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Atom self capacitance

by nuby
Tags: atom, capacitance
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nuby
#1
Dec2-08, 01:27 PM
P: 364
can electron energy levels just be considered the self capacitance of an atom?
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cubeleg
#2
Dec3-08, 03:03 AM
P: 15
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
[tex]E=\frac{Q^2}{2C}[/tex]
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
#3
Dec3-08, 09:15 AM
P: 364
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

[tex]E=\frac{Q^2}{2C}[/tex]

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

nuby
#4
Dec3-08, 09:20 AM
P: 364
Atom self capacitance

Seems to work with inductance and LC resonance as well.
cubeleg
#5
Dec3-08, 11:06 AM
P: 15
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
#6
Dec3-08, 12:33 PM
P: 364
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
#7
Dec3-08, 02:28 PM
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Quote Quote by cubeleg View Post
I have to say that this coincidence in the energies is strange.
It's not a coincidence. You put it in to get the Bohr radius, and then you get it out again.
edguy99
#8
Dec4-08, 02:04 AM
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Quote Quote by nuby View Post
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
#9
Dec4-08, 02:33 PM
P: 364
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
#10
Dec4-08, 05:24 PM
P: 364
Vanadium 50, or anyone else, What do you make of this?
Vanadium 50
#11
Dec4-08, 11:03 PM
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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
#12
Dec5-08, 05:07 AM
P: 15
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
#13
Dec5-08, 04:04 PM
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Quote Quote by nuby View Post
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 dont 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
#14
Dec5-08, 04:32 PM
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Quote Quote by cubeleg View Post
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
#15
Dec6-08, 01:49 AM
P: 364
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/v...cial/art03.pdf
Vanadium 50
#16
Dec6-08, 07:22 PM
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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
#17
Dec6-08, 07:39 PM
P: 364
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
#18
Dec7-08, 11:21 AM
P: 111
Quote Quote by Vanadium 50 View Post
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.


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