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I know that because Schrödinger equations solution for probability of that region is 0, but I was looking for an intuitive explanation.

How can you intuitively explain the existence of nodes in an orbital?

M.A.R.
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ahmad
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  • There are nodes in orbital (like 2s orbital has one node i.e, probability of finding electron in that region is zero). So my question is why electron can not appear in node, just because we say electron can not be found in node. So is there any reason which sounds logical? – ahmad Aug 24 '16 at 16:05
  • It's a result we obtain from Schrödinger equation. What's wrong in having any? We could help you visualize the nodes if you brought the correct diagram or picture of an atom. – Akshar Gandhi Aug 24 '16 at 16:11
  • Why electron can not go in nodal region? Why it is restricted to go there? Just because Schrödinger equations solution to this region is zero. – ahmad Aug 24 '16 at 16:14
  • Yes, because of that. What's wrong with that? – Ivan Neretin Aug 24 '16 at 16:15
  • Is there any logical answer which fits into mind that why orbital has nodal region – ahmad Aug 24 '16 at 16:17
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    I have no way of knowing what would fit in your mind and what would not. – Ivan Neretin Aug 24 '16 at 16:21
  • Nothing will fit into your mind if you don't open it. Some things in Chemistry just *have* to be absorbed. Just the way you absorb that atoms are there, without actually confirming their existence by seeing them physically. – Akshar Gandhi Aug 24 '16 at 16:21
  • That being said, if you'll solve the Schrödinger equation for a variety of situations where it can be solved (harmonic oscillator, etc), you'll start to see the pattern. – Ivan Neretin Aug 24 '16 at 16:23
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    I don't think kids in high school have the tools to do that @Ivan. – Akshar Gandhi Aug 24 '16 at 16:25
  • Define "logical" answer? Why isn't " the wavefunction is zero at that point" not a logical answer? – getafix Aug 24 '16 at 16:25
  • I will repeat that question why electron can not appear in nodal region is there any reason like proton electron attraction or electron electron repulsion Ar any other factor which does not allow electron to be present there – ahmad Aug 24 '16 at 16:33
  • I think you guys are not getting the point behind my question – ahmad Aug 24 '16 at 16:34
  • @getafix they're perhaps looking for an intuitive explanation. – M.A.R. Aug 24 '16 at 16:34
  • Thanx dead for your contribution – ahmad Aug 24 '16 at 16:37
  • Well, in that case, quantum mechanics defies intuition (at least it defies mine). Our intuition comes from observations in the macroscopic world, and will not serve us well in the microscopic world. However, you asked for factors..factors which affect the functional form of the solutions are the shape of the potential, and the boundary conditions of the problem – getafix Aug 24 '16 at 16:41
  • Its sound better... – ahmad Aug 24 '16 at 16:45
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    @ahmad The point of all this discussion is, there is another property of matter, which is not intuitive at all. The "property" $F=ma$ is intuitive because we see it everywhere. Schrodinger's equation is another such "property", which is not at all intuitive. It is this property that gives birth to those nodes. You will have to study a little bit of quantum mechanics to understand more of it. Food for thought: "Properties" like the electrostatic force and so on also apply at that scale, along with this new one. – FreezingFire Aug 24 '16 at 17:41
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    https://en.wikipedia.org/wiki/Vibrations_of_a_circular_membrane – permeakra Aug 24 '16 at 19:07
  • http://chemistry.stackexchange.com/questions/35672/how-do-electrons-cross-nodes-in-orbitals http://chemistry.stackexchange.com/questions/8655/structure-of-atom-and-nodes – Mithoron Aug 24 '16 at 23:05
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    @getafix Let's keep it friendly, please (re: your first comment). Thanks! – jonsca Aug 25 '16 at 00:33

1 Answers1

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It is simply because the wave nature of the functions.

Imagine a tight rope with fixed ends (like a string in a guitar). If you shake it it will vibrate. Both ends remains fixed. If you take a high frame rate video and see it in slow motion, at a fixed horizontal length (let say $x$ positions) the rope will oscillate up and down with some amplitude. It can be seen one or more intermediate $x$ positions that remains always with null amplitude (if it is in state close to a stationary one). There you have nodes in one dimensional string.

Visual example

You would have more complex patterns going to a two dimensional system, and even more in a three dimensional case. They all have nodes, like the 1D case. The 3D case can be represented mathematically by using the spherical harmonics. The angular part of the solutions for the hydrogen atom are those spherical harmonics. The only intuitive explaining that I found is their wave nature. Of course it is not as visual as in the 1D case which is easily found in the daily life. And clearly, what is more weird is the wave nature of matter.

I hope that this answer address your question.

user1420303
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    Just to add to this, the 3D analogue of the "fixed ends" of the rope is the requirement that the wavefunction be square-integrable (aka normalisable), i.e. $\psi \to 0$ as $r \to \infty$. That would explain the presence of the radial nodes, angular nodes are a bit harder to justify imo. – orthocresol Aug 25 '16 at 04:41