# Bohr/De Broglie simplfied model - joining orbitals

I understand that Quantum Mechanics has taken over and fully explains this but I'm struggling to understand in terms of the old model. Bohr's model as modified by de Broglie suggested that orbits involved the wave function of the electron becoming a standing wave around the nucleus.

My question is:

• In this old (and wrong) model, how did the electron decide to change from simply flying past the proton free to take any path to joining a quantised orbit around the nucleus?
• why the hell was this question down voted? I'm so sick of people just going and down voting every single question without a single suggestion for edit in the comments. How am I supposed to ask 'better' questions when they always just get down voted to oblivion until no one will answer with no explanation? :( – J-S Apr 13 '15 at 12:11
• Seeking for an explanation of an effect within a model that doesn't actually claim to explain said effect simply isn't a very useful question. – ACuriousMind Apr 13 '15 at 12:29
• Well I didn't know that, hence asking the question.... this seems to pretty obvious to me that someone asking an invalid question could possibly not know its invalid? – J-S Apr 13 '15 at 12:30
• Of course. Downvotes are not a judgement of you, but of the question. And at least two people thought this isn't a very useful (useful to others, or in general, not to you personally, mind you) question to ask. That's all there is to a downvote, don't get too upset about it. – ACuriousMind Apr 13 '15 at 12:33
• @user2353082, you give others too much power over you by taking such offense. Also, anyone that finds something in your question interesting and considers writing an answer as a productive use of their time, will unlikely be be dissuaded to answer due to downvotes. However, they might be dissuaded by your response to the downvotes. – Alfred Centauri Apr 13 '15 at 16:05

This is a tough one. I'm going to take the liberty of rewording the question, and then use analogies to hopefully give some kind of answer that gets us part of the way there with this arguably obscure but worthy issue.

How did the electron change from simply flying past the proton to adopting a quantised orbit around it?

Because it was attracted towards the proton via linear and rotational electromagnetic force, and because it's a "spinor" with a wave nature which we can depict like this:

It isn't some point-particle thing that goes round the proton like a planet orbits the Sun. See atomic orbitals where electrons "exist as standing waves", and remember the wave nature of matter. We make electrons out of light waves in pair production, and we can diffract them. The electron is more like a wave stuck in a Dirac's belt configuration, like Saturn's rings with a twist. And it goes from just going round itself all on its own, to also going round a proton. For an analogy think of a cyclone going round and round, and also going round and round an intense anticyclone at its centre. Alternatively think of a hoop spinning like a spokeless wheel, then think hula hoop. Then think of the quantised orbits as something like gears. When you hula your hoop, you can go from one wavelength per hula to two or three etc. But if it isn't an integer number, you can't keep up the rhythm.

• This makes a lot of sense, so as the electron wave rotating on it's own approaches the proton it simply spins behind it naturally? I'm guessing I'm pushing the (simplified) model by asking how the little wave moves through space? – J-S Apr 13 '15 at 21:51
• Sorry, I'm not sure what you mean. I think the best way to get a handle on this is via cyclones and anticyclones, wherein counter-rotating vortices attract and co-rotating vortices repel. The cyclone and the anticyclone approach one another and move round one another, only if one is more massive, it doesn't move so much, and if it's smaller it can sit in the middle of the other. This isn't a perfect analogy of course, but IMHO it's much better than the Sun-and-planet analogy that most people tend to think about when it comes to the Bohr atom. – John Duffield Apr 13 '15 at 22:14
• Ok so how does the anti-cyclone 'get in' the cyclone? What I meant was how does the way the cyclone move through space allow it to jump on top of the anti cyclone? Does it just come from above in 3D space? But then what happens if the cyclones are spinning on the same plane? Surely the edges would hit? Or is the electron wave not just spinning around the curve but rather in all three dimensions? – J-S Apr 13 '15 at 22:37
• Oh I just realised my mistake, one side passes straight through the nucleus doesn't it because the wave is probabilistic so it can pass through and then the attraction and repulsion on each side for the wave causes it to stop moving? So the wave can pass through the nucleus the probability of the electron being there just collapses to 0 as it passes through? – J-S Apr 13 '15 at 22:51
• By the way just thought I'd said thank you very much for such a great explanation. I've been trying to develop some sort of visual model of Bohr and de Broglie's complete but couldn't figure out how to model the joining and leaving of orbits and this really helped however I do need to reference sources so can you suggest anywhere to reference in my assignments? – J-S Apr 14 '15 at 4:01

What makes you think that the question has an answer? The Bohr model has limited validity and this was realized from the start.

In essence, you're describing a transition from an unbound state of the electron (with positive total energy) to a bound state (with negative total energy). This cannot happen all by itself, as the extra energy needs to go somewhere, but it can conceivably happen with the emission of a photon.

In this case, the transition is no different to any transition between bound states. The Bohr model has very little to say about transitions. In essence, it states

A bound electron can only occupy the orbits in the set $\{\cdots\}$, and it can transition between them by emitting or absorbing radiation

but it doesn't say anything about the probability of such transitions happening or the mechanisms that induce them.

Unless, of course, you're thinking of an electron which (i) is already near the nucleus, and (ii) already has a low enough velocity to be in a bound state. In that case, your question "how did the electron decide to change from simply flying past the proton free to take any path to joining a quantised orbit around the nucleus?" essentially boils down to "how did the electron decide to suddenly notice the nucleus?", which you should be able to see is a ridiculous question to ask.

• So you're saying the Bohr model did not predict when an electron would join/orbit an atom? – J-S Apr 13 '15 at 12:19
• What do you mean by "join/orbit an atom"? What sort of situation would the electron be in before it "joined" the atom? This is an ill-posed question and you are not giving many handles on how to approach it. As to "when would an electron orbit an atom?", what else would it do? Consider, in particularly, that classical electrodynamics was well understood at that point. – Emilio Pisanty Apr 13 '15 at 13:24