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I made the edit adding a warning to some of the links relating to orbitals - I was not logged in at the time so my user name appears as a number. Also there is a picture at the top of the article that also includes an incorrect d orbital etc - but I do not know how to edit it. Unfortunately I cannot find a link to an image of a set of 5 more correct d orbitals on the web - sorry. HappyVR 18:28, 11 February 2006 (UTC)
We need to pick a page to explain electron shells in general: Electron shell, Orbitals, Atomic orbital, Electron configuration are all valid candidates, and none of them explain the basic ideas yet
- I agree but I am not a chemist, I am more a general knowlegist. Also I am only 16 and this subject is not one i know well. - fonzy That's too bad because you're starting out at the intermediate level of fuzzy thinking.
I think there needs to be a different page for each part of this. Atomic orbitals, their own page, Electron configuration, their own page, and etc. It would help separate different parts of the Atomic structure. I'm doing research on one specific part: Atomic Orbitals, and when all of the information is meshed, it keeps it from being allowed to be expanded upon. I don't know, just putting in my two cents.--- JulieRaven
I agree with User:JulieRaven - the articles need to be kept separate - they are all quite long as it is - although there is quite a lot of duplication between them I think this to be expected as they all cover closely related topics. As for a place to start the explanation of electron shells - how about with the first experimental evidence for them - I think this was Balmer/Lyman lines in the sun's spectra - this leads to (amongst others) Bohr's model of the atom (first example of a theory involving quantisation?) and eventually to quantum theory. I think it is important to include the experimental data/physical phenomana in an explanation of a model that attempts to explain it - if these lines in the spectrum hadn't been found we wouldn't have this article in the first place... HappyVR 20:49, 12 February 2006 (UTC)
It is interesting to note how the mathematicians have grabbed the need to subdivide the 3 dimensional space around the nucleus of an atom and used it to develop an elaborate concept of spacial occupation and probability values. From the Bohr concept the first thing that was abandoned was the Physical principle that the Conical orbit concept required that the angular momentum related to the motion be a constant throughout the distance of the path. Instead we have a definition that the level of lost free energy is a constant and changes in accordance with calculated probability of location properties. Next we have a decision that it is a spherical volume of space that is to be subdivided up into certain discrete quantities related to a desired mathematical series such that the filling of the volume coincides with the end of the series, and when that results in overlapping of the spacial subdivisions we have exceptions to the rule. And at the end we run into so many permutation possibilities that cant be differentiated that the explanation lacks cohesion and intelligibility. And this is all based on the idea that an electrons are unattached particles moving in association with an atomic nucleus and having the property of being able to interact and exchange energy with it. I surely hope that this elaboration of mathematical concept leads to a better understanding of the physical and chemical activities of the atom. But there are alternate methods of conception of how the electron interacts with the atomic nucleus and I hope they are likewise explored. WFPM ( talk) 19:20, 21 April 2010 (UTC)
I've pulled the following content from the article, because I think that at least one of the following conditions applies: (a) It's duplicated at Molecular orbital; (b) It's false. -- Smack 03:56, 14 Oct 2004 (UTC)
In the quantum-chemical treatment of molecules, it is usually necessary to express the solutions as linear combinations of one-electron functions which are centered on the nuclei of the constituent atoms of the molecule. These functions are referred to as atomic orbitals even though they may not actually be solutions of the Schrödinger equation for those atoms taken in isolation. This method is referred to as the linear combination of atomic orbitals molecular orbital method (LCAO MO method).
The orbitals used in the LCAO method are usually either exponentially decreasing from the atomic center (radial component of the form , referred to as Slater-type orbitals) or decreasing as a Gaussian function from the atomic center (radial component of the form , referred to as Gaussian orbitals), though other forms have been used.
There was an anonymous edit correction (possibly?). I am no expert in this topic, so please check if the minor edit was factual. -- AllyUnion (talk) 10:28, 10 Dec 2004 (UTC)
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I've amplified the introduction to say what an orbital is, and is not, and linked to the electron configuration and periodic table pages. The former page duplicates quite a bit of this one, but why not? Having the same material in several places may not be efficient storage wise, but can help the reader. Similarly, I reckon its helpful to have large topics slpit into smaller pages, so wouldn't want to consolidate everything together. I've also clarified the description of the p and d atomic orbitals, and their relation to the orbital's energy - it isn't the shape that determines it, but the detail of the probability density in the radial direction.-- Ian 10:02, 30 Jan 2005 (UTC)
Below is a link to a video produced by astronauts at the international space station that shows wave patterns in a very large sphere of water (something not attainable on Earth). It reminded me of the various orbitals within an atom. It would be particularly useful for demonstrating the electron wave patterns of hydrogen.
http://www.youtube.com/watch?v=zaHLwla2WiI
Notice that at 0 & 180 deg. to the initial energy pulse, the oscillations resembled a p-orbital along that axis, but the globule retains the basic (lower energy) spherical shape throughout the course of its vibration, and eventually comes to rest back at that ground state (you can almost pick out the other two p-orbitals as well, but they are not well resolved. Also, the multitude of concentric rings running up and down the axis of the initial pulse seem to me to resemble one of the possible d-orbitals (dSubscript zSuperscript 2) and f-orbitals (I think it is the fSubscript x)Superscript 3Subscript - 3/5xrSuperscript 2). These patterns are all simultaneously present, oscillating from one orbital type to another and back again, or even appearing and vanishing again. I found it very interesting to see the one lobe of the p-orbital mimetic appearing in one direction, and then vanishing again as the lobe in the opposite direction appears.
These vibrational patterns appear to me to be analogous to an atom absorbing a photon, kicking an electron to a higher orbital, followed by the atom relaxing back to its ground state as it remits the photon and that orbital shape dissapears (although the possibility for the orbital to reappear is always present when the next photon interacts with it).
It would be interesting to see the result of using a more energentic pulse to initiate the globual's vibration. I suspect that at higher energy, a smaller water droplet would be ejected from the larger globual, similar to what is observed with the photoelectric effect, where only photons with sufficient energy can kick electrons from a metal plate to complete a circuit.
Many students find the entire subject to be confusing in the extreme, and seem to fixate on the idea that these orbitals are solid, tangible objects hiding under the surface of the atom like steel girders in a building). Perhaps this video could help (assuming no one here finds serious fault with my interpretation).
There are some other very interesting videos on cymatics (the study of wave behavior) given below:
1. http://www.youtube.com/watch?v=8ik6RgdoIMw (The sequence from ~ 0:43 sec to 0:50 sec reminds me of benzene, with its alternating pi-bonds, and equivalent resonance structures.)
2. http://video.google.com/videoplay?docid=2795869048702157810&q=cymatics&hl=en
3. http://video.google.com/videoplay?docid=7253148167375317006&q=cymatics&hl=en
Since I am not certain that this wiki page is the best location for any this material, I felt that placing it here for further discussion would be best.
Thanks, DF 72.48.34.162 04:21, 4 December 2006 (UTC)
Although mathematically, the s orbitals have a maximum probability at the origin, is it possible that in reality, this is not the case if you factor in the spin angular momentum of the electron?
Regards
Geoff e j (
talk) 05:57, 28 February 2011 (UTC)
220.101.3.150 (
talk)
01:59, 9 March 2011 (UTC)
The discussion regarding the shapes of orbitals is not complete until the Heisenberg picture view of the Hydrogen atom (and more generally: the Kepler problem) is included. The two sets of parameters that determine an orbit's shape and size in the classical Kepler problem (angular momentum and eccentricity/direction of closest approach) have magnitudes that assume perfectly well-defined eigenvalues in the quantum version of the Kepler problem for each orbital state; hence the shape of the orbital is, itself, well-defined. The uncertaintly actually applies to the orientation of the orbit, not its shape or size.
In the quantized problem the two vectors generate a constrained version of SO(4) (hence the term "Hydrogen SO(4)"); or E(3) for parabolic orbits, or SO(3,1) for hyperbolic orbits. Both the eccentricity e and the magnitude of the angular momentum |L| assume eigenvalues in the orbital states. The orbital shapes resulting from the eigenvalues both supersede and refine those that had historically been associated with the Bohr-Sommerfeld orbits; namely that the major axis (a) is proportional to the square of the energy number n; the semilatus rectum is proportional to 1 + l(l + 1) (in contrast to Bohr-Sommerfeld's l squared), where l is the angular momentum quantum number. The terms in the correction 1 + l to the Bohr-Sommerfeld figure arise, respectively, from the uncertainty in the direction of the closest approach, and in the components of the angular momentum.
More generally, there should be a discussion concerning the Heisenberg picture and Hydrogen SO(4) -- either directly here, or provided by a link. -- Mark, 23 October 2006 '—The preceding unsigned comment was added by 129.89.32.142 ( talk • contribs).'
I'm distressed by these modifications. I don't have the expertise to corroborate or dispute their factual correctness, but one thing is clear: they're inaccessible to anyone without extensive training in mathematics and quantum mechanics. Wikipedia is not a physics reference text; it's supposed to be written so as to be readable by as many people as possible. The corrections should be written into a special section, and the remainder of the article be left as it was. -- Smack ( talk) 02:31, 15 July 2005 (UTC)
I believe the section Hydrogen-like atoms should be moved to the article Hydrogen atom or to a new article which could be "derivation of the hydrogen atom formulae" which solution would be preferred since the article Hydrogen atom is very good as it stands and should not be expanded anymore.
Atomic orbitals are quite different from the eigenfunctions of the hydrogen atom. The hydrogen atoms are one electron atoms only and this is a big conceptual difference. Of course one can use the Hydrogen atom eigenfunctions as atomic orbitals but one does not have to. In practice one often does not! -- 131.220.68.177 08:23, 26 July 2005 (UTC)
Well I agree with you we don't need it so suppress it because what this paragraph is all about is explaining people a bright example of separation of variables which is summarized in the hydrogen atom article and can be found in any low level text book! Do you really think someone interested in atomic orbitals wants to know something about how to derive their mathematical formula in the very special case of hydrogen-like atom - information which can be found easily on wikipedia anyway -- 81.209.204.11 08:16, 7 August 2005 (UTC)
orbital]]. I would suggest you to merge this with hydrogen atom but this is just my opinion.-- 81.209.204.4 15:39, 7 August 2005 (UTC)
sorry i have a ques. and am not finding it`s answer.so am posting it here.In a p-subshell we have 2 electrons in each orbital which are accomodated by 2 lobes in each orbital and between 2 lobes there is a zero probability region called node.the ques. that arises in my mind is why there is zero probability if electrons can oscillate between two lobes they have to pass through node then there must be some probability of finding electrons there. Raje80887 ( talk) 10:04, 5 July 2008 (UTC)
The giguere periodic table is a very simple table . It classifys its elements according to what orbital the electrons end in. Oh and I do'nt appreciate what you talked about about the p or s block it just not right
The top of this article states "A less formal description of the electrons in atoms can be found at Electron configuration.", wehereas the Electron configuration article states "The discussion below presumes knowledge of material contained at Atomic orbital."!
Basically, both articles are stating that if you are new to the subject you should read the other one first. Can this please be rectified by someone who understands the subject. I expect the best solution is to rewrite the Electron Configuration article to work as a standalone introduction for newbies, and for this article to be a more technical treatment of the subject, but other solutions are possible. -- HappyDog 01:29, 21 December 2005 (UTC)
I'm still concerned that the pictures associated with this text as well as some of the links (appear to) show incorrect (ie non degenerate) d orbitals - I can't see the point of including an image for visualisation purposes if the image gives the wrong impression. I refer to [electon_orbitals.png] and also the external link "the orbitron" and "David Manthey's Orbital Viewer renders orbitals with n ≤ 30" also gives incorrect d orbitals - I can't check the other links at the moment. Previously I added a warning to the external links but that was removed. HappyVR 19:37, 17 June 2006 (UTC)
So, is an orbital a "region in which an electron may be found", or is is a "mathematical description"? There are geometric and a methematical definitions. This needs to be clearer or we are looking at a confusing start to an inherently difficult topic. Dr Thermo 19:44, 12 June 2007 (UTC)
While presenting at the 1979 Sanibel Symposium, I had the occasion to ask Per-Olov Löwdin for his definition of an orbital. Without hesitation, he told me that it was first used by Robert S. Mulliken "in 1925 as the English translation of Schroedinger's use of the German word, 'Eigenfunktion'." Mulliken had been working in Germany in 1925 with many of the founders of Quantum Mechanics and particularly in 1927 with Friedrich Hund on the beginnings of molecular orbital theory. Mulliken presented his work at that time in Physical Review. Löwdin told me to look there for the first use of a hydrogen "orbital" in English. He also agreed that a suitable definition of an orbital would be "a mathematical function that describes the wave-like behavior of an electron". I will edit the definition to reflect this usage of the term as a mathematical function, but also connect it to the more general description of an orbital as a "region of space" that can be calculated from the function. The advent of graphing calculators has enabled even high school students to grasp the definition of an orbital as a mathematical function. I invite educators to have their students graph the "simplified' 1s orbital, y = exp(-abs(Z.x)), where Z=1,2,3( Atomic Number). This simple exercise can display the effects of electronegativity and the fact that atoms and isoelectronic ions "decrease" their size in going to the right in a row in the periodic chart. The bonding and antibonding sigma MO can also be displayed by y = exp(-abs(Zx+1) + or - exp(-abs(Zx-1) . After graphing functions, students can grasp the idea of "combining" functions (atomic orbitals) to get other functions (molecular orbitals), and what is meant by the + and - signs or the red/blue, white/gray colors of the orbitals. Laburke 21:13, 25 October 2007 (UTC)
The third paragraph of the "Connection to uncertainty relation" section doesn't seem to tell me why an electron must be in a specific set of states. It basically says there are several laws that apply and more-or-less leaves it at that. (The Bohr model page similarly fails to explain why there are discrete quanta.) How is a reader to understand why an electron can't be at n=1.5? I think this article needs to explain why the wave state collapses to the states at n=1, 2, 3, .... Thanks.— RJH ( talk) 16:25, 31 January 2008 (UTC)
The "Connection to uncertainty relation" section states "...this does not mean that the electron could be anywhere in the universe" and concludes with the sentence "An electron's location... stops at the nucleus and before the next n-sphere orbital begins." The first sentence of the "Shapes of orbitals" section states "... a given electron, regardless of which orbital it occupies, can at any moment be found at any distance from the nucleus and in any direction due to the uncertainty principle." This apparently contradictory text will surely confuse an unknowledgeable reader. It certainly confuses me! The text of both sections needs to be amended by a subject matter expert to clear up this seeming contradiction. Ross Fraser ( talk) 17:56, 18 March 2008 (UTC)
The basic reason Heisenberg implies a limitation to how closely you may localize bound particles in space, is that particles are waves, and the only way you can localize a wave is to localize a wave packet. Such packets need spreads in wavelength (which means momentum, in quantum mechanics). For low energy/momentum packets, the localization of the particle and wave-packet becomes bad, and thus the packet is large, and that's why the electron can't be found at any location smaller than a certain range of distances from the nucleus. But this is a property of all kinds of waves, as Bohr pointed out. The Heisenberg relationship just gives the scale of localization, once particles are connected with wave packets. Born supplies the last connection, with how you decide the connection of particle and wave: the complex congugate of the wave in any volume gives the probability density of finding the particle within that volume. S B H arris 02:02, 3 May 2008 (UTC)
I have created a new set of orbital images at much higher resolution than the pre-existing: please review, comment & include if appropriate. I am happy to fulfil requests for further orbitals to be generated (within reason). Dhatfield ( talk) 15:24, 5 October 2008 (UTC)
I would actually vote for a constant size depiction, since they size of any given orbital is semi-arbitrary anyway, and can be scaled up or down depending on the Z (charge) of the nucleus. That said, I'm curious as to why the f-orbital images here are so small-- isn't the fact that they must be at least at the 4 primary quantum number more or less mean that they're going to be larger than the 1,2, and 3 orbitals of all types? Again, though, I don't think understanding would be severely hurt to show all orbitals as large as the available box space available to contain them allows. This shows detail of smaller inner nodes (which is not seen in books too often-- I wonder how many chem students have thought about the extra nodes in 3p and 4p orbitals?
Another issue I bring up, is the matter than these are pictures of the Ψ function, and not the ||Ψ||2, and thus they are a bit more bulbous than the Ψ2 solutions we often see which are more physical because they show the actual volumetric density of the electron. Have you considered using a set of these, instead? Yes, we lose the alternating colors of the lobes between nodes (since this is phase and is squared out), but on the other hand, do we really need it? The lobes are separated by nodes anyway, so it's clear where they are. You could even put in "false color" representations of adjoining lobes (as now), with the explanation that the color now doesn't represent anything at all, but is put in for contrast. What do you think? Anyway, nice job! S B H arris 00:44, 15 December 2008 (UTC)
I agree, these are great pictures! I especially like the fact that the z-axis is consistent, which does not appear to be the case in the present diagram.
And for what it's worth, my two cents of input: I also agree with the note above that the table is too wide. The pictures works fine on my Mac at home, but on my PC in the lab where I work I can't see the final column. I'm not sure how I feel about the proposal to square the functions. They're certainly prettier with the two colors, but I guess SBHarris is right above about that being a little bit non-physical. However, I don't think squaring can change the shape of the orbital. If is constant on a given contour surface, then will also be constant, and thus contour lines for the two functions will have the same shape (see Levine, Ira "Quantum Chemistry" p. 151). Dhatfield, do you know the probability of finding an electron within the contours you rendered? That information would be nice.
My biggest concern is with the notation used to identify the orbitals, both in the current article's picture and in the proposed revision. There seem to be two systems of orbitals being conflated here. If you identify orbitals by angular momentum number and magnetic quantum number , you are, at least from a physicist's point of view, choosing orbitals that are eigenstates of the projection of momentum along the z axis. These are NOT the same as the "real hydrogenlike wave functions" that chemists use. I come from a physics background, so maybe I don't fully understand the chemists' notation, but something should be mentioned to clarify this difference. I recommend using a notation that specifies absolute value of , such as in
http://www.sccj.net/publications/JCCJ/v5n3/a81/text.html
Alternatively, real hydrogenlike orbitals are frequently identified by their relation to Cartesian axes ( etc.) Is this the system mentioned above? Csmallw ( talk) 18:46, 16 January 2009 (UTC)
Some of the other comments: I think somebody earlier commented that that nodes and antinodes in the various lobes are not due to the radial part of the wave equation, but that's wrong-- of course they are. They come from the Laguerre polynomial zeros, and are the most prominant feature of the radial solutions at higher energies; these are just like higher vibrational modes in a pipe with one end closed and one open (and of course distorted here from the 1/r potential, too). But otherwise, the same idea. Every radial function gets more nodes and antinodes as the energy goes up (n= higher principle quantum numbers), simply due to the shorter wavelengths of the faster particle "confined" in the potential well. As to the angular looking no different from the 's I can't see how that can be. The simplest ones I can easily check by "hand" are the angular part functions for 2p along the Z axis, which depend only on cos(theta) (theta = the angle from the z axis). You can see that the simple psi function is a sort of double squashed pumpkin, but if it's not squared it goes from z=1 at theta = 0, and falling off to 1/sqrt(2)=.707 at 45 degress off the z axis, then back to zero as you get to the x-y plane. But if you square it, it gets to be a near double sphere with z= 0.5 at 45 degrees, then back to z=0 on the x-y plane. Clearly, a different shape. And add in the fact that with psi^2 you're really doing an integral of [psi^2]dV from the origin to your point of interest, if you're looking at surfaces denoting "90% of the electron probability is inside THIS". That integration should give you again something slightly different than the surface of psi^2 which is the probability density itself, which you can really only probe by taking slices of it and looking at the shading or something, which is not the same thing as looking at the summed-up function which can be respresented by looking at the other thing. So I suppose we really three different spacially dependent function to consider, here. S B H arris 08:18, 17 January 2009 (UTC)
But even the comment about the contours of psi and psi^2 are wrong, so far as I can see. Cos(theta) = z for a polar coordinate system where theta is the angle from the z axis, is NOT the same shaped function as Cos^2(theta) = z. So I have no idea what the author is talking about. The psi function of theta is not shaped like the psi^2 function on theta in this case. That's what *I* mean. I don't know what HE means. S B H arris 00:46, 20 January 2009 (UTC)
It is important to remind that m of an orbital is not necessarily certain. Surely s and pz have m = 0, but m is uncertain for px and py, let alone more intricate d and f orbitals in the real form. Surely the “doughnut” p orbitals for m = ±1 are well-defined, but the m basis is important for atomic physics and is less important for chemistry where “dumbbell” p orbitals are predominantly considered. Incnis Mrsi ( talk) 18:16, 10 August 2019 (UTC)
I modified the table and went ahead and put it into the article (better off there than here). I also made an attempt to rectify issues of notation (physics vs. chem). The rest of the article could use an overhaul with respect to this issue, though. Csmallw ( talk) 09:23, 21 January 2009 (UTC)
I'm relatively new to quantum mechanics here so I might be wrong, but the article says p stands for principal, shouldn't it be principle? Psycholian ( talk) 23:06, 18 February 2009 (UTC)
SUMMARY: can we add the chemical symbols of the atoms that have each shape in the orbital shape table?
A didactic suggestion. The text states The orbital table shows all orbital configurations for the real hydrogen-like wave functions up to 7s, and therefore covers the simple electronic configuration for all elements in the periodic table up to radium.
So I take it each cell is a given element. If the chemical symbol for that element were added to the table, then I for one would find this chart a key bridge between the world of physics (orbitals) and chemistry (bonds; the shape of molecules).
Thanks for all this community has slogged through on the way to a "B" rating. Perhaps this suggestion is a sign that the page has matured -- both correct and accessible.
--jerry
Jerry-va (
talk)
13:13, 31 May 2009 (UTC)
The article on electron cloud was never good, and the only thing saving it was one cite where Feynman uses the phrase, and the fact that an atoms' electron cloud isn't really the same as its atomic orbitals or even the sum of them. But the last is sort of getting at the right idea-- there is a sense in which for complex atoms the total electron cloud is ALMOST a sum of 1-electron orbitals for hydrogenic atoms out of the Schroedinger equation: if that weren't so, we wouldn't have the periodicity of the periodic table, which can be seen in the Schrodinger hydrogenic solution. That fact is a remarkable thing, when you think about it!
So, in order to get rid of the awful electron cloud Wiki (bring it up if you don't believe me) which ahs been sitting there with no improvement for a year with a merge tag, I've re-written the LEAD of this article, to make it clear that there is an electron cloud, and that it is "sort of" composed of atomic orbitals, but not exactly. It's an appoximation. And that about does it for the electron cloud--- and now it can be done-away-with. So I was bold and redirected it to here. I left the TALK page. You can look at the history for what it was like.
Feel free to rewrite this LEAD, but as you do, remember how it got to where it is, and what we're trying to do. Our best "picture" of the "electron cloud" of a complex atom, bad though it is, is a bunch of filled-in atomic orbitals ala Shroedinger, for 1-electron atoms. So it's in THIS article, if anywhere, that we have the chance to give a picture of what all these things look like, and how they go together. S B H arris 06:36, 16 June 2009 (UTC)
I was glad to see that Feynman found simple intuitive ways of understanding things, including negotiating the math. His simplicity does not survive on a wiki though, as there is an academic force that has not embraced the value of making things simple, and it is easier to complicate topics than simplify them (Feynman spent about 10hrs to prepare each 1hr lecture). For example, look at the wiki article on Feynman diagrams, which have a fairly simple explanation in his Book QED (quantum electro dynamics). Hilbert has a similar stature in math.
I was hoping that interested folks, especially the upcoming generation would achieve greater progress by knowing what is important, and the value of simple language and notation to achieve more with the limited time we all have. The term electron cloud was really a visual depiction for a first brush with the concepts needed to explain the double slit experiment, and understand shroedingers model of the atom. JeffTowers ( talk) 17:02, 3 September 2010 (UTC)
I am concerned by this wording: "Despite the obvious analogy to planets revolving around the Sun, electrons cannot be described as solid particles. In addition, atomic orbitals do not closely resemble a planet's elliptical path in ordinary atoms. A more accurate analogy might be that of a large and often oddly-shaped "atmosphere" (the electron), distributed around a relatively tiny planet (the atomic nucleus)." Actually, that's a terrible analogy because it leads to wrong physics. Firstly, electrons ARE point charges, as far as anyone can tell, and so a solid particle is not a bad description. If you treat an electron as an extended charge distribution given by the ground state of the hydrogen atom and apply Gauss's Law you will see that the nucleus is almost entirely shielded; if this were the case hydrogen would not form molecules. I guess I would say that there is a cloud which tells you where you are likely to find the point-particle electron, and that's just fundmentally not like a satellite in orbit or a smeared out cloud of charge. Happy to discuss. Shrikeangel ( talk) 16:01, 9 August 2011 (UTC)
message to User talk:71.217.73.148
I see that you were adding a lot of informtion to atomic orbital that was simply mathematized versions of what is already discussed in the main article. I've moved it to an old version of spin-orbital, see here. But the math probably isn't appropriate here, but in the Schroedinger equation wiki. So don't be disheartened. Use the talk page.
To other editors-- this editor was obviously adding material in good faith, but has been bitten and treated a bit shabbily, unless I've missed something. What he was doing certain wasn't vandalism.
S B H arris 01:46, 14 November 2010 (UTC)
There is a lengthy section in this article which is about the development of atomic models (ancient Greeks --> Dalton --> Rutherford --> Bohr), and not about the modern atomic orbital model at all. It would be better to move this into the Atomic theory article, which discusses the historical development of atomic theory, and keep this article on subject. Djr32 ( talk) 18:17, 29 December 2008 (UTC)
Does anyone have any views on merging the articles Atomic orbital and Atomic orbital model? I don't think that either of them work alone, and a combined article would seem more coherent. Djr32 ( talk) 22:21, 30 December 2010 (UTC)
I agree with the essential gist of the above. We only need one article. It should be called atomic orbital, so atomic orbital model should become a redirect. Technically this would be a merge, but I too see little content to merge. -- Bduke (Discussion) 01:17, 31 December 2010 (UTC)
BTW, I'm going to add a bit to the drum vibration section, which is interesting. Notice that the first set of modes (u0x) are the only ones where the center moves, exactly like the s orbital set, which are the only ones with a center antinode. None of the other drum modes have a moving center, and the same is true for the atom-- these are all counterparts to orbitals with angular momentum. In these images, the electron is mostly "likely" to be in the places where the surfaces are moving the most. The analogy is closer with a 2-D surface (a drum) than with full spherical harmonics on a sphere. This is strange, but appears to be due to the fact that this allows the drum surface displacement in the third-dimension, to correspond to the electron radial coordinate (and thus energy). Thus, the process of modeling energy for bits of a 2D surface, as 3D displacement, works to show energy intuitively as a 3D coordinate. S B H arris 23:11, 8 January 2011 (UTC)
I'm confused by:
as I understand it, the idea that the electrons have speeds is not the QM view; indeed, ealier the article says "The electrons do not orbit the nucleus in the sense of a planet orbiting the sun, but instead exist as standing waves." If they had speeds, they would be accelerating electrical charges and they would radiate William M. Connolley ( talk) 09:48, 16 January 2011 (UTC)
Today's edits by Spiral5800 call attention to the last paragraph of this section which begins "Although Heisenberg used infinite sets ...". The whole paragraph is still quite confusing and has now accumulated two "citation needed" and one "dubious - discuss" tags. My opinion is that it adds little to the article and that we should just delete this paragraph. Comments? Dirac66 ( talk) 15:13, 11 April 2011 (UTC)
In lieu of putting up the template noting a need for more inline citations in this article, I instead am bringing up this issue here. For an article of this length and detail, I find myself longing for more inline citations through which I can fact-check various claims. I also noticed that in addition to a significantly noticible lack of inline citations, this article has only 15 cited references at the end. Not only do we need more inline citations, but more sources as well.
The template is obtrusive and because I otherwise find this to be a rather high quality article, I decided against the {{no footnotes}} template in favor of hopefully fruitful discussion and eventual resolution here. Thanks! Spiral5800 ( talk) 11:22, 13 April 2011 (UTC)
I'm confused about this chart in the orbital energy section:
1 | 1 | ||||
---|---|---|---|---|---|
2 | 2 | 3 | |||
3 | 4 | 5 | 7 | ||
4 | 6 | 8 | 10 | 13 | |
5 | 9 | 11 | 14 | 17 | 21 |
6 | 12 | 15 | 18 | 22 | 25 |
7 | 16 | 19 | 23 | 26 | 29 |
8 | 20 | 24 | 27 | 30 | 32 |
Why is the 8p subshell followed by the 6g subshell? Shouldn't it be followed by the 9s? Or am I missing something? The pattern displayed for the first 20 subshells would seem to imply that it should be:
1 | 1 | ||||
---|---|---|---|---|---|
2 | 2 | 3 | |||
3 | 4 | 5 | 7 | ||
4 | 6 | 8 | 10 | 13 | |
5 | 9 | 11 | 14 | 17 | 21 |
6 | 12 | 15 | 18 | 22 | 26 |
7 | 16 | 19 | 23 | 27 | |
8 | 20 | 24 | 28 | ||
9 | 25 | 29 |
Is the chart given in the article correct? If so, why is the pattern broken after 8p? XinaNicole ( talk) 01:27, 25 April 2011 (UTC)
In the last paragraph of the section "The Bohr Atom," shouldn't it be "and the n=3 state can hold 18 electrons"?
JKW ( talk) 13:08, 15 May 2011 (UTC)
Fortunately for Wikipedia, the contributions to the Discussion section do not seem to get scrambled as the articles do. So, here is the definition and explanation of an atomic orbital from someone who has published in the field of Quantum Chemistry since 1974 and has taught what orbitals are and how to use them in university courses at the introductory, intermediate, and advanced undergraduate and graduate levels (and even taught high school students with the aid of a graphing calculator) since 1980.
1) When you mention the word orbital to someone in the field of Quantum Chemistry, that person usually thinks you mean a mathematical function that describes the wavelike behavior of one particle, usually an electron.
2) When you say Atomic Orbital, one of two things is implied. Either you are talking about:
a) (Exact case, used rarely and only in one system) a mathematical function that describes the wavelike behavior of the electron in a hydrogen atom or ion containing only one electron (He+, Li2+, etc.) These are exact in that the forms of the functions (1s, 2s, 2px, etc.) provide the correct (non-relativistic) energy levels and these forms can be found without resorting to any mathematical approximations. These forms are called solutions to the Schrödinger equation.
b) (Approximate case, the usual case) a mathematical function that provides a starting point to approximate the wavelike behavior of two or more electrons in an atom, molecule, polymer, or crystal. The term, atomic orbital model, implies the use of approximate (i)methods and (ii)functions.
i) (Approximate methods) Since the time of Isaac Newton, physicists and astronomers have not found a way through calculus to describe the motions of the sun and two or more planets exactly (by consulting integral tables, solving differential equations and such). They resort to numerical techniques, which usually consist of putting more and more bits of the puzzle together to finally get close to the whole picture. Three of these techniques in Quantum Chemistry are configuration interaction(CI), perturbation theory, and density functional theory. Let's take CI as an example. The true but known wave function for an atom is approximated as a weighted sum of the ground electron configuration (1s22s2 for the Be atom) and excited configurations (e.g. 1s22s12px1, 1s22s02px2, etc.) The more excited configurations that are used, the better the approximation becomes and the more the approximate energy approaches the true energy of the atom. What is meant by a weighted sum of configurations is that they can each be assigned a coefficient (ci) and a best set of coefficients can be found through calculus (dE/dc = 0). The percentage that each configuration makes to the overall wave function can be indicated by the value of each weighting coefficient.
Here's an illustration using the Be atom.
In high school and first year chemistry (US), one learns that the electronic configuration of the Be atom is
ΨBe = 1s22s2 (resulting E = -14.566764 atomic units, STO-3G)
Then, in third year chemistry (US), one learns about the variational principle and LCAO techniques. Using the CI method for the Be atom, a wave function with six participating electron configurations atom might be
ΨBe = (90%)1s22s2 + (3%)1s22s02px22py02pz0 + (3%)1s22s02px02py22pz0 + (3%)1s22s02px02py02pz2 + (0%)1s22s12px12py02pz0 + (<1%)1s22s03s2 (E = -14.613493 atomic units, or 0.046729 a.u. more stable, STO-3G/CISD)
The percentages are derived from the weighting coefficients that are found for each configuration. The ground configuration contributes the most, 90%, to the wave function but not 100%. In modern Quantum Chemistry, wave functions with only one configuration are rarely acceptable in research. Thus, an atomic orbital is a mathematical function that describes the wavelike behavior of one electron and this function is used as a start in approximating the wavelike behavior of each electron in a multi-electron system.
ii)(Approximate functions) The functions shown in this article are the exact functions found by solving an equation for the hydrogen atom but they are almost never used for many electron atoms or molecules. In practice the functions in the atomic orbital model only resemble these functions. The reasons for this are that (1) the form of a hydrogen orbital makes solving the equations exceedingly difficult when there are several functions (orbitals) on the atom, (2) the hydrogen orbital can itself be approximated by a weighted sum of simpler functions ( LCAO). The two most popular approximate orbitals are the Slater-type orbital and the gaussian orbital.
The 2s orbital in an abbreviated form for these three types is:
2s(H like) = NZ (2 - r) e- | Z r | ... Z = atomic number, NZ = normalization constant
2s(Slater type) = Nζ e-| ζ r | ... ζ = effective atomic number, Nζ = normalization constant
2s(Gaussian type) = Nα e- α r•r ... α = effective atomic number, Nα = normalization constant
If you look in a first year chemistry text, you will probably see the 1s, 2s, 3s, and 4s orbitals plotted and you will see that each has (n-1) nodes. These come from a polynomial in front of the e function, (2 - r) for 2s. J. C. Slater dropped this polynomial but linear combinations of STOs can approximate the H orbital. Likewise, the similar gaussian functions, which contain an r squared term in the exponent, can be combined to form an STO.
Please forgive this old professor for giving you this Exercise. A trick question in chemistry exams is, "Does the atomic radius increase, decrease, or remain the same when going to the right in a row for the Representative Elements in the Periodic Table? Most students who haven't memorized the answer usually pick increase. Some pick remain the same because there are the same number of electrons and protons in each atom.
Plot 2s (x= -5 to 5) for a C atom using a gaussian, Ψ2s,C = Nα e- α x•x ... α = 6, Nα = 2.732
Plot 2s for a F atom using a gaussian, Ψ2s,F = Fα e- α x•x ... α = 9, Nα = 3.703
The area under each curve corresponds to the electron density. An orbital is defined as the mathematical function for one electron. So the total areas are equal. What is different is that the density for a 2s electron in F is closer to the nucleus than in C. This is found for all the orbitals. Therefore, the F atom is smaller than the C atom. The nuclear charge is one greater in F, but all the electrons are described by the same type of orbitals, a mathematical function that describes the wavelike behavior of ONE electron at a time.
BTW, if you want an index for electronegativity, you can use ζ or α.
The rational basis and the conceptual basis for almost every electronic property of substances and reactions in Chemistry are built on the wavelike nature of electrons. Functions no more difficult than sine or gaussian functions can be used to 'picture' electronegativity, bonding, conjugation, hyperconjugation, aromaticity, symmetry in pericyclic reactions, etc. In fact, the idea of vibrations on a string often suffice and can be taught in first year chemistry. That's the reason for my breaking Wikipedia rules and writing a very long Discussion section. I am sick and tired of having students arrive in mid-level chemistry courses who are burdened with the intellectual dead-end concepts of regions, shapes, and clouds. Thank you for your patience. Again BTW, that was a great idea to put in the moving images of vibrations on a drum head! Do you know what you get when you do it for vibrations on a sphere? (It rhymes with 1s, 2s, 2px, etc.) Slán, Laburke ( talk) 02:50, 16 May 2011 (UTC)
This is a most interesting account that is valuable here. However, like a lot of experts (and I am one too, I suppose) you miss the obvious. You say "Three of these techniques in Quantum Chemistry are .." but you miss Hartree-Fock theory, which is generally the reference function for CI and PTn methods and in itself gives useful results and simple pictures for students. Orbitals in both atoms and molecules are almost always, and certainly best seen as, Hartree-Fock orbitals which are optimised to give the lowest energy when each is in the mean field of electrons in all the other occupied orbitals. It is important to recognise that orbitals are generally approximations and obtained by improvement just as you describe for CI. They have no obvious form, except for the one-electron atoms and of course for symmetry derived parts such as the angular part of atomic Hartree-Fock orbitals. The CI and PTn approximations simply can not be understood without understanding the Hartree-Fock approximation. DFT is best understood by students as a form of Hartree-Fock theory, although of course it is not. An article on atomic orbitals should focus on Hartree-Fock along of course with the simple pictures of Hydrogen-like orbitals. -- Bduke (Discussion) 22:26, 16 May 2011 (UTC)
Can we begin at the beginning? When chemists put a standard electron configuration for an element, what do those numbers represent? Do they mean to suggest that each of those electrons in a subshell occupies a mere Slatter determinant?!? That they sit in things that are no more real than a basis function, like the cartesian axes are basis functions for vectors? And any old set of basis functions could be used instead? Or do these electrons reside (in pairs of different orientation) in sets of Hartree-Fock orbitals which now just-so happen to be called 3d something-or-other, as though they WERE sets of hydrogenic atomic orbitals that make up a subshell (even though they aren't)? What DO those numbers mean, in an atom's electron configuration notation? IOW, are they (2p, 3d, 4f, etc) the first two quantum-numbers of the one-electron Hartree-Fock wavefuctions, and we're now hijacked Schroedinger hydrogenic notation for them-- but forgot to tell chem students? Inquiring minds want to know. S B H arris 17:52, 17 May 2011 (UTC)
If you would like to close this discussion, please allow me. I wanted to point out that in English an orbital is generally understood to be a mathematical function that describes the wavelike behavior of one electron. The mathematical function depends on the coordinates of one electron.
I have found that students understand many concepts in Chemistry in a qualitative, but still important way if they can use sine functions on paper or exponential functions on a graphing calculator (sometimes the calculator is not even needed). These functions are orbitals.
Thanks to computers, we are going beyond orbitals when we want to calculate chemical properties very precisely. There are even some reactions that can not be adequately described by orbitals alone. Without explicitly naming any mathematical technique, this is how I would like them to see where orbitals historically fit into our calculations: 1) If we have the mathematical function that describes the wavelike behavior of the particles in a system (say, the nuclei and electrons of an atom, molecule, polymer, crystal, etc.), we can calculate the energy and any other physical property of that system. 2) However, the mathematics presently available to us will not let us find the exact form of this function if there are two or more electrons in the system, and so the energy of this system can not be calculated exactly. 3) We have been developing mathematical methods over the last seventy years to take advantage of the development of computers and are getting energies and properties closer to experiment (and in some cases more precise than experiment). Many of these approximate methods start with an atomic orbital for each electron in an atom or molecule and then apply these new techniques to get a mathematical function that describes the wavelike behavior of all the electrons in the system. The atomic orbitals usually all have similar forms but they are all mathematical functions that depend on the coordinates of one electron. 4) Several decades ago we started using a technique that combines atomic orbital functions for each atom in a molecule gave us another type of orbital, the molecular orbital, which, being an orbital, is a mathematical function which describes the wavelike behavior of one electron in a molecule. 5) Although the energy and other chemical properties of a molecule can be calculated using molecular orbitals, they too can be used as starting points for better mathematical functions that describe the wavelike behavior of all the electrons in a molecule together and not one-by-one as in orbitals. Laburke ( talk) 20:17, 23 May 2011 (UTC)
Recently an editor has changed a lot of nice simple |ψ|s into |ψ(r,θ,φ)|s and I don't see that this helps at all, except to make it uglier and more complicated in notation. After all, these are the very same graphs as if you used (say) |ψ(x,y,z)|s or any other spacial coordinate choice. Why don't you just change them back to the simpler form? Are you trying to show a spacial dependence? Just say they're being graphed in terms of spacial dependence and then you don't confuse the reader (by implication) into thinking that perhaps choice of coordinate systems makes some kind of difference. S B H arris 19:44, 1 November 2011 (UTC)
Earlier today the edit summary "Revert vandalism" was used to describe the removal of the sentence "Atomic orbitals are the regions or volumes in space in which the probability of finding electrons is highest" and its replacement by the correct mathematical definition of an orbital as a one-electron function. While I do agree with the edit, I think the word "vandalism" should be reserved for edits which are totally irrelevant to the article, or so obviously incorrect that the error must be deliberate. In this case the sentence removed is a simplistic description which is often repeated or implied by teachers at an elementary level, so it is most probably an honest attempt which should be described as a "good-faith edit" or even an "imprecise description" since it has some merit.
I have taught both theoretical (quantum) chemistry and first-year chemistry. I try to tell students that an orbital is a mathematical one-electron function. But in first year when their eyes glaze over and they ask what the orbital drawings mean, the usual answer is that they show the region in space in which the probability of finding electrons is highest for a given quantum state. Yes I know, the drawing is not the orbital, but at a first-year (or high-school) level this is not very clear. Dirac66 ( talk) 19:47, 13 January 2012 (UTC)
What I don't like is that by calling it an "orbital", they're trying to relate it in some sneaky way to a legitimate conic orbit, which has a fixed amount of angular momentum as well as additional amount of exchangeable free to kinetic energy. Can you imagine a motion path of an electron around an atomic nucleus that has a constant amount of lost free energy but with a zero to some amount of angular momentum? The only thing I can think of is a tethered orbit, where the electron is moving around in a circle at a fixed distance from the center of attraction. WFPM ( talk) 18:52, 13 April 2012 (UTC)
Are you sure the definitions of p_x and p_y are corrrect? I think they should be switched, such that p_x=-1/sqrt{2}*(p_1-p_{-1}) and p_y=i/sqrt{2}(p_1+p_{-1}). — Preceding unsigned comment added by Mariussimonsen ( talk • contribs) 08:00, 16 April 2013 (UTC)
I think that the previous relation was right. The sign of the spherical harmonics associated to p(1) and p(-1) are opposite. So if you add them, a sin(phi) will appear corresponding to p(y). Thisis in agreement with the real spherical harmonics page. [1] As it is said in the text about spherical harmonics [2] different conventions exists. — Preceding unsigned comment added by 193.50.159.70 ( talk) 16:47, 26 March 2015 (UTC)
Ok, I have made what may be considered a major revision to the Real atomic orbitals section. It is possible I overreached, if so please let me know, educate me on my editing approach, and feel free to revert. I tried to keep all that I could from the previous version. I am trying to more clearly and explicitly explain the relationship between the real and complex spherical harmonics. I would say I have done 3 things to the section. (1) I spell out the mathematical relationship very clearly, making clear link to the corresponding relationship for spherical harmonics which is already illustrated in Table of spherical harmonics, (2) I switch the section to using the Condon-Shortley phase predominantly because this is consistent with the Wikipedia pages on spherical harmonics (and frankly I prefer this convention since it's predominant in my personal literature-base) and (3) I give some exposition and add a talbe about how the Cartesian expansion of the real spherical harmonic is used to generate the common "atomic orbital" nomenclature for different orbitals. I could see this third thing I do being split out into a separate subsection.
I'm a new editor, so like I said, please educate me if I've done something wrong here. I've tried to modify this section to add clarity, but perhaps I take an approach that is too pedagogical and not encyclopedic enough. I may also be too lengthy in some of my explanations or lack references in important places. I also think there's a risk that this exact explanation I've given doesn't appear in the literature and is something that I have put together from looking at various Wikipedia pages and references there-in. If this explanation does not exist in the literature I wish it did and that's why I'm including it here, but maybe my efforts would be better spent somehow getting this kind of explanation into the peer-reviewed literature.
Anyways, I hope folks here can help me figure out how to fit these contributions onto this page in a nice way. The relationship between these two descriptions of hydrogen orbitals confused me for a long time but I've finally found clarity that I would like to share. Thanks for any help! Twistar48 ( talk) 01:43, 22 February 2022 (UTC)
References
In the current article these lines don't make sense to me:
If such a particle were gravitationally bound to the Earth it would not escape, but would pursue a series of passes in which it always slowed at some maximal distance into space, but had its maximal velocity at the Earth's center (this "orbit" would have an orbital eccentricity of 1.0). If such a particle also had a wave nature, it would have the highest probability of being located where its velocity and momentum were highest, which would be at the Earth's core.
Generally speaking this is wrong. The particle would have the highest probability of being found where its velocity is lowest. This is because the particle spends a higher fraction of its time in locations where its velocity is lowest. The above either needs to be completely removed or better explained. — Preceding unsigned comment added by O. Harris ( talk • contribs) 08:18, 27 May 2013 (UTC)
At the end of Bohr's Atom section there is following statement: "Ultimately, the relationship between orbital occupation and chemical behavior was resolved by the discovery of modern quantum mechanics and the Pauli Exclusion Principle. Namely in helium, all n=1 states are fully occupied; the same for n=1 and n=2 in neon."
But in next inert gas Ar n=3 is not fully occupied, so as for Kr, Xe and Rn n=4,5 and 6 are not fully occupied. Instead, n=3 is fully occupied for Zn and n=4 is fully occupied in Yb. Therefore, this is a poor basis for the statement which implies that all noble gases are characterized by closed electron shells. Drova ( talk) 02:47, 3 November 2013 (UTC)
user:AWomanWithAPlan is clearly formerly blocked IP user 103.10.64.20, see [1], and has now reverted 3 times a change two editors want. I've had it. S B H arris 06:20, 17 October 2014 (UTC)
User:Pandaron is also a sockpuppet. AManWithNoPlan ( talk) 14:12, 17 October 2014 (UTC)
Why is J omitted? 108.65.83.125 ( talk) 18:52, 27 October 2016 (UTC)
I have concerns about two statements:
If one is plotting the spherical harmonic and only giving the magnitude of that function in a certain direction (that is, plotting Y as a distance for each θ and φ), then these are accurate. But this is deceptive, since Y contributes to a magnitude of ψ at each point in space.
It's more common (and probably more correct) to plot an isosurface, all the values of ψ at a triple (x,y,z) or (r,θ,φ). These isosurfaces cannot be tangent to each other (or to the nodal plane), since for all any arbitrary value of |ψ| > 0, the distance of the closest point of an isosurface is always going to be at a positive, non-zero distance away from zero. This misconception is presented in a number of Journal of Chemical Education and articles and quantum chemistry textbooks. Olin ( talk) 15:33, 22 November 2016 (UTC)
I find it interesting that there can be no orbital below s and yet Muon orbitals are below s.
Anyone care to explain this?
The current article has
px = (p_1 + p_-1)/Sqrt[2]
when I simplify this, I get
Exp[- constant r] y.
And for
py = (p_1 - p_-1)/i Sqrt[2]
I get
Exp[- constant r] x.
Thus, I think they are likely backwards in the article. — Preceding
unsigned comment added by
WCraigCarter (
talk •
contribs)
09:11, 13 July 2018 (UTC)
The black hole's central region is so degenerate that it looks like the atomic orbitals, and has different energy levels (both the singularity and the ringularity violate Planckian shrinkage limits; the Big Bang exploded [it didn't shrink in more] because nothing can violate the Planckian threshold of degeneracy = maximal degeneracy = precosmic state; actually the black hole's central region less degenerate than the "precosmic state"). But we need more on the specifics. — Preceding unsigned comment added by 2a02:587:4114:20de:49:ffd3:fa6f:fc35 ( talk) 00:37, 17 July 2021 (UTC)
I recently made a draft page you can see here: /info/en/?search=Draft:Gallery_of_Atomic_Orbitals which was rejected. I think much of the content that appeared there would clarify some topics in this article. I think this article along with hydrogen atom and hydrogen-like atom are overcluttered and share a lot of redundant information. This is unfortunate and makes me not want to put in more material to clutter further, but perhaps the way of Wikipedia is to jam in too much information, sometimes in bad form, and then clean it up after the fact.. or don't.. I don't know.
In any case I propose to make the following adjustments: (1) Reformat the existing table of spherical harmonics to match that on the draft page. This is a more logical sorting that showcases that patterns between orbitals much better. (2) include a second table of complex orbitals next to the real orbitals for comparison. (3) ensure these tables follow the Condon-Shortley phase for consistency with the Table of spherical harmonics. (4) general cleanup of the text to be more concise in explaining the geometry of orbitals, (5) Include the formula for the solution to the Schrodinger equation for hydrogen like atoms on this page.
Regarding point (5), I know that that equation already appears on Hydrogen-like atom and hydrogen atom, but I don't understand why it appears there and not here. If that equation can't appear on this page then I don't think visualizations of those orbitals should appear so prolifically on this page. Regarding point (3) above, unfortunately the existing table of real spherical harmonics, while nice, and of very high quality, does not follow the Condon-Shortley phase as far as I can tell. Unfortunately this will spoil a little bit the comparison between real and complex orbitals, so long term it would be best to generate new images in the table which do follow that phase convention.
Folks should let me know if they think any of these updates would be "Wikipedia worthy" or valuable otherwise and I can get to work on them. Especially let me know what should be done about the inclusion of the Hydrogen orbital equation.. my main point there is that it is silly to have this page with so many orbitals visualized but without the equation. It makes the pictures difficult to talk about. My opinion is that this is the page that should have the equation and visualizations, and if that is too much for one page then it should be broken out into a specific page like the draft page I already made, not smattered across three largely redundant pages. — Preceding unsigned comment added by Twistar48 ( talk • contribs) 03:31, 23 February 2022 (UTC)
Also, make it easier for laypeople to understand. Azbookmobile ( talk) 00:00, 29 August 2022 (UTC)
At the end of the first paragraph are three equations for (real)psi(n,l,m). The lower right-hand corner reads "for m < 0". Common sense dictates this should be "for m > 0". Then again, common sense only plays a minor role in quantum physics. Could somebody more knowledgeable than me make the edit, or explain why we have two possible equations for m<0 and none for m>0? Thanks. 2600:6C5E:517F:E91D:2A:BF1A:6A3:1A5D ( talk) 02:26, 15 February 2023 (UTC)
This section (Shapes of orbitals) says "there is a non-zero probability of finding the electron (almost) anywhere in space". [1] Does this apply to all of an atom's electrons, or just those in the valence shell?
I'm going to suppose that holds for all electrons. Consider, for example, a (stable, non-radioactive) potassium atom, K. Suppose an electron in the 1s orbital (radius 3.175 pm) wanders off in the general direction of the 2s orbital (radius 14.82 pm). [2] Can it move very close to the 2s orbital, in apparent violation of the Pauli exclusion principle, because it "really" belongs to the 1s orbital? [3] If not, how close can it get to the 2s orbital before the exclusion principle takes over? [4] How would that "critical distance" be calculated, and does it depend on the position of the 2s electron with the same spin as the wandering 1s electron? Thanks for any help. JohnH~enwiki ( talk) 23:11, 13 March 2023 (UTC)
The text and concepts as presented are extremely confusing. I understand that there are historic reasons and conventions, but if something in less fit to function, it should be deprecated.
Atomic Orbit is a concept from classical physics, representing the path of an electron around the nucleus of an atom. It assumes electrons occupy specific, fixed paths at defined energy levels This has been proven to be inexact. There are no orbits, not paths only a field.
The Electron Field, the quantum mechanical concept describing the probability distribution to finding an electron near the nucleus. It accounts for the probabilistic nature of electron positions and the dynamic, wave-like properties of electrons. Why continue to muddle the concept when it serves no purpose and creates a mental model distant our consensual reality...
Unify and correct the nomenclature, making the historic links when necessary. It will be easier to read and understand. 89.114.174.221 ( talk) 03:41, 21 July 2024 (UTC)