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

[nuby]

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

 

[Marco_84]

check perturbation theories ;)

 

[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!

 

[nuby]

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

 

[jtbell]

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.

 

[ZapperZ]

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.

 

[nuby]

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.

 

[ZapperZ]

"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.

 

[nuby]

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?

 

[ZapperZ]

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.

 

[nuby]

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

 

[ZapperZ]

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.

 

[edguy99]

"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".

 

[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?

Thanks in advance

 

[ZapperZ]

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.

 

[nuby]

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.

 

[ZapperZ]

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.

 

[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?

 

[granpa]

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.

 

[nuby]

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?

 

[granpa]

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.

 

[nuby]

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?

 

[granpa]

read post 21 again

 

[nuby]

"the reason the electron can't fall into the proton is that it is too big." What is this supposed to mean?

 

[granpa]

it means that it (the electron) is too big

 

[granpa]

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

 

[ZapperZ]

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.

 

[granpa]

can you please read post 19.

 

[ZapperZ]

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.

 

[Vanadium 50]

can you please read post 19.

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.