# LC circuit model of hydrogen atom

1. Dec 25, 2008

### nuby

I thought these were weird similarities between macroscopic electronic circuits and (Bohr) hydrogen model. What do you guys think?
.

hydrogen self-capacitance (energy level "capacitance")
C = 4*pi*eo*br = 5.88798e-21 Farads

eo = vacuum permitivity
m = electron mass
e = elementary charge
w = angular frequency
f = frequency (Hz)

hydrogen "inductance" (at ground state):
L = ((br^2) * m) / (e^2) = 9.93734e-14 Henries

Orbital (LC resonant) frequency of ground state electron:
w = sqrt(1/LC) = 4.134e16 rads/sec

Orbital frequency in Hz
f = 4.134e16 / (2*pi) = 6.57e15 Hz

Orbital Frequency of Hydrogen:
v / (2*pi*br) = 6.57e15 Hz

v = 2.187e6 (m/s)

Here's something else I found interesting. On the macroscopic level step up/down transformers convert current to voltage and vice versa. Viewing current as mass only (electrons), and voltage as the velocity of the electrons (or force moving electrons), the energy level transitions can resemble step-up, and step-down "transformers". I.e electron velocity decreases, and mass increases from n=1 to n=3.

Last edited: Dec 26, 2008
2. Dec 27, 2008

### nuby

can (macro) electronic circuit mechanisms occur without the same effects happening (collectively) at the atomic level?

3. Dec 27, 2008

Staff Emeritus

As I pointed out to you there - multiple times - these relationships that you are "discovering" are merely consequences of algebra. You put the Rydberg constant in, do some algebraic manipulations, and get it back out again.

Are you just going to keep posting this over and over?

Last edited by a moderator: Apr 24, 2017
4. Dec 27, 2008

### nuby

I wanted a different perspective (outside of the box), so I posted this to the philosophy forum. I'm not sure how it got to General.

Last edited: Dec 27, 2008
5. Dec 27, 2008

### Gear300

Probably because of the physics.

6. Dec 27, 2008

### ZapperZ

Staff Emeritus
Since you obviously no longer need it, the other thread is now closed.

Zz.

7. Jan 12, 2009

### granpa

hydrogen self-capacitance (energy level "capacitance")
C = 4*pi*eo*br = 5.88798e-21 Farads

how do you derive this? what formula for capacitance is it based on?

edit:nevermind. I found it:
the self-capacitance of a conducting sphere of radius R is given by:

heres a formula for a spherical capacitor:
http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/capsph.html

the equation for the energy levels of a hydrogen like atom is of course:

making the spectrum equal:
http://mooni.fccj.org/~ethall/rydberg/rydeq.gif [Broken]

Last edited by a moderator: May 3, 2017
8. Jan 12, 2009

### nuby

9. Jan 19, 2009

### nuby

Here's something I found interesting regarding to the "orbital frequency" . The LC resonant frequency from above, seems to be the same as the circular frequency of the electron's "trembling motion" (wiki: Zitterbewegung), if you use the mass-energy of the ground state electron (13.605 eV / 2.425e-35 kg)

2mc^2 / hbar

(2 * 2.425e-35 kg * c^2)/hbar = 4.134e16 rad/sec

10. Jan 19, 2009

Staff Emeritus
Nuby, I am trying to be polite, but these messages of yours are bordering on crackpottery.

Like I keep saying - and you keep blowing me off - these numerical features you find are simply algebraic rearrangements of a single constant. You put the Rydberg in, you get the Rydberg out.

11. Jan 19, 2009

### granpa

never heard of that before. thanx :-)

http://modelingnts.la.asu.edu/pdf/ZBW_I_QM.pdf [Broken]

David Hestenes
Abstract. The zitterbewegung is a local circulatory motion of the electron presumed to be the basis of the electron spin and magnetic moment. A reformulation of the Dirac theory shows that the zitterbewegung need not be attributed to interference between positive and negative energy states as originally proposed by Schroedinger. Rather, it provides a physical interpretation for the complex phase factor in the Dirac wave function generally. Moreover, it extends to a coherent physical interpretation of the entire Dirac theory, and it implies a zitterbewegung interpretation for the Schroedinger theory as well.
1. INTRODUCTION
The idea that the electron spin and magnetic moment are generated by a localized circulatory motion of the electron has been proposed independently by many physicists.
Schroedinger’s zitterbewegung (zbw) model for such motion is especially noteworthy, because it is grounded in an analysis of solutions to the Dirac equation.(1,2,3) Surely, if the zbw is a real physical phenomena, then it tells us something fundamental about the nature of the electron. However, the role ascribed to the zbw in standard formulations of quantum mechanics has been metaphorical at best.

... I shall show that the complex phase factor in the electron wave function can be associated directly with the zbw. I call this the zbw interpretation of quantum mechanics.
...A simple change in the definition (i.e., interpretation) of the electron velocity implies that all components of the electron wave function (including its phase) directly describe kinematical features of electron motion.

Last edited by a moderator: May 3, 2017
12. Jan 19, 2009

### nuby

Why does it matter how the pieces come together if the solution makes sense? Please explain why you think this "frequency" is insignificant.

13. Jan 19, 2009

### granpa

before the moderators close this thread would you please show me what formula you used to calculate:
hydrogen self-capacitance (energy level "capacitance")
C = 4*pi*eo*br = 5.88798e-21 Farads

I've looked an wikipedia but cant find anything

14. Jan 19, 2009

### granpa

http://modelingnts.la.asu.edu/pdf/Spin&uncert.pdf [Broken]

[6] Spin and uncertainty in the interpretation of quantum mechanics

Abstract: A rigorous derivation of the Schroedinger theory from the Pauli (or Dirac) theory implies that the Schroedinger equation describes an electron in an eigenstate of spin. Furthermore, the ground-state kinetic energy is completely determined by the electron spin density. This can be explained by interpreting the spin as an orbital angular momentum, which is necessarily accompanied by a kinetic energy. Thus, the spin is a zero-point angular momentum associated with the zero-point energy of the electron

http://modelingnts.la.asu.edu/pdf/MysteriesofDirac.pdf [Broken]

Last edited by a moderator: May 3, 2017
15. Jan 19, 2009

### granpa

d--n it. I meant to ask what formula you used to calculate this:
hydrogen "inductance" (at ground state):
L = ((br^2) * m) / (e^2) = 9.93734e-14 Henries

16. Jan 19, 2009

### granpa

Last edited by a moderator: Apr 24, 2017
17. Jan 19, 2009

Staff Emeritus
I'm glad everyone agrees this should be closed.

18. Jan 20, 2009

### nuby

V50, are you going to answer my question? Or just leave snide remarks?

19. Jan 20, 2009

### granpa

for now, I think we should limit the discussion to this:
hydrogen "inductance" (at ground state):
L = ((br^2) * m) / (e^2) = 9.93734e-14 Henries

if capacitance is energy/charge then I guess that inductance is energy/current.
what does the m in your equation stand for? surely not mass.

20. Jan 20, 2009

Staff Emeritus
I've answered this question nine times already, on two different threads. Would a tenth make any difference?

21. Jan 20, 2009

### nuby

"m" is the rest mass of an electron,
"br" is the bohr radius, and "e" is elementary charge. I'm still not sure if that equation is correct, but nobody has called it invalid yet..

22. Jan 20, 2009

### granpa

well inductance doesnt involve mass. that would be moment of inertia.

23. Jan 20, 2009

### nuby

Well, can you have inductance without electrons?

24. Jan 20, 2009

### granpa

since we are discussing math coincidences I thought I would add this.

if the charge of the electron is thought of as being a sphere of constant charge density then the frequency at which it would oscillate around a proton is by my calculations (which should always be checked)
2.485*10^15/sqrt(r^3)
where r is, of course, the radius of the charge cloud

its not exact but its very close to the Rydberg frequency of 3.2898*10^15 hz

25. Jan 20, 2009

### ZapperZ

Staff Emeritus
This pointless thread has gone long enough and degenerated into the ridiculous. It is now done.

Zz.