Atom Self Capacitance: Electron Energy Levels

[nuby]

can electron energy levels just be considered the self capacitance of an atom?

 

[cubeleg]

Looking at the definition of capacitance, the ratio between the charge and de potencial in a system of charges, I would say that in some sense your guess is right.
If I understand correctly, the capacitance gives you the charge that you have to introduce in a conductor to increase the voltage up to 1V. In the case of self capacitance the reference for that voltage is an esphere of infinite radius. But this is a classical definition, and usually is used in macroscopid systems because the energy of the conductor is given by this easy relation
$$E=\frac{Q^2}{2C}$$
But in a quantum system this rule is not true. So I would say that you can look at the energy levels as a self capacitance, but this is not useful because all the information is already in the energy levels, why to introduce another parameter?.
Hope this helps.

 

[nuby]

I just thought it was an interesting concept, and was curious if was useful...

Using the Bohr hydrogen model with the capacitance equations:
C = 4 * pi * electric_constant * bohr_radius = 5.8878e-21 F

$$E=\frac{Q^2}{2C}$$

E = (1.60217646e-19 C)^2 / (2* 5.8878e-21 F) = 13.60 eV

 

[nuby]

Seems to work with inductance and LC resonance as well.

 

[cubeleg]

I have to say that this coincidence in the energies is strange.
Anyway to consider a single hydrogen nucleus as a conductor sphere is a very rough approximation, isn't it? Another point is that assuming your arguments as valid would imply that to introduce a second electron in the hydrogen atom you have to to provide again the same energy, this is not correct, as far as I know.
Regarding your second post, I don't understand what you try to say.

 

[nuby]

I'm not sure if this is correct. I used the following equation to find the inductance of ground state H:

((bohr_radius^2) * electron_mass) / (elementary_charge^2) = 9.93734e-14 H

The units seem to work.

Then I tried using the L and C variables with the LC resonance equation: w = sqrt(1/LC)
To get w = 4.1341e16 rad/s or f = 6.57968e15 hz

Then checked the "orbital frequency" of hydrogen with: f = v / wavelength
Assumed the wavelength was equal to (2*pi*bohr_radius), and velocity of hydrogen electron (a * c)

f = (a*c) / (2*pi*bohr_radius) = 6.57968e15 hz

 

[Vanadium 50]

I have to say that this coincidence in the energies is strange.

It's not a coincidence. You put it into get the Bohr radius, and then you get it out again.

 

[edguy99]

I'm not sure if this is correct. I used the following equation to find the inductance of ground state H:

((bohr_radius^2) * electron_mass) / (elementary_charge^2) = 9.93734e-14 H

The units seem to work.

Then I tried using the L and C variables with the LC resonance equation: w = sqrt(1/LC)
To get w = 4.1341e16 rad/s or f = 6.57968e15 hz

Then checked the "orbital frequency" of hydrogen with: f = v / wavelength
Assumed the wavelength was equal to (2*pi*bohr_radius), and velocity of hydrogen electron (a * c)

f = (a*c) / (2*pi*bohr_radius) = 6.57968e15 hz

Interesting topic, hope this isn't a dumb question, but how do you know the "velocity of hydrogen electron (a * c)" and what are a and c?

 

[nuby]

a = fine structure constant
c = speed of light

(a*c) is the velocity of a ground state hydrogen electron according to the Bohr model.

 

[nuby]

Vanadium 50, or anyone else, What do you make of this?

 

[Vanadium 50]

Like a capacitor, an atom stores energy in electric fields, and I suppose one can calculate an "equivalent capacitance". I'm not sure there's much physical insight to be gained here, as you're not going to plug one into a circuit.

Like an inductor, some atoms also store energy in magnetic fields, and I suppose one can calculate an "equivalent inductance". Here, though, you've gone astray and assumed all of the energy is stored in the magnetic field. That's not the case.

An LC circuit moves energy back and forth between the capacitor and the inductor. This is not what happens in the atom. The reason why you got the Rydberg constant out was that you put it in, in the form of the Bohr radius.

 

[cubeleg]

Like a capacitor, an atom stores energy in electric fields, and I suppose one can calculate an "equivalent capacitance". I'm not sure there's much physical insight to be gained here, as you're not going to plug one into a circuit.

Like an inductor, some atoms also store energy in magnetic fields, and I suppose one can calculate an "equivalent inductance". Here, though, you've gone astray and assumed all of the energy is stored in the magnetic field. That's not the case.

An LC circuit moves energy back and forth between the capacitor and the inductor. This is not what happens in the atom. The reason why you got the Rydberg constant out was that you put it in, in the form of the Bohr radius.

I have to agree with you that the coincidence is an artifact introduced in the "model".
About the physical sense of the capacitance is exactly what I try to say in my first post.
Regarding the LC, in my opinion, although the analogy is not very useful, the bohr model obtain those number assuming that the speed and potencial energy are equilibrated in fixed levels. This can be seen as current-voltage exchange, which essentialy is what you see in the LC circuit. But I insist that this a quite artificial point of view and all number are there as Vanadium50 correctly said, so is not surprising that it "works".

 

[edguy99]

Vanadium 50, or anyone else, What do you make of this?

The picture of a proton that this draws for me is an empty 3d shell 53 picometers in radius, much like you see in molecule pictures using the space filling options. There is no center to the proton, it is just a shell of charge, much like a Van der Graaf generator.

The "Shell theorem" from Newtons time suggests that the electron would feel no forces inside this shell. It also means protons and electrons don't crash into each other as electrons can simply pass right through protons (the proton is not a point charge)... and lots of other neat things...

 

[edguy99]

I have to say that this coincidence in the energies is strange.
Anyway to consider a single hydrogen nucleus as a conductor sphere is a very rough approximation, isn't it? Another point is that assuming your arguments as valid would imply that to introduce a second electron in the hydrogen atom you have to to provide again the same energy, this is not correct, as far as I know.
Regarding your second post, I don't understand what you try to say.

In this kind of model, less energy would be needed for the second electron as one electron is inside the sphere providing a push against the second electron.

 

[nuby]

I just found a document regarding the "LC Bohr atom model", this guy did the same thing but took it a few steps further.

http://www.scielo.cl/pdf/ingeniare/v16nespecial/art03.pdf

 

[Vanadium 50]

That "model" is wrong. Equation 6 has him saying a given quantity of energy is in two places at once: in kinetic energy and in a magnetic field. The rest of the paper has him rediscovering the Bohr-Sommerfeld model of the atom, albeit with less rigor, less generality, less motivation and less clarity, but keeping all the problems.

Had he written it in 1911, it might have been interesting.

 

[nuby]

Oh well.. It was the closest thing I could find to the above so I figured I'd post it. I had a feeling it would have some issues. Thanks for checking it out.

 

[Reality_Patrol]

That "model" is wrong. Equation 6 has him saying a given quantity of energy is in two places at once: in kinetic energy and in a magnetic field. The rest of the paper has him rediscovering the Bohr-Sommerfeld model of the atom, albeit with less rigor, less generality, less motivation and less clarity, but keeping all the problems.

Had he written it in 1911, it might have been interesting.

So what? Energy is additive after all.

His physical description of the de Broglie wavelength is brilliant and as far as I know a first.
I look forward to seeing this model applied to other atoms.

NO model is ever correct, as long as it offers unique insight and some novel predictions it can be very useful.

 

[Vanadium 50]

So what? Energy is additive after all.

That's exactly why it's a problem. You can't have the same joule in kinetic energy as you have in a magnetic field. That makes two joules.

 

[Reality_Patrol]

That "model" is wrong. Equation 6 has him saying a given quantity of energy is in two places at once: in kinetic energy and in a magnetic field.

Not exactly. He is saying there are 2 kinds of energy present: kinetic (magnetic) and potential (electrostatic). One joule comes from the electrostatic field and 1 joule from the magnetic field - that's what I meant by "energy is additive".

Equation 6 is saying that the electron's orbital kinetic energy IS the magnetic energy. Uhh, he is making an "identity" of the 2 - saying they're the same thing. To do so he assigns a new fundamental property to the electron, an "inductance" (Le). Of course, as this is a new hypothesis experimental proof will be required - but that's probably the subject of a future paper.

A theory is only scientific if it's testable, this one appears to be.

 

[Vanadium 50]

Equation 6 is saying that the electron's orbital kinetic energy IS the magnetic energy. Uhh, he is making an "identity" of the 2 - saying they're the same thing.

This is the mistake. This is for exactly the reason you said: energy is additive. If you don't like the word mistake, substitute "new and non-mainstream physics".

 

[Reality_Patrol]

This is the mistake. This is for exactly the reason you said: energy is additive. If you don't like the word mistake, substitute "new and non-mainstream physics".

Yep, it usually comes down to semantics.

 

[nuby]

Here is something else interesting that I noticed the other day.

The hydrogen orbital frequency I mentioned earlier of 6.57968e15 hz, be figured from the inverse of the magnetic flux quantum (Josephson constant) 4.835978e14 Hz/V

When multiplied by the potential within ground state (Bohr) hydrogen. 13.60 V

13.60 V * 4.835978e14 Hz/V

The result is the 'orbital frequency' 6.576e15 hz . What does this mean, anything?

 

[Vanadium 50]

Like I said the last couple of times, you are putting the Rydberg constant in (perhaps in a disguised form), and you're getting it back out.

 

[Reality_Patrol]

Here is something else interesting...

13.60 V * 4.835978e14 Hz/V

The result is the 'orbital frequency' 6.576e15 hz .
What does this mean, anything?

Nuby,

I'd suggest you look for some more papers by same guy who wrote the first paper you found. If you find nothing, then you may have found an area open to some of your own creative theorizing. Maybe you could work something out and publish it? I really think this is a topic that deserves more attention.

Here's some food for thought, check out this link:

http://en.wikipedia.org/wiki/Josephson_effect

If you look at the equation for the inverse Josephson effect, I think you'll see a similarity to your own calculation. But these formulas in no way apply to what your modeling. The formalism needs to be redone to apply the effect to the hyrogen atom. The result of that would likely be similar formulas, but with different geometry.

See what I mean? This is open territory for some fresh theorizing. Someone needs to take the emerging model discussed here a step further and work out some new predictions that could be tested experimentally. That would be good science - even if falsified.

 

[Vanadium 50]

I disagree with Reality Patrol. This is not a new area at all - this is a century old: trying to describe the hydrogen atom without quantum mechanics. The fact that numbers seem to be related is not surprising - as I've said before, you put the Rydberg in, you get it back out.

 

[nuby]

I agree there is nothing impressive about the numbers (put it in, get it out) .. But the way they come together with units and equations, makes it seem like there could be some significance.

You can also say the same thing about the Josephson constant, the magnetic flux quantum, radius of a hydrogen atom, etc ... They all just come from the Rydberg constant.

 

[cubeleg]

I have to agree with Vanadium50. About the josephson effect, although this a bit out of the topic, of course the quantum of flux is involved, but where is radius of the hydrogen atom? and how this is related to this topic? it is interesting because you are dealing with a macrospic system and you can explain it with quantum mechanics. In you calculation you are taking a quantum mechanical system and trying to explain with classical mechanics. It's not the same.
Using this arguments you are obtaining the energy of the first level of the hydrogen atom, but nothing else... the QM gives you everything and explain all the periodic table. I think that your approach cannot go further, but maybe I'm wrong.

 

[Vanadium 50]

About the josephson effect, although this a bit out of the topic, of course the quantum of flux is involved, but where is radius of the hydrogen atom?

The key is that nuby said "multiplied by the potential within ground state (Bohr) hydrogen. 13.60 V". That's where the hydrogen atom came in.

 

[Reality_Patrol]

Listen folks, for the record, QM is king and for a lot of very good reasons, no argument there.

My point to Nuby is merely that this seems to be a potentially useful alternative model of the hydrogen atom, and possibly even more complex atoms and polyatomic molecules. I mean there's still only a handful of exact solutions to the SE, most solutions used in chemistry are from approximations. Even if they are very accurate and useful, the underlying math is complicated and tends to prevent intuitive understanding for most people.

But what if an "equivalent circuit" model of atoms could be shown to provide the same, or even better, level of approximate answers? Wouldn't that be very useful in many ways? If nothing else it would provide more of an intuitive understanding that could guide application.

Finally, a technical point. Nuby's first equations "put the Rydberg constant in and then got it back out". However, the paper he found does not. So, the newer equation (Josephson effect) doesn't "put it in" either if the approach taken in the referenced paper is used as a basis for the latest equation. That's the only way to consistently apply a model.

So, "yes, it's put in if one starts from the Bohr model" and "no, it's not put it if one starts from the model given in the paper".

Not saying the paper is correct, I'm merely saying this is the formal way a theory must be applied to achieve testable predictions from first principles.

 

[edguy99]

The empty shell provokes some interesting thought when considering the orbit of an electron. Assume there is no proton/electron coulomb force if the electron is inside the proton shell.

Some simulations. First is an electron orbiting a proton with enough energy that it gets a reasonable orbit. The second simulation shows a lower energy electron completely trapped within the proton. The third simulation shows the kind of orbits you get with more objects (two electons and one proton).

[PLAIN]http://upload.wikimedia.org/wikipedia/commons/7/7c/Protonelectrontrapped.gif[ATTACH=full]196589[/ATTACH][/URL]

 

[Vanadium 50]

Assume there is no proton/electron coulomb force if the electron is inside the proton shell.

But that's demonstrably not true. You have proton-electron scattering experiments, and you have atomic spectra: particularly with muonic atoms. (Jim Rainwater always felt the Nobel committee gave him the Nobel prize for the wrong thing, and that he should have gotten it for muonic atoms)

 

[edguy99]

But that's demonstrably not true. You have proton-electron scattering experiments, and you have atomic spectra: particularly with muonic atoms. (Jim Rainwater always felt the Nobel committee gave him the Nobel prize for the wrong thing, and that he should have gotten it for muonic atoms)

It is correct that scattering experiments suggest a proton size of 1-2 femtometers, not 53,000 femtometers (53 pm) as drawn here. It suggests in this type of model that the large shells have a thickness to them of 1-2 femtometers. Protons only really "crash" into each other if they are centered almost exactly on top of each other.

In other words, in this type of world, proton shells can overlap each other and often would. Normal forces continue to push the protons apart even if they are overlapping. Electrons caught in the overlapping shells are the "glue" that hold the protons together.

 

[nuby]

Something else I found interesting using this 'model'.

Using the Rydberg constant you can figure out the moment of inertia:

KE_electron = (1/2) * electron_mass * (fine_structure_constant * c)^2 = 13.605 eV
or

KE_rotational = (1/2) * I * w^2 = 13.605 eV

w = angular velocity = 6.57968395e15 * 2 * pi = 4.134e16 rads/sec
I = moment of inertia = 2.55075e-51

The moment of inertia for a thin circular hoop is: I(z_axis) = mass * radius^2
I = electron_mass * bohr_radius^2 = 2.55088e-51

This view seems to depict the electron shell as a 2D hoop (in a single frame).Another thing I thought was interesting:
The coulombs force between the proton and electron in ground state hydrogen:

F(coulombs) = (1/(4*pi*electric_constant)) * elementary_charge^2/bohr_radius^2
F(coulombs) = 8.2387e-8 N

The centripetal force of the ground state hydrogen: m * (velocity^2 / bohr_radius)
F(centripetal) = electronmass * (fine_structure_constant * c)^2 / bohr_radius
F(centripetal) = 8.2387e-8 N

 

[Vanadium 50]

It is correct that scattering experiments suggest a proton size of 1-2 femtometers, not 53,000 femtometers (53 pm) as drawn here. It suggests in this type of model that the large shells have a thickness to them of 1-2 femtometers. Protons only really "crash" into each other if they are centered almost exactly on top of each other.

In other words, in this type of world, proton shells can overlap each other and often would. Normal forces continue to push the protons apart even if they are overlapping. Electrons caught in the overlapping shells are the "glue" that hold the protons together.

Is this model described in the literature anywhere? This doesn't sound like the conventional description.