Energy Principle and Hydrogen Atom

[sharma_satdev]

hydrogen atom is formed by the combination of electron and proton initially separated by in finite distance ,therefore, energy of hydrogen atom is expected to be equal to loss of electrostatic potential energy,but according to quantum mechanics it is not so.Is basic energy principle violated?

 

[CompuChip]

You mean: why is the energy of the hydrogen atom (made up of a proton and an electron) smaller than the energy of the proton plus the energy of the electron?

Then the answer is, that the hydrogen atom is a bound state of the proton and the electron. There is some bonding energy E_bs, that becomes available when the proton and electron combine to the configuration known as "hydrogen atom". Since this energy is positive, it is energetically favorable to make a hydrogen atom whenever possible, instead of leaving the proton and electron floating about separately. Of course it is possible to separate them again, but for that you need to add at least energy E_bs to a hydrogen atom to "shoot" the electron out of the atom.

Although the value of E_bs can be exactly calculated using quantum mechanics, the idea itself is, IMO, not really quantum mechanical. It can be qualitatively explained in terms of energy, like above.

(By the way, in chemistry, this leads to the concept of endothermic and exothermic reactions)

 

[sharma_satdev]

the bond energy is equal to energy in the initial state-energy in the final state=energy lost=electrostatic potential energy.The energy in the initial state is zero therefore bond energy is equal to electrostatic potential but according to quantum mechanics it is not so the question is not stupid if you think over it .It may be beyond your capability

 

[Frame Dragger]

the bond energy is equal to energy in the initial state-energy in the final state=energy lost=electrostatic potential energy.The energy in the initial state is zero therefore bond energy is equal to electrostatic potential but according to quantum mechanics it is not so the question is not stupid if you think over it .It may be beyond your capability

 

[ZapperZ]

the bond energy is equal to energy in the initial state-energy in the final state=energy lost=electrostatic potential energy.The energy in the initial state is zero therefore bond energy is equal to electrostatic potential but according to quantum mechanics it is not so the question is not stupid if you think over it .It may be beyond your capability

It is not. You're neglecting the fact that there is a kinetic energy part of the whole energy equation, not just the loss in PE=bond energy.

Zz.

 

[sharma_satdev]

what is the source of potential energy ,potential energy is the source of kinetic energy ,therefor, potential energy should be equal to kinetic energy.When electron is attracted by the proton it should follow straight path ,how the path is deviated?

 

[sharma_satdev]

In Schrödinger wave equation E-V IS equal to kinetic energy ,kinetic energy is equal to potential energy V,hence E should be zero which makes Schrödinger equation meaningless

 

[humanino]

There are many ways to calculate the spectrum of hydrogen. If you like old semi-classical pictures, it is possible to write the balance between the energy radiated by the accelerated electron and the backreaction in the vacuum around the proton. Bohr did it. J. Dalibard, J. Dupont-Roc and C. Cohen-Tannoudji have also shown how can lift the ambiguity in the counting in J. Phys. 43 (1982) 1617

This is also for instance in Milonni "the quantum vacuum... introduction to QED", explicitly for the hydrogen atom in section 3.3

 

[muppet]

what is the source of potential energy ,potential energy is the source of kinetic energy ,therefor, potential energy should be equal to kinetic energy.When electron is attracted by the proton it should follow straight path ,how the path is deviated?

This does not mean that K=V. It means that if all of the potential energy were converted to kinetic energy, then the final kinetic energy would be equal to the initial potential energy.

This is nothing to do with quantum mechanics in particular, but something you should have understood at school; the effect of quantum mechanics is to blur the distinction between the two, as it no longer becomes possible to say where an electron is or how fast it is moving, and hence how the total energy is divided up.

I'd also suggest that Compuchip never opined that your question was stupid; (s?)he just gave some of his time up in trying to answer it, for your benefit rather than his own. If he answered a slightly different question, I suspect that's probably more indicative of the phrasing of the original question than it is of his capability as a pedagogue or as a scientist.

 

[SpectraCat]

In Schrödinger wave equation E-V IS equal to kinetic energy ,kinetic energy is equal to potential energy V,hence E should be zero which makes Schrödinger equation meaningless

Hmmm ... do you think it is more likely that the Schrödinger equation is meaningless, or that you have a simple misunderstanding that is preventing you from seeing its significance?

Are you saying that you think K=V in all cases? You are sitting down right now as you read this ... what is *your* kinetic energy? What is your potential energy? If the floor disappeared, would you start to move?

Also, in your initial question, you neglect to account for the fact that the electron can lose energy by emission of radiation as it makes transitions between the H-atom energy levels after it is captured by the proton. So, energy is not conserved in the transition from a free-electron/free-proton pair to the H-atom. This is essentially what Compuchip was saying in his post.

EDIT: Actually, I just realized that you asked this question before, and I gave essentially the same answer:

https://www.physicsforums.com/showthread.php?t=373636

Are you just repeating yourself, or do you have a new wrinkle to your question?