# I Electron jelly model and Hydrogen Atom

1. May 18, 2017

### jonjacson

Hi folks,

I am reading "Purcell Electricity and Magnetism" and in the problem 1.77 he says:

"
Imagine a sphere of radius a filled with negative charge of uniform
density, the total charge being equivalent to that of two electrons.
Imbed in this jelly of negative charge two protons, and assume that,
in spite of their presence, the negative charge distribution remains
uniform. Where must the protons be located so that the force on
each of them is zero? (This is a surprisingly realistic caricature of
a hydrogen molecule; the magic that keeps the electron cloud in
the molecule from collapsing around the protons is explained by
quantum mechanics!"

My question is, Why is it a good caricature of the Hydrogen atom?

I mean he says that statement but then does not justify it, I don't see him talking about energy levels or density of probability distributions. So does anybody know where can I read about it?

What properties of an hydrogen atom could I calculate using the jelly model?

It looks very interesting.

Thanks!

2. May 18, 2017

### dextercioby

It is molecule, not atom. There are two protons (forming two nuclei) and two electrons.

3. May 18, 2017

### jonjacson

Ok, but anything about the model?

4. May 18, 2017

### vanhees71

It has not much to do with the true model, which is necessarily quantum mechanical. One should note take Purcell's book too literally ;-)).

5. May 18, 2017

### jonjacson

6. May 18, 2017

### Staff: Mentor

But he was presenting this exercise partly as an interesting problem in classical electrostatics, and partly because it is interesting that this very simple model produces results that are order-of-magnitude close to what we find when we do the much more complex quantum mechanical calculation. He wasn't suggesting it as a serious description that would produce serious new insights, but more as a way to get an idea of the scales involved and where the practical lower limits of classical thinking lie.

A historical note: when Purcell was teaching at Harvard forty years ago, the physics students went through his E&M textbook a full year before their first course on quantum mechanics.

7. May 19, 2017

### DrDu

I don't doubt that this model gives a reasonable approximation of the distance in the hydrogen molecule once you choose correctly the size of the sphere. Thats where QM kicks in.

8. May 19, 2017

### vanhees71

Sure, and Purcell was a Nobel Laureate. So for sure he knew the physics, but his E&M book is a nuissance. In his attempt to be pedagogical he obscured the subject. The problem is that many people think that pedagogics in physics means to avoid math, but that's wrong. There is a minimal level of math you need, and to avoid tensor calculus in relativity makes this subject very difficult to understand rather than helping the students to get used to it and to understand the physics behind it. Math is the language in which Nature talks to us, as far as the natural sciences are concerned, and there's no other way to study physics than to learn also the language you need to formulate it.

I'd rather recommend to use the Feynman Lectures, which is (in my subjective opinion) the 2nd-best pedagogical treatment of theoretical physics ever written. It uses as much math as you need to understand the subject, and it is very clear that Feynman thoroughly thought about how to present the essence of physical arguments leading to a result, using the right minimal level of math for an introduction to each subject.

The unbeaten No. 1 in terms of best pedagogy of theoretical physics for me still is the 6-volume lecture series by Sommerfeld. The only problem is that it is restricted (almost completely) to classical physics only, and there's no quantum-mechanics book in the series. Of course, Sommerfeld has written a brillant book about "Wave Mechanics" (2nd Vol. of "Atombau und Spektrallinien"), but that's pretty outdated :-((.