." and all those effects related to, and have to replace them with the counterparts belonging to waves and wavefunctions. For example, instead of stating that the electtron was at an atom  (orbiting at, for example, the distance of the notorious Bohr radius), now the only thing you could say is, that if you integrated the wave function, you'll have it represented : [itex] \int \Psi  \Psi ^* = 1 [/itex]

as you see, allmost all of those "decisions" you've been thinking of cease to have a meaning - except of the bit ref. "nodes".
Yes , the wavefunction representing the electron in the vicinity of the nucleus has to follow certain rules, meet a certain "standard", amongst them not to interfere with the wavefunctions already "there" in an extincting manner (for this, all the wavefunctions affected will have to make some amendments, so in total the new situation will be harmonic again).

So, the "nodes" will need to meet this criteria , yes.


regards

Ingo


==================
"A person who wasn't outraged on first hearing about quantum theory didn't understand what had been said."
- Niels Bohr

[Borek]

all the physical effects related to "distance, speed, ..." become meaningless.
this, for example , includes Coulomb forces.

I was always under impression whole quantum chemistry is about Coulomb forces, just not between point charges.

[KAJLogic]

So electrons that are near the nucleus behave this way or all electrons at all times?

Now if you will, pretend I am a small child. When the electron gets near the nucleus (or if it's proximity to the nucleus doesn't change this at any time) what happens? I can understand the electron moving, then it gets near a nucleus and (is transformed into quarks?).

Finally, where can I find the mathematical formula for an electrons location? What will the variables be in this formula (just nodes and electron energy?)?

I really appreciate everything your doing magician your time, as noted by your knowledge, is clearly valuable.

[magician4]

I was always under impression whole quantum chemistry is about Coulomb forces, just not between point charges.

In a certain sense it is, yes - but not the "point - to - point " type of coulomb forces, but their wavefunction type equivalent instead, i.e. Hamiltonians obeying the uncertainty principle
(besides other problems, that's what makes advanced QM-calculations, i.e. ab initio calculations and thatlike, that demanding , esp. if you'd choose to have Hamiltonians of the relativistic type)

However, there were early / simplified approaches in QM that claimed that the outcome of their calculations would be quite close to "the real thing" -  even if they included those "wrong" assumptions like an "orbit" for an electron, a spin, even spin/orbit coupling and all that ( as they had to, with nothing else left to calculate from, besides those)
... but are much easier to calculate for, esp. if we'd include measured and/or approximate, even "best guess" type values into those equations: semi-empirical calculations :

The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simpler approach, one that has been employed since the inception of quantum mechanics, is to treat charged particles as quantum mechanical objects being acted on by a classical electromagnetic field. For example, the elementary quantum model of the hydrogen atom describes the electric field of the hydrogen atom using a classical [itex]\scriptstyle -e^2/(4 \pi\ \epsilon_{_0}\ r) [/itex] Coulomb potential. This "semi-classical" approach fails if quantum fluctuations in the electromagnetic field play an important role, such as in the emission of photons by charged particles.

(from: link)

All this however is not proof positive that indeed the electron was a point-type object, attractive to the nucleus but repulsive to other electrons in the classical sense(!) (though those calculations might give you results that might come close to reality!)
... and this is a huge source of misconceptions, even for scientists both in physics as as in chemistry and thatlike.
Bohr's radiii are dead and gone, no orbiting electrons whatsoever ( as these electrons are kind of "smeared" from hell to breakfast with their wavefunction: those stretch across the whole of the universe!!!) - and still this keeps on popping up every other day.
In my opinion it's mainly because nobody yet came up with a clever, psychologically pleasing to people - type picture for those wavefunction-interactions representing the quantummechanical equivalent of those classic Coulomb forces (and others), that those "old" concepts still keep on walking like undead Zombies

we're human, after all

regards

Ingo

[KAJLogic]

I will shrink my question down to where can I get, or what search terms should I use to find, the electron's wave formula.

[magician4]

So electrons that are near the nucleus behave this way or all electrons at all times?

electrons are quantummechanical objects, and hence will reveal a behaviour depending on the experiment they're subjected to: this is a consequence of the wave/particle dualism.

Choose an experiment where the "particle type" side of their nature is forced (for example, a cathode-ray tube) , and you might even generate TV-pictures from that
Choose a different experiment, for example the vicinity of an atom's nucleus, and the wave-type behaviour will be forced
Choose a mixed experiment, and mixed behaviour will result (i.e. fire single electrons from a cathode - ray tube at a double slit experiment: though you will observe single, located "hits" at the detector, nevertheless with several shots their local distribution will show a wave-interference picture

Now if you will, pretend I am a small child. (...)

If I had to explain this to a child, I usually would use a picture (of which I know that it's not completely correct, but will reveal the gist of the effect nevertheless) or "experiment" like this: I would show the child a coin, and make it look at the two different pictures backside and front.
The child will agree that each of the pictures can be recognized clearly, and that they are different from each other, but nevertheless are "two sides of the same coin": it will accept that things can have "two natures", depending of the way we observe them.
Then I will take that coin, put it upright on a table, and make it turn very fast. I then will ask the child what it sees, esp. which of the two pictures it will see, and the answer will be: none of the pictures (as it's turning too fast)
That's how I teach "dualism" to the child: its like a fast turning coin, and insofar "undecided" with respect to either side. Only if we "force" the coin to make a decision (i.e. if it falls down flat) it will reveal one of its two natures, depending on the physics in the moment it falls down.

Finally, where can I find the mathematical formula for an electrons location?

In the classical sense, you can't, if it came to electrons in atoms, as under the influence of this experiment they become undefined both in space and time  (though the "time" part usually is neglected in discussion, as this is even more strange than the "place" part. However, you can even see this in experiments, as electrons in a certain sense "seem to know" the experiment they will be subjected to in a future, that however still didn't happen (in our "human" sense), beforehand. Very strange, disturbing and mind boggling, I agree )

... and if you wish to find the mathematical formula for the equivalent for a "location" with wavefunctions, you'll need to look into quantum mechanics, or even quantum electro dynamics (if you wish to learn about this under relativistic conditions)
maybe you'll find something, that in your perception will satisfy for a "location" there

I didn't

ref. literature: Wikipedia might give you a first impression of what you're up to and against, if you wish to go for it anyway, and has a lot of usefull notes and references at the end, as usual
http://en.wikipedia.org/wiki/Quantum_mechanics

have fun, study, do research ... and maybe come up with something more usefull for the next generations than the what we old farts could provide to you


regards

Ingo

[KAJLogic]

Excellent thanks very much. So the idea of bonding using the outer P&S orbitals is based on particle like electrons. And, orbital volume is based on wave like electrons? To sum up at our current point we can justify holes in either by assuming it is behaving one of two ways? Assuming this is correct, if I was going to fully understand electrons I would know their behavior as waves and as particles correct? Finally I hope everything I said makes sense because if I tie this back to Einstein's special relativity; I always felt I had a grasp, however tenuous, of this I relate it to the idea of mathematics as not a stagnant singular repetition but a build up of further complex combinations using a (I don't want to say algorithm which would pervert the metaphor)  pattern to determine the next levels'.


========= Less Important Ramblings =========
The more I get acquainted with college the more I am disappointed. I learn in kind of a haphazard method; I cannot learn something that doesn't make sense to have it tied up later. I have always needed that logical justification during. Not only this but it also seems my professors are just reading ahead. I get the feeling that college isn't set up to, like I thought, catch you up to what humans have learned so far. It seems more like it is set up to manufacture new bits to drill forward in their respective fields linearly (not that they are stupid- they do teach you to recognize inconsistencies- just it seems to assume that given all the information I will reach the same conclusion/s) . I am rambling so I will stop now before this gets too tedious for magician to sort through; I just want to say that none of this is meant to assume that I am in any way superior to my predecessors/peers.
===========================================


P.S: Everything I will say on this forum is done in the hopes that if someone reads it and has a critique or a correction they will aid me by letting me know.

[Borek]

So the idea of bonding using the outer P&S orbitals is based on particle like electrons.

p & s orbitals contain wave like electrons to use your nomenclature. Actually p & s orbitals are solutions of the Schroedinger's equation for hydrogen atom, and solutions of the Schroedinger's equation are nothing else but wave functions of the single electron. Just because electrons behave like waves doesn't mean you can't count them (you just don't count point like particles, but the wave functions).

because if I tie this back to Einstein's special relativity

You can't run before knowing how to walk, forget about Einstein for now.

[curiouscat]

========= Less Important Ramblings =========
The more I get acquainted with college the more I am disappointed. I learn in kind of a haphazard method; I cannot learn something that doesn't make sense to have it tied up later. I have always needed that logical justification during.

Simple. Change your learning style. You can't always get something just because you think you "needed" it.

Not only this but it also seems my professors are just reading ahead.

What do you mean?

I get the feeling that college isn't set up to, like I thought, catch you up to what humans have learned so far. It seems more like it is set up to manufacture new bits to drill forward in their respective fields linearly

If you wanted to catch up with everything humans have learnt so far, college would optimistically last 7 decades. It just doesn't make sense.

An apprentice electrician needs to understand Voltage and Currents to do his job. But you cannot expect to drill him in the nuances of Quantum Mechanics for 8 years till he has mastered why exactly an electron behaves the way it does in all circumstances.

One must work on a need to know basis at times.

(not that they are stupid- they do teach you to recognize inconsistencies- just it seems to assume that given all the information I will reach the same conclusion/s) .

Glad you acknowledge that they are not stupid.

My advice is go with the flow, keep asking questions, but don't be stubborn to the point where a tiny un-understood bit stands in way of understanding whatever it is that you need to understand for a class or your major.

[KAJLogic]

If you wanted to catch up with everything humans have learnt so far, college would optimistically last 7 decades. It just doesn't make sense.

I vehemently disagree with you. I don't need to go through all the trial and error it took for everyone to get to the point we are at. For example it may have taken Descartes' all his life (or most of it) to get the coordinate system down. I fully understand it now in only a few years, because I started with already constructed accurate information. That being said, I meant within the fields of (mathamatics, physics, biology, and chemistry); I realize that sounds childish but I feel that a logical understanding hastens this process and strengthens it.


Question:
Lets just say then I wanted to test to see if the electron configuration for oxygen (1s2,2s2,2p4) was accurate. I know that the energy level 2 orbital p is housing an un-equal -in terms of its orbital volume not literal amount- (thus unstable) amount of electrons, but I want to go through all the motions to mathematically test this configurations accuracy where do I begin?

[magician4]

(...) but I want to go through all the motions to mathamatically test this configurations accuracy where do I bein?

As I take it you'd need it (else you wouldn't put this question) : just brush up your math a bit, then set up the Schroedinger Equation belonging to the oxygen atom, and solve it (an introduction to the "how to" you'll find in the link, and the literature given there)

Don't bother with semi-empiric pathways to do so, but better go for the real thing , i.e. something like the ab initio approaches, and do it the relativistic way, just to be on the safe side.
You might need a computer to help you out a bit with numbers, however...

regards

Ingo

addendum:
your results however might disturbingly differ from what you've learned sofar with respect to "orbitals..." , as almost all of these orbtal considerations taught to you are valid for hydrogen-atom type systems exclusively.
Unfortunately however, there's no such thing as "hydrogen-atom type systems" at all - except of the hydrogen atom, as ALL other systems will have more than just one nucleus, one electron - and hence are higher multi-body problems of sorts.

ever wondered why (semiempirical ! i.e. "under the influence of measured reality") MO orbital descriptions from N₂ to O₂ suddenly change that drastically?


(MO-scheme for N₂ , from: link )


(MO-scheme for O₂ , from : link as above)

it's because of "small energy difference" Δ2s,2p  (for the N atom) or "huge energy difference" Δ2s, 2p ( for the O atom)
see? so much for "...can be treated as hydrogen type system"
even when simply going from nitrogen to oxygen, the influence of the additional electron becomes that huge, that it shifts the Δ that drastically !

[Borek]

If you wanted to catch up with everything humans have learnt so far, college would optimistically last 7 decades. It just doesn't make sense.

I vehemently disagree with you. I don't need to go through all the trial and error it took for everyone to get to the point we are at. For example it may have taken Descartes' all his life (or most of it) to get the coordinate system down. I fully understand it now in only a few years, because I started with already constructed accurate information. That being said, I meant within the fields of (mathamatics, physics, biology, and chemistry); I realize that sounds childish but I feel that a logical understanding hastens this process and strengthens it.

You seriously underestimate how much we know. It takes a college and graduate studies to become specialized in a very narrow field. There are many thousands of such fields. Even if the knowledge in many cases overlap it is still at least months for each field. Do the math. 70 years suggested by curiouscat is generously low.