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In a hydrogen atom an electron is orbiting around a proton, similarly to a moon around a planet. The orbit of a moon around a planet is flat (2D) whereas the orbit of an electron around a proton is spherical (3D). Why is this?

Qmechanic
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Laff70
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    This is why students should be weened off the Bohr atom at the very earliest opportunity, and one should always clearly distinguish between "orbit" and "orbital". – dmckee --- ex-moderator kitten Nov 22 '15 at 18:48
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    "In a hydrogen atom an electron is orbiting around a proton, similarly to a moon around a planet"...no, it isn't, see e.g. What is wrong with the Bohr model?, Trouble understanding the Bohr model of the atom – ACuriousMind Nov 22 '15 at 18:48
  • @dmckee: no more 'lies to the children!' ;-) – Gert Nov 22 '15 at 18:51
  • @Gert Lies to children are important and useful, but once they aren't literal kiddies anymore students should know when they are being lied to. If only so that they know that the model they've been given now is incomplete and more is coming later. – dmckee --- ex-moderator kitten Nov 22 '15 at 18:54
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    @qftishard on the contrary, the answer is that it isn't in an orbit at all. – dmckee --- ex-moderator kitten Nov 22 '15 at 18:55
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    @dmckee: there's an argument to be made for teaching modern QM of the H atom first and later discussing Bohr as a matter of history. Education systems are full of baggage due to inertia. – Gert Nov 22 '15 at 18:58
  • @Gert That is the right way to teach modern physics, but what do you tell students in middle school or high school? They don't have the background for the real thing, but they need some idea of how an atom works to handle the level of chemistry they are ready for. – dmckee --- ex-moderator kitten Nov 22 '15 at 19:00
  • Laff70, in addition to the links @ACuriousMind offers there is http://physics.stackexchange.com/q/89351/ and several other links on the site about the relationship between atomic electrons and their nuclei. – dmckee --- ex-moderator kitten Nov 22 '15 at 19:01
  • @dmckee: the version of Bohr they get fed at MS is diluted too. It's possible to teach the SE at a fairly simple level, then build from there. I was taught simple Q Chemistry from about 17. Still learning today... – Gert Nov 22 '15 at 19:02
  • I do know about the idea that it isn't really an orbit and instead it is more of a probability of the electron being found in a certain place due to the electron's wave function. It just doesn't make any sense from a logical perspective. I think I'm going to try to simulate a hydrogen atom again later today but this time make the center of force emission different from the center of gravity and give it some torque. Hopefully it'll make the electron get into a more 3D orbit. – Laff70 Nov 22 '15 at 19:05
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    @Laff70: "It just doesn't make any sense from a logical perspective". No, it does make perfect logical sense. QM seems at first counter-intuitive but one gets used to it very quickly. To see why your model is bound to fail, just study the paradoxes Bohr's model leads to. – Gert Nov 22 '15 at 19:07
  • @Gert I don't think the notion that particles such as electrons and photons can manifest as waves is correct. Waves need a medium to propagate through(hence why scientists searched for the ether). Electrons and photons have no said medium and as such can't be waves. Instead I think there are complex force-based interactions which give rise to wave-like properties. Since the current model of the atom requires electrons be waves, I think it isn't correct. – Laff70 Nov 22 '15 at 19:17
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    @Laff70 Note that you said "searched for". They didn't find it because it isn't there. Electromagnetic waves need no "medium" in the sense that water waves, sound or waves on a string need a medium, but they still exist. I'm afraid you rather more wrong than right on this: we do experiments in which we employ the diffraction and interference of such objects as electrons, neutrons and even $\mathrm{C}_{60}$ atoms, so their wavelike behaviors are a matter of experimental fact. – dmckee --- ex-moderator kitten Nov 22 '15 at 19:23
  • @Laff70 - This is a (very) tangential comment, but you should know that a planet/star/black hole orbiting "close" to a fast rotating large black hole will not orbit in a simple 2D plane like our planets. Given enough time (ignoring decaying orbits), the satellite will effectively cover an entire spherical shell around the large black hole. The distortions due to gravitational waves and frame dragging can change the fields and space-time metrics so that 2D orbits are no longer possible... – honeste_vivere Nov 22 '15 at 19:31
  • @Laff70: "I don't think the notion that particles such as electrons and photons can manifest as waves is correct." Apart from the relevant comment by dmckee (not all waves need a medium), the matter waves we talk about in QM aren't to be equated with Classical waves like sound or water waves. Yet the probability amplitudes are wavy and quantum particles show wavy behaviour like diffraction. – Gert Nov 22 '15 at 19:38
  • @Laff70 Don't bother trying to model hydrogen using classical physics. You can try different force laws, but you'll be missing the point entirely. The force in the (simplest model of) a hydrogen atom is simply the inverse square law from a point charge. Changing that takes you nowhere useful. – garyp Nov 22 '15 at 19:40
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    @garyp: let him try within mainstream physics and post his progress here as a question. I, for one, would be all ear (no snark). – Gert Nov 22 '15 at 19:42
  • @dmckee I don't think there is an ether. – Laff70 Nov 22 '15 at 19:47
  • @honeste_vivere could you point me to some more information about that phenomena please? – Laff70 Nov 22 '15 at 19:51
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    @garyp I still plan on trying. – Laff70 Nov 22 '15 at 19:51
  • The answer to your question is that the Hamiltonian is symmetric under 3-dimensional rotations. – WillO Nov 23 '15 at 05:34
  • I would have a look at this page to help clarify the "electron as a wave" thing, and one of these two (1) (2) pages for information concerning the form of electron orbitals. – CoilKid Nov 24 '15 at 02:05

2 Answers2

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One has to distinguish between, on one hand, an orbit and an orbital motion, which are classical notions; and on the other hand, an orbital, which is a quantum mechanical notion, cf. above comment by dmckee.

If the question is really Why quantum mechanics?, then have a look at e.g. this Phys.SE post and links therein.

Here we will assume that OP accepts quantum mechanics as is, but is genuinely puzzled why the electron is not confined to a 2D plane?

By rotation of the coordinate system, we may assume without loss of generality, that the hypothetical 2D plane corresponds to $z=0$.

Quantum mechanically, this question actually can be realized. It corresponds to a wave function $\psi$ that has support at $z=0$, say, because of a wave function collapse after measuring that $z=0$.

However, if one calculates the average energy $\langle \psi |\hat{H}| \psi \rangle$, it would be positive, because of the non-constancy of the wavefunction in the $z$-direction packs a lot of positive kinetic energy.

So the electron would no longer be bound to the nucleus. The precise measurement $z=0$ intuitively transfered so much energy to the electron that it is no longer bounded.

Now the observable $\hat{z}$ does not commute with the Hamiltonian $\hat{H}$. If we want the electron to be bounded to the nucleus, and hence that the average energy $\langle \psi |\hat{H}| \psi \rangle$ is negative, we cannot know the $z$-position very well, cf. Heisenberg's uncertainty principle (HUP).

In other words, the wave function must be have support in a 3D bulk rather than in a 2D plane. Phrased differently, a 3D spherical symmetric wave function is energetically favored, in order to have as little energy as possible.

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Qmechanic
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Electron in a ground state hydrogen atom has zero angular momentum $L^2$, l=0.

Moon has a huge angular momentum. Therefore it is a poor comparison.

If moon would have zero angular momentum, in classical physics, it would fall down and hit earth.

Electron in an hydrogen atom, in l=0 state gets constantly pulled to the center, but this is countered by the quantum mechanical kinetic energy making the orbital finite.

If there would be an electron with the mass, angular momentum and position uncerainity of the moon, this would be a linear combination of very high (l=1853728172728993937272292662182829 and so) angular momentum states. In other words, It is possible to create angular wave functions which are planar. They exist already in molecular level.

Mikael Kuisma
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