Science a GoGo's Home Page Forums General Discussion Physics Forum How closely can an electron approach a nucleus?

This is an oversimplification, but I wonder if it has any merit in terms of a layman-level explanation.

If the energy levels in an atom are considered as orbitals, and the associated electrons as waves, it would follow that only waves of which a whole number of half-wavelengths fitted exactly on an orbital would be able to occupy that energy level.

An increase in the energy of an electron moves it to a higher energy level; that is away from the nucleus. A decrease in energy moves it towards the nucleus.

Energy is inversely proportional to wavelength, so decreasing energy involves increasing wavelength. A point must be reached where one half-wavelength equals one orbital. This would be the point of closest approach to the nucleus, as no other wavelength would fit a closer orbital.

Comments, please.

There is no merit in it at all, you are trying to resurrect something like a modified Bohr atomic model and it will fail in everyway possible even at the simplest level.

Even using the old chemistry orbitals you have to create strange shape for the orbitals and weird sets of rules for how they fill and there energy level. The problem is as you introduce isotopes all the rules will collapse and are meaningless.

As for where the electrons are you can show by creating a "hollow atom" that there is a non zero probability that the electrons will occupy the sme space as the nucleus.

There are plenty of texts around on the old chemisty orbital models and it's rules and there is no point trying to simplify lower than that even for a layman.

There's something I certainly couldn't explain to someone else!
Could you say a bit more about that, please.

Eg:
What is a "hollow atom"?
How do you "create" it?
Do the nucleus and electron both have to be seen as waves to occupy the same space?
What happens to their opposite charges?

Here is a reasonable article on how we bend, shape, twist and manipulate atoms.

http://www.scientificamerican.com/article/giant-heavy-and-hollow-physicists-create-extreme-atoms/

It's reasonably laymanish and keeps most of the discussion to classical concepts.

The charge in the atoms are waves the same as you are familiar with in radio waves I have seen you discussing EB fields in them. So nothing really to add on that regard.

It's really hard to discuss how we are targetting and manipulating the atomic structure unless you do consider them as waves. That is why I have real issues with your simplification because it leads to really wrong conclusions. It really is much easier to just make a pile of waves describing the nucleus and a few bigger area waves describing the electrons. It's just as wrong as you idea but at least all naive ideas lead to the right sorts of conclusions.

I actually cant see any naive extension of your idea that will be correct. From the article where are the highest energy levels and where does your model predict them to be?

Interesting link, thanks.

The question I was, slowly, working towards was “How can beta decay of a neutron take place if an electron cannot be inside the nucleus?”

Before this thread dies, I'm going to have another shot at getting to grips with the situation.

I am aware that the Bohr model of the atom, which was quite adequate for mineralogy, is decades out of date. Energy levels are a bit more up to date, but constitute an oversimplification.

Would a more realistic model be something like: When the electron is not being measured, it could be anywhere in the Universe. However, the likelihood that it will be found outside a specific distance from the nucleus is vanishingly small. The possibility of finding the electron inside the nucleus is only slightly more likely, but must occur in forms of beta decay.

The most likely places to find an electron would be at one of a number of levels within the “specific distance” mentioned above. The particular level at which it is found will be linked to the energy of the electron, and will be subject to the Pauli exclusion principle in the case of an atom with more than one electron.

Did I leave it too late?

Sorry missed this one.


Let me first deal with this statement which is both not needed and I feel you have turned into a statement of "reality" because that is what lots of science media does.

That statement comes back to a mathematical solution called the path integral formulation (https://en.wikipedia.org/wiki/Path_integral_formulation). The problem here is that it is a calculation process not something ever observed, and observation is expressly denied. For myself given those two conditions I don't consider it "real" but I have no objection if others do because we can never settle the argument. To me this is just fluff around the answer.


Correct and I would start with that.


It occurs a lot more than slightly electrons in s-shell have significant probability of overlapping the nucleus which is easiest to see if we display their wave functions in drum mode.
This is 1s,2s and 3s orbitals



If you run a classical Bohr calculation the s electrons will be orbiting inside the measured nucleus diameter and be fully captured.


At the moment you have distance rings there is no discussion of shape look at the orbital shape pictures again.


Agreed but I have concerns you are treating the electrons like tagged objects that electron 1 is in this orbital and electron 2 is in another. That is most certainly not the case the electrons will freely exchange positions the probability formulas tell you that and it is important in pair bonding etc.

You see what I am getting at here trying to make electrons solid classical objects just leads to wrong conclusions. How does one bring two solid electron balls together in an energy favourable way?

Some time ago I thought that a major problem with thinking about QM was that I was trying to fit quons to classical images. It worked well when I was studying rocks and minerals, but I am gradually trying to replace this by telling myself that we have no exact matches between quantum and classical realms, and that the analogies we use are just that - analogies.

I just need some time to follow up on your post before commenting further.

Statements like: “When the electron is not being measured, it could be anywhere in the Universe” are not uncommon in Pop Sci books, etc; so I need to reach a point where I think I can understand what the people who make that statement are getting at.

I think the point I have reached, so far, is that the nearest one could get to regarding the electron as being anywhere in the Universe would be to say that an electron is an excitation of the electron field, which is everywhere in the Universe.

Obviously the possibility of finding an electron within the radius of the nucleus is commoner than I thought. What about the possibility of finding the electron in the centre of the nucleus? Is trying to identify the centre of the nucleus a non-starter?



What, then, is the significance of energy levels, and what is it that the Pauli Exclusion Principle prevents electrons from doing with respect to those levels?

My understanding would be that these “levels” are significant only when the electron is observed. Is that on the right lines?