Quantum mechanics and electrons.

[quantizedzeus]

Quantum mechanics and electrons...

Can anyone explain according to QM why do electrons move around nucleus...? And how does QM explain electrons' orbit or electron cloud...?...

 

[Polyrhythmic]

Quantum mechanics doesn't explain why electrons move around the nucleus, it explains why they don't. In Quantum mechanics, electrons are described by wave functions. You can calculate the solutions of the Schrödinger equation, and if you take the potential of the nucleus into account, you arrive at wavefunctions for the electrons in an atom.Those wavefunctions can be used to calculate a so-called probability density, which gives the probability of actually measuring an electron somewhere. The shapes of the probability densities are given by what we know as orbitals.

 

[quantizedzeus]

Quantum mechanics doesn't explain why electrons move around the nucleus, it explains why they don't.
If the electrons don't move around nucleus...then what do they do in atom...?...

 

[Drakkith]

They occupy the orbitals as a wave. An electron is not a little ball that orbits the nucleus like a planet orbits a star. A full description would delve deep into Quantum Mechanics and require you to understand what a Wave Function is along with a lot of other math and such. There are plenty of books online or at a bookstore or a library that you can find however.

 

[alxm]

The problem here is that the concept of 'motion' at the quantum scale is very different from the classical idea of motion. A quantum-mechanical object doesn't have a precise location or momentum. You can only know the probability of finding it in various locations. It can act as if it's 'in two places at once', having large probabilities at being found at two points in space separated by a large distance. That can even be the case in combination with an exactly zero probability of finding the particle in some intermediate location, meaning it can, in a sense, get from point A to point B without passing intermediate points.

Electrons moving around atoms don't follow the much-perpetuated picture where you have electrons wizzing around in elliptical 'orbits'. They can't move that way, because an orbit implies both a well-defined location and momentum. You can calculate the average position of an electron in an atom. You can calculate it's average momentum (which is zero of course, since an electron with a net average momentum would simply fly away from the atom!). You can calculate its average kinetic energy, or the average magnitude of the momentum though, and those values are non-zero.

Does an electron in an atom move? I would say yes, and I think most physicists would say yes. (in fact 'electron motion' is a quite established term among those who study it). But at the same time, it's understood that it's not 'moving' the classical sense of the word. You cannot predict where an electron may be located other than as a probability. Knowledge of where an electron is at one point in time does not enable you to predict where it's going and where it'll be measured next.

Now if you as "Why do electrons in an atom move?", that question only makes sense in terms of classical physics. Classically, an electron could simply lose all its kinetic energy; classical electrodynamics say that it actually must do so by itself, because an accelerating charge gives off radiation. But the mechanism by which it might lose its kinetic energy doesn't really matter - in principle it should be able to lose that kinetic energy and just sit still at the nucleus, where its potential energy is lowest - since the positive charge attracts it.

Quantum-mechanically, this is not permitted. You can rationalize that in terms of what I already said: A quantum mechanical object doesn't - and can't - have a definite location in space. The reason for this is that its probability distribution for position and momentum aren't independent of each other, unlike in classical mechanics where those are separate quantities. That's the basis of the famous uncertainty principle. If the electron was exactly located at one point in space (100% probability at x, 0% probability everywhere else), then it would have infinite momentum, and so, infinite kinetic energy. This is basically the 'wave-like' nature of the electrons in effect.

So in short, the more confined the electron is to a particular region of space, the higher its kinetic energy. On the other hand, the more spread out the electron is in space, the farther it is from the positively-charged nucleus. So you have potential energy working to 'pull' the electron in, so to speak, and kinetic energy working to 'push' it out. As a result, the only stable states of the electrons are where these two 'forces' balance each other out. (This is basically a verbal statement of the Schrödinger equation) And the lowest possible stable state is what we call the ground state. And unlike in classical mechanics, that state doesn't have zero kinetic energy, but merely the minimal amount of kinetic energy.

 

[Jacques_L]

The two models, the planetarian one, and following the Schrödinger equation, differ strongly in the symmetries and angular momentum they predict.

In the planetary model, the symmetry is like a turn of current. The angular momentum stay in a definite plane, the plane of the orbit, and this plane is a plane of symmetry.

In the Schrödinger's model, in the lower state of the hydrogen atom, the symmetry is completely spheric, no angular momentum at all.

Clearly, it is not at all the same physics.

 

[Drakkith]

You are correct Jacques, it is not the same physics. Quantum Mechanics replaced Newtonian at the atomic scale about 90 years ago. The "Planetary Model" is simply an easy way of showing the concept of the atom to people. It isn't accurate.

 

[kshitij123]

Can anyone please explain to me what actually is a wave function and what it describes. I don't get how a wave function helps us to understand atomic orbitals? Please explain.

 

[jtbell]

Hi Kgarbageij, welcome to Physics Forums!

Try reading the Wikipedia page

http://en.wikipedia.org/wiki/Wave_function

and then ask questions about specific things that you don't understand. That might work better than for us to guess exactly what you're looking for.

 

[timmyeatchips]

What about Einsteinian effects? I've heard many phenomena (most famously the colour of gold) explained as relativistic effects due to the speed of electrons around heavy nuclei. How does that fit?

 

[kshitij123]

Hi Kgarbageij, welcome to Physics Forums!

Try reading the Wikipedia page

http://en.wikipedia.org/wiki/Wave_function

and then ask questions about specific things that you don't understand. That might work better than for us to guess exactly what you're looking for.

Thank you. I went to the link and read the article. I want to know what is denoted by the sign ψ and its significance. I studied about atomic orbitals and i want to know, how actually in a 3 d space these orbitals and sub shells and shells are arranged inside an atom.

thanks for your reply.

 

[alxm]

What about Einsteinian effects? I've heard many phenomena (most famously the colour of gold) explained as relativistic effects due to the speed of electrons around heavy nuclei. How does that fit?

"Einsteinian"? Anyway, it fits fine. I don't understand what answer you're looking for. Either you use the Breit-Pauli Hamiltonian or solve the Dirac equation, or model it as an "effective core potential". (A. L. Bruce here is wrong - you do not usually use quantum field-theoretical methods to handle relativistic effects in atoms.)

Anyway, it amounts to a shifting of the levels and contraction of the orbitals (famously the lanthanide contraction is in part due to relativistic effects), which becomes more pronounced in heavy atoms.

In gold, the band gap which is in the UV in silver gets shifted down into the blue, giving blue absorption and yellow color.

 

[Naty1]

For those looking into electron orbitals, another complementary article to the one posted above is here: http://en.wikipedia.org/wiki/Atomic_orbital

Some of the terminology seems a bit confusing, for example "orbiting electrons" is actually referring to wave functions not point particles.

 

[Naty1]

I would also note that, and this is likely going to generate howls of protest from purists, that we don't really know WHY electrons behave as they do. We don't even know why they have the mass nor the charge we observe. But very smart people have worked around such limitations in building up mathematical models that explain much of WHAT we observe.

Can anyone explain according to QM why do electrons move around nucleus...? And how does QM explain electrons' orbit or electron cloud...?...

...

So I think all the above posts address the second part, not so much "why" of the first part.
I think it's critically important to keep such distinctions in mind...there is still more to learn!

You can get a feel for this several different ways: We have, for example, the "Pauli exclusion principle"...that means somebody observed certain behavior, could not really explain it from fundamentals, and so established a "principle" reflecting experimentl behavior.

Wikipedia explains it this way:

Pauli looked for an explanation for these numbers, which were at first only empirical. At the same time he was trying to explain experimental results in the Zeeman effect in atomic spectroscopy and in ferromagnetism.

Another example is:

In other words, the spin-statistics theorem states that integer spin particles are bosons, while half-integer spin particles are fermions.

http://en.wikipedia.org/wiki/Spin-statistics_theorem

There is further discussion of a "proof" of the theorem: So we have a set of mathematics that explains what is happening, but not necessarily WHY...and we can show consistency between different portions of our models.

A third example are the symmetries of the Standard Model of particle physics: It unifies the three fundamental forces (gravity does not fit) by splicing together the symmetries of the individual forces. Why what is the origin of these symmetries/ Why do they exist? I don't think anybody really knows yet.

 

[Naty1]

I intentionally omitted the Heisenberg uncertainty principle from the prior post.

I'd be interested in comments about whether of not we know "why" this applies to the standard model...for me, there seems some additional underlying logic that goes beyond the examples in the prior post, but that may just reflect my own limited knolwedge.

Wikipedia has a good discussion on uncertainty...interpretations, derivations,etc:

Any two variables that do not commute cannot be measured simultaneously — the more precisely one is known, the less precisely the other can be known. Heisenberg wrote:

It can be expressed in its simplest form as follows: One can never know with perfect accuracy both of those two important factors which determine the movement of one of the smallest particles—its position and its velocity. It is impossible to determine accurately both the position and the direction and speed of a particle at the same instant.[

 

[alxm]

I didn't say that. I said in general you need field theory in combining SR and QM, and if you think you don't I advise you to publish your findings on the arXiv so we can proceed to give you a Nobel prize and hail you as a god .

Dirac already got the Nobel back in 1933, and I already cited three different methods used to take SR effects into account in electronic structure calculations. Pick up any book on relativistic effects in atoms/molecules and read all about it.

There is simply no truth to the statement that accounting for SR effects require field theory. (or for that matter, that all field theories are relativistic) That's just a common misconception rooted in the fact that most curricula go from non-relativistic QM to QFT with a minimal treatment of what's in-between. Fully accounting for quantized-field effects generally requires a QFT description (by definition). Generally a distinction is made between "relativistic effects" and "QED effects", precisely because the former is routinely taken into account in electronic-structure calculations, and the latter is very rarely calculated. (Specifically, the yellow color of gold does not involve QED effects.)