# Ground state energies

1. Dec 24, 2008

### nuby

What regulates the ground state energy of a hydrogen atom? Why is it constant (more or less)?

2. Dec 24, 2008

### Marco_84

check perturbation theories ;)

3. Jan 8, 2009

### saray1360

hi,

as far as I know there are theoretical relations by which you calculate the ground state of a system. Like Kohn-Sham equation and ...
The density functional theory texts may help you. The atomic systems usually converge to a ground state energy which is unique, but theoretically very hard to calculate....

Hope it helped.

Good luck!

4. Jan 8, 2009

### nuby

Thanks for the post. I was mostly wondering which force regulates the ground state, and if it is related to the Lorentz force.

5. Jan 8, 2009

### Staff: Mentor

The ground state energy of hydrogen comes from the solution of Schrödinger's equation for the Coulomb (electric) potential energy function of the electron and proton.

6. Jan 9, 2009

### ZapperZ

Staff Emeritus
What exactly do you mean by "regulate"?

Zz.

7. Jan 9, 2009

### nuby

"Holds" the binding force (potential?) at around -27.2 eV , and electron kinetic energy at +13.6 eV.

8. Jan 9, 2009

### ZapperZ

Staff Emeritus
Binding force potential? Kinetic energy?

Even in the simplest Rydberg atom model, is it not obvious that we have a Coulombic potential? I mean, you have a positive nucleus, and a negative electron. Is there something here that I'm missing?

Zz.

9. Jan 9, 2009

### nuby

That works too, the Coulombic potential of ground state. What controls it?

10. Jan 9, 2009

### ZapperZ

Staff Emeritus
Er... this is classical E&M. If you have a spherically symmetry + charge at the origin, what is the electrostatic potential at point r?

Zz.

11. Jan 9, 2009

### nuby

I meant "what controls it" .. I edited my post right after you responded.

12. Jan 9, 2009

### ZapperZ

Staff Emeritus
Control?

This is meant to clarify?

What's the issue that you have with electrostatic potential?

Zz.

13. Jan 9, 2009

### edguy99

I am guessing you mean that why does the electron not gain more then 13.6 ev of kinetic energy as it falls closer to the proton?

On the lower end, I dont think that the electron needs to keep at least 13.6 ev of kinetic energy, the electrons kinetic energy can be much lower and I think usually would be. Hydrogen gas with electrons buzzing around with 13.6 ev of energy would be considered very "hot".

14. Jan 10, 2009

### nuby

these might make more sense.

1.) Why does the electron energy remain constant in ground state hydrogen, as well as the average size of the atom?

2.) Why don't protons and anti-protons interact like protons and electrons?

15. Jan 10, 2009

### ZapperZ

Staff Emeritus
Because when you set it up quantum mechanically, you get solutions to the Hamiltonian that corresponds to the "stationary" solutions that you get when you solve the classical Hamiltonian. Based on the physics that we know, this is the definition of the ground state.

Because a proton is a baryon and an electron is a lepton, where is a proton/anti-proton are both baryon and the physics indicates that they are "mirror image" of each other, separated only by a few symmetry operations. You can't do the same with proton and electrons, which are both matter and not even identical to each other in many respects.

Have you looked at basic physics text (or even the internet) to actually do your own legwork on the obvious difference between these two sets of conditions that you have asked? I mean, I'm sure you would have realized that proton-antiproton are more alike to each other than proton-electron. They do at least teach such a thing in high school, don't they, regarding the "scale" of things, such as the different in mass between proton and electron?

Zz.

16. Jan 10, 2009

### nuby

So the forces between the two leptons (electrons / positrons) behave a lot differently, than between leptons and baryons.

17. Jan 10, 2009

### ZapperZ

Staff Emeritus
You notice that you have changed topic.

I still want to know why you are having problems with a simple, straight-forward electrostatic potential.

Zz.

18. Jan 17, 2009

### nuby

I guess I'm wondering if the ground state electrostatic potential (or electron) interacts with the zero-point-field, and if the ZPF dictates the ground state energy?

19. Jan 17, 2009

### granpa

I doubt it.

the reason the electron cant fall into the proton is that it is too big. a proton and an antiproton are the same size so they can cancel each other out completely. a proton and an electron cant do that.

how big the electron is depends on how you define it. I prefer to think of the size of the electron as the size of its charge cloud.

20. Jan 18, 2009

### nuby

This seems strange. Are you saying a proton can't fall into an electron because they don't have the same mass-energy, or volume?

Last edited: Jan 18, 2009