Understanding Atomic Scale Potentials: The Role of Electrons as a Continuum

[Cyrus]

Hi tide,
A while back I asked you about potential. And you said to consider the electrons as a continuum when we talk about a body having charge on its surface. Its clear that if you have any finite number of point charges, (the electrons), then there is no way you can arrange them so that the surface is equipotential. So how is potential fixed for this problem when working at the atomic scale. I don't see how you could have an equipotential surface at the atomic scale when dealing with point charge electrons.

 

[Tide]

Hi tide,
A while back I asked you about potential. And you said to consider the electrons as a continuum when we talk about a body having charge on its surface. Its clear that if you have any finite number of point charges, (the electrons), then there is no way you can arrange them so that the surface is equipotential. So how is potential fixed for this problem when working at the atomic scale. I don't see how you could have an equipotential surface at the atomic scale when dealing with point charge electrons.

Hey, Cyrus! How's it going?

At the atomic scale you don't have a nice smooth spherically symmetric equipotential surface (corresponding to the surface of the spherical conductor of our earlier discussion). The atomic level equipotential surfaces in that case vary wildly in both space and time as the electrons (and ions) jitter about. It's the difference between the macroscopic and the microscopic worlds.

To make the point, consider a pane of glass. Visually and tactually, it is very smooth. But if you could move in (perhaps using a scanning electron microscope) REAL close - right down to the atomic level - your notion of the glass being smooth will evaporate when you see the vast open areas punctuated by metaphorical boulders rumbling about in a bizarre game of dodgeball.

 

[Cyrus]

So is there no such thing as equipotential surface at the microscopic level? I was just wondering if there was some sort of a bridge that could connect the macroscopic and the microscopic to have something that is consistent when dealing with one case or the other. As for your analogy, I see what you mean, but at the same token there is more charge on the outer surface. Building on your analogy, if I zoomed in on that glass pane, I have to see some charge somewhere because its charged, in fact i should see it on the surface on the pane.

 

[Tide]

There are, in fact, equipotential surfaces at the atomic level. They are just not the same ones as the nice smooth macrosopically spherically symmetric equipotential surfaces we use as idealizations!

Here's another analogy for you. We talk about "sea level" even though the sea is not level or even smooth with all the waves, eddies, turbulence, tides and currents. Nevertheless, it's a very useful concept!

 

[Cyrus]

STOP WITH THE ANALOGIES! . I get the point of your analogies! Can you explain to me (no analogies this time), how does that problem get corrected for at the atomic level. Can you tell me exactly how physics got around this problem when dealing with the problem I presented. Because point charge electrons can't make an equipotential. Is this where the concept of electrons as a wave instead of a particle comes into play? Not trying to be rude tide, but this is like the 6th analogy you gave me, and I am looking for a real anwser so to speak.

 

[rayjohn01]

He already gave you the answer -- surfaces at the atomic level can be considered to exist but they are dynamic not static and they are not very useful, physics usually deal with the average of such situations or probablistic based on energy flow in interactions -- whay is it you really want to know -- you can ask all sorts of questions does not mean there is some perfect answer.

 

[Tide]

Cyrus,

Im looking for a real anwser so to speak.

I have already given you the real answer with which you seem to continue having difficulty so I resorted to analogies. Perhaps someone else will have better luck.

 

[Cyrus]

Thats ok, thanks for trying tide, I am a hopeless cause. Hey btw, can you check what I did in the circular motion post tide. I am not sure If i solved the problem correctly or not, and I think zapperz pretty much thinks my solution is trash. It was quite a lively conversation, to say the least.

 

[pmb_phy]

Thats ok, thanks for trying tide, I am a hopeless cause. Hey btw, can you check what I did in the circular motion post tide. I am not sure If i solved the problem correctly or not, and I think zapperz pretty much thinks my solution is trash. It was quite a lively conversation, to say the least.

Once you get down to the atomic level classical thinking breaks down. It can be useful to think of electrons as point particles which buzz around nuclei etc. But that is simply a mental picture, and an inaccurate one at that.

In actuallity the idea of "potential surface" in the sense that you're thinking of it, is rather meaningless at the atomic level. Since its impossible to even speak of an electron as following at a particular trajectory it is meaningless to speak of an equipotential surface. If you were ever to see a picutre of a quantum mechanical model of an atom then you wouldn't see electrtons orbiting the atom, you'd see what would appear to be a "cloud" of electrons.

There are some diagrams at this URL

http://www.chemguide.co.uk/basicorg/bonding/orbitals.html

Some of them show "points" but that is an inaccurate representation in a certain sense. It might be more accurate to think of those "point" clouds as an experimental result, i.e. successive measurements of the location of electrons

Pete

 

[Cyrus]

Ok, thanks that was the anwser I was looking for pete.

 

[Cyrus]

Am I going crazy? I could have sworn that pete had posted an anwser for me in here and I replied to his anwser and now its gone.

 

[Cyrus]

Whoa, it just showed up again, what's going on in the PF?

 

[rayjohn01]

The concept of potential surface is not quite useless at the atomic level it is actually the very idea upon which the tunnelling microscope is based -- it can 'see' atoms their location and movement -- I wonder how it does that ?