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Perhaps speaking of direction of an electron isn't quite correct. But does QM indicates a kind of way whether all electrons are going e.g. 'clockwise' or not? Of course QM just gives a probability where the electrons are, but can you emerge whether they are going, in some way, in the opposite direction of each other?

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If you are asking about electron Spin, rather than electron Orbitals, then IIRC, by the convention of the Right-Hand rule, all electrons spin counter-clockwise wrt their magnetic (north) pole and all positrons spin clockwise. (though I may have that backwards). – RBarryYoung Feb 9 at 16:15
up vote 25 down vote accepted

As you intuit, it is indeed pretty hard to define a sense of "direction" for an atomic electron within quantum mechanics when the electron doesn't have an orbit but it is instead some fuzzy ball of probability, but it is doable and in fact it is one of the central constructs in atomic physics.

What ends up mattering is angular momentum, i.e. how much the electron's motion "turns" around the nucleus. As it happens, it is perfectly possible to define a fuzzy ball of probability for the electron which does not have a definite position and does not have a definite (linear) momentum, but which does have definite angular momentum. A bit weird, but that's what it is. Most atomic electrons are in states like this.

As to your broader question - whether all the electrons are going around in the same direction or not - the answer is simply "it depends".

  • Some atoms, like the noble gases, the alkaline earth metals, and the zinc-cadmium-mercury right-hand edge of the transition metals, have "full shells" which roughly means that for every electron going clockwise about a given axis there is another electron going counterclockwise.

  • Some atoms, like vanadium, cobalt or nickel, have many unpaired electrons, and have a fairly large overall angular momentum of the electronic motion.

In general, the angular momentum of any closed electron shell is zero (i.e. the electrons in the inner shells have one counterclockwise electron for every clockwise one) and it is the outermost, 'valence' shell that determines the angular momentum properties of the atom.

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Do you mean by 'for every electron going clockwise about a given axis there is another electron going counterclockwise' the spin of an elektron (up or down) which have to be according to Pauli equal at each orbital? – Marijn Feb 9 at 15:49
There are two contributions of angular momentum, orbital and spin. In a closed shell, each slot has two electrons of equal but opposite spin, and each slot with nonzero orbital angular momentum has a corresponding full slot with equal but opposite orbital angular momentum. The total angular momentum is therefore zero (for a full shell). – Emilio Pisanty Feb 9 at 18:47
Are you saying that for a particular element the angular momentum is always the same, so we wouldn't have one case of (say) one atom of nickel with two extra clockwise electrons while a different atom of nickel has two extra counter clockwise electrons or a third which might have extra four clockwise electrons? And second, it seems you are saying electrons don't always pair directly, so you can have more than one extra electron with the same angular momentum? – Michael Feb 9 at 22:27
@Michael This is a (hopefully obvious) gross simplification of how angular momentum works inside atoms, to match the OP's terminology. Electron pairing is a relatively complex procedure, but indeed you can have two electrons with the same orbital angular momentum (but opposite spin). The description here applies only to the atomic ground states, and for any given atom you can always "spin up" the electron motion by driving to excited states. That said, any two (say) nickel atoms in their ground state will have the same amount of total angular momentum, differing only in its direction. – Emilio Pisanty Feb 9 at 22:58

Yes, quantum mechanics allows you to speak of clockwise or anti-clockwise motion, but it comes with the usual caveats of quantum mechanics. The tool that tells clockwise from anti-clockwise motion is the angular momentum. Motion is anti-clockwise around an axis, say the $z$-axis, if the component of angular momentum along that axis is positive. There is an observable for $L_z$ in quantum mechanics, so this carries over. But it comes with the usual caveat that in quantum mechanics $L_z$ need not have a definite value. (Some people would phrase this as that the motion can be "both clockwise and anti-clockwise at the same time" just like certain cat is supposedly "both dead and alive". I think this is trying to force QM to be CM "under the hood", when in reality it's exactly the opposite.)

As for the degree to which atoms have definite angular momentum: in a hydrogen-like atom, the interaction respects rotation symmetry. Therefore, the angular momentum will be conserved and can have a definite value at the same time as the energy does. The conserved angular momentum is, however, the total angular momentum, which is the sum of orbital angular momentum and the spin of the electron. (The sum can have a definite value even though each term does not.)

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Do electrons in an atom always have the same 'direction'?

No. They can have different 'directions'. Note the wikipedia atomic orbitals article which says an atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. Later on, 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. The thing about standing waves is that they look motionless, but there's a hidden motion present, and there's a direction associated with this. For example if you have a photon trapped as a standing wave in a cavity, when you open the box the photon is off like a shot in some direction at c from a standing start. However it didn't instantaneously accelerate from 0 to c, because it was always moving at c, back and forth in some direction.

Perhaps speaking of direction of an electron isn't quite correct. But does QM indicates a kind of way whether all electrons are going e.g. 'clockwise' or not?

'Direction' isn't quite correct, and nor is 'clockwise'. For an analogy, imagine a glass clock, without any numbers on its face. The hands are rotating in a clockwise direction. However from the back, the hands are rotating in an anticlockwise direction. So if you spin the clock like a coin, it's very difficult to say whether the motion of the hands is clockwise or anticlockwise. But you can spin the clock one way with your left hand or another way your right hand, and this does give you two different "bispinor" spins. Calling one clockwise and the other anticlockwise doesn't quite get the difference across. But the angular momentum is genuine. Check out the Einstein-de Haas effect, which demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics.

Of course QM just gives a probability where the electrons are

Take care with that. Spherical harmonics is all to do with wave motion. Not the probability of finding a point-particle at some location. The electron is not a point particle. We can diffract electrons. Electrons have a wave nature.

but can you emerge whether they are going, in some way, in the opposite direction of each other?

Yes. For electrons in atomic orbitals the "hidden" motion isn't totally hidden. It's like the standing wave isn't quite standing. For example in a hydrogen atom the electron is said to move at 137th the speed of light. There's a motion going on, and it can go one way or the other. A bit like that spinning clock. But since that's hard to visualize, think instead of a hula-hoop. You can hula your hoop one way or another, and if you were really good at it, you could hula one hoop one way, and another hoop the other. In atomic orbitals, in the closed shells, it's something like that.

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In my opinion, in stable atoms part of its electrons should rotate in opposite direction of other electrons to maintain stable conditions.
This means that if it loose an electron or gain the atom charge will change and called ion.

In our old understanding only losing and gaining is from out orbit. I believe this is completely wrong thinking because the atom and its electrons are believed to change shape and electron orbits were believed that electrons are moving in circular forms they are moving in spiral form around the nucleus.

And this type of movement is the explanation for forming what is known to us magnetic field. When potential difference been applied on what is known the area of electron rotation space or orbit.

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protected by Qmechanic Mar 30 at 11:50

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