Is the Rutherford model invalid due to a violation of Gauss's Law?

[jmfrank63]

TL;DR Summary

The original publication was clearly invalid, not just inaccurate. Why is this of no concern?

Our current model of the atom is still based on the original publication of Rutherford. However, this publication is clearly invalid. I am not talking about inaccurate. I am using the word invalid, and that is for a reason. People have often criticized historic publications, one example is Euclid's equilateral triangle. Yet, Euclid's proof might be inaccurate, but it is certainly not invalid. But Rutherford's paper is not simply inaccurate, it is actually invalid.

Here is why:
In his original publication, you can read early this sentence:

Consider an atom which contains a charge ±Ne at its centre surrounded by a sphere of electrification containing a charge ±Ne [N.B. in the original publication, the second plus/minus sign is inverted to be a minus/plus sign] supposed uniformly distributed throughout a sphere of radius R.

If you want to verify the quote, here is a replica of the original article, page 671 first paragraph:

https://personal.math.ubc.ca/~cass/rutherford/r.pdf

This is a clearly invalid assumption, such an object can never exist, for it is clearly violating Gauss's Law. Here I am talking to physicists, so I do not give a detailed explanation on how the law works, I just will point out the uniform sphere surrounding the centre will prevent any field lines to leave to the outside. I am curious if, in a physics forum, this needs further explanation or this will already make clear that the assumption is invalid. I am happy to give an in-depth explanation if asked for.

Now, given the invalid assumption, you can show about anything. While the mathematics in the paper is impressive, it does not help, based on a wrong assumption it is worthless. I also think, the peer review should have caught this.

Why is this not of any concern, and why is this not discussed? How does quantum mechanics fix this? I've never heard of quantum mechanics replacing classical mechanics, only of extending it. So if it extends, how does it make an invalid object valid?

 

[Nugatory]

for it is clearly violating Gauss's Law... the uniform sphere surrounding the centre will prevent any field lines to leave to the outside.

How is it violating Gauss's Law? No force lines leaving to the outside is just another a way of stating that the atom as a whole is electrically neutral. Negative charge at a greater distance from the nucleus than the penetrating particle has, by the shell theorem, no effect on the particle, so effects from the electric field of the nucleus are expected within the shell.

 

[PeterDonis]

Our current model of the atom is still based on the original publication of Rutherford.

No, it isn't. It's based on modern quantum mechanics, which is nothing like Rutherford's original model.

I've never heard of quantum mechanics replacing classical mechanics, only of extending it.

Then you evidently have not looked very hard. Classical mechanics makes obviously wrong predictions, one of which is that atoms cannot exist--electrons would emit EM radiation and spiral into the nucleus. Quantum mechanics does not extend classical mechanics in this, as in other cases--it replaces it with a new, different, incompatible theory that makes new, different, incompatible predictions. And the QM predictions are the correct ones, as extensive experiments have shown over the past century or so.

 

[Dale]

it is clearly violating Gauss's Law

Do you have a professional scientific reference that says the Rutherford model violates Gauss’ law? We don’t do personal speculation here.

There are many subsequent papers that corrected Rutherford model and fixed the theoretical and experimental problems with it. To the best of my knowledge, none of them make the objection you make.

 

[Dale]

@jmfrank63 before you post again, please post the professional scientific paper that supports your specific complaint. I can restore your recent post once it is clear that it is based on the professional scientific literature and not just personal speculation

 

[jmfrank63]

@jmfrank63 before you post again, please post the professional scientific paper that supports your specific complaint. I can restore your recent post once it is clear that it is based on the professional scientific literature and not just personal speculation

I need to find a scientific paper to ask a question? I don't understand. Did I make a mistake in the simulation?

 

[Dale]

I need to find a scientific paper to ask a question? I don't understand. Did I make a mistake in the simulation?

You are not asking a question. You are making a specific claim that the Rutherford model violates Gauss law.

This thread is closed. If you wish to open a new thread please read the rules and ensure that either you have a professional scientific reference to support any claims you make or that you actually ask questions without making unfounded claims.