Ground State Energy: What Regulates & Why is it Constant?

In summary: I don't know if there is a direct correlation between binding energy and size, but I think it's probably related.
  • #1
nuby
336
0
What regulates the ground state energy of a hydrogen atom? Why is it constant (more or less)?
 
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  • #2
check perturbation theories ;)
 
  • #3
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
Thanks for the post. I was mostly wondering which force regulates the ground state, and if it is related to the Lorentz force.
 
  • #5
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
nuby said:
What regulates the ground state energy of a hydrogen atom? Why is it constant (more or less)?

What exactly do you mean by "regulate"?

Zz.
 
  • #7
ZapperZ said:
What exactly do you mean by "regulate"?

Zz.

"Holds" the binding force (potential?) at around -27.2 eV , and electron kinetic energy at +13.6 eV.
 
  • #8
nuby said:
"Holds" the binding force (potential) at around -27.2 eV , and electron kinetic energy at +13.6 eV.

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
ZapperZ said:
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.
That works too, the Coulombic potential of ground state. What controls it?
 
  • #10
nuby said:
That works too, the Coulombic potential of ground state. How is it determined?

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
I meant "what controls it" .. I edited my post right after you responded.
 
  • #12
nuby said:
I meant "what controls it" .. I edited my post right after you responded.

Control?

This is meant to clarify?

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

Zz.
 
  • #13
nuby said:
"Holds" the binding force (potential?) at around -27.2 eV , and electron kinetic energy at +13.6 eV.

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 don't 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
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?

Thanks in advance
 
  • #15
nuby said:
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?

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.

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

Thanks in advance

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
ZapperZ said:
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.
Zz.

So the forces between the two leptons (electrons / positrons) behave a lot differently, than between leptons and baryons.
 
  • #17
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
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
I doubt it.

the reason the electron can't 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 can't 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
granpa said:
I doubt it.

the reason the electron can't 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 can't do that.
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?
 
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  • #21
there is nothing in my post about a proton falling into a proton which would be strange indedd since they would electrostatically repel one another.

all I said was that the electron is (much) bigger than a proton.
 
  • #22
granpa said:
there is nothing in my post about a proton falling into a proton which would be strange indedd since they would electrostatically repel one another.

all I said was that the electron is (much) bigger than a proton.

I meant proton / electron. I'm still not clear on what your are saying. Are you saying the electron is so small it passes through the proton, which is why they don't 'crash' into each other?
 
  • #23
read post 21 again
 
  • #24
"the reason the electron can't fall into the proton is that it is too big." What is this supposed to mean?
 
  • #25
it means that it (the electron) is too big
 
  • #26
of course, the electron does fall into the proton during electron capture. the result is a neutron. but neutrons are unstable. they spontaneously break back down into protons and electrons (beta decay) with a considerably release of energy.

you might find this interesting.
http://physics.nist.gov/GenInt/Parity/expt.html [Broken]
 
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  • #27
granpa said:
it means that it (the electron) is too big

Can you please go to the Particle Data Book and show me where an electron is "much bigger" than a proton?

Zz.
 
  • #28
can you please read post 19.
 
  • #29
granpa said:
can you please read post 19.

I did! That is why I asked you to look up in the Particle Data Book and (i) find out what is meant by the SIZE of an electron and (ii) why it is significantly larger than a proton.

According to your definition, if I throw a tennis ball around a tennis court, the SIZE of the tennis ball is as large as the tennis court itself. Does this make any sense to you? And more importantly, is this ACCURATE?

Zz.
 
  • #30
granpa said:
can you please read post 19.

granpa said:
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.

Proof by preference?

ZapperZ is exactly right with his tennis court analogy.
 
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  • #31
an interesting approach to the problem of hydrogen ground state can be found here:

http://arxiv.org/abs/quant-ph/0307154" [Broken]

cheers


oops, sorry, have not seen that nuby already mentioned ZPF.. but that paper might be related to his post 18
 
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  • #32
nuby said:
"Holds" the binding force (potential?) at around -27.2 eV , and electron kinetic energy at +13.6 eV.

If you're referring to the particular numbers, they're in arbitrary units but 13.6 comes from the rest mass of the electron in eV and the fine structure constant. So the question really boils down to why the dimensionless fine-structure constant is what it is, and I don't think anyone has an answer to that question.
 
  • #33
nuby,

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

You don't need to go into particle physics to answer this question! You have a coulombic potential between the electron and proton. This is a quantum mechanical system! If you solve the Hamiltonian for this system you get a set of eigenvalues which correspond to stationary energies. Stationary energies are energies which correspond to a minimum in the 3-dimensional energy surface. For the hydrogen atom there are 3 quantum numbers: n, l, ml which describe the wave function for the system. I am disregarding the spin quantum number since the electron spin isn't effect by the Hamiltonian. The restriction is that these quantum numbers must be integers. These integers correspond to stationary solutions. If by some perturbation that n went from n = 2 to n = 2.1. The electron would spontaneously go back to n = 2 because that is a stationary state - it's at the bottom of the hill.

modey3
 
  • #34
How does the zero-point field come into the equation?
 
  • #35
Random oriented zero-point field overpowers the directed (along the line between electron and proton) attraction between proton and electron at short distances and makes, sloppy speaking, the electron "lose its way on its fall towards proton"

To my knowledge ZPF is not included explicitly in the Hamiltonian approach where you rely (by assumption) on the fact that a hermitian operator has a lower bound in its spectrum. By "explicitly" I mean: ... well ... you can always discuss what the physics behind the existence of a lower bound of a hermitian operator is.

What about positronium, why does that thing annihilate ? Here the interaction between the components is also coulombic, at least at large distances.
 

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