Looking for Layman's Physical Explanation for the lowest energy level in atoms

[feynmann]

I'm looking for a simple physical explanation of the lowest energy level in atoms, so I can provide a brief explanation to interested laypeople (not to mention just to help myself understand better). Does anybody want to take a crack at it? Or am I asking for the impossible?

Since electron can't crash into the proton if it has a lowest energy level.
So the Bohr's model of electron orbiting the proton explains the stability of atoms.
But the problem with Bohr's model is that we know there is No orbiting angular momentum in the ground state of hydrogen atom, so Bohr's model is wrong in this case and we can't use it to explain the stability of hydrogen atom

 

[DeShark]

I'm looking for a simple physical explanation of the lowest energy level in atoms, so I can provide a brief explanation to interested laypeople (not to mention just to help myself understand better). Does anybody want to take a crack at it? Or am I asking for the impossible?

Since electron can't crash into the proton if it has a lowest energy level.
So the Bohr's model of electron orbiting the proton explains the stability of atoms.
But the problem with Bohr's model is that we know there is No orbiting angular momentum in the ground state of hydrogen atom, so Bohr's model is wrong in this case and we can't use it to explain the stability of hydrogen atom

I guess it all comes down to the commutation relation between position and momentum. i.e. the Heisenberg uncertainty principle. For the electron to be in a state of lowest energy, it would have to be described by the dirac delta function centred in the nucleus. But this would cause an uncertainty in momentum and thus the electron would have more kinetic energy. My physical intuition says that the electron wants to find the midway point between this extra "uncertainty" kinetic energy and the coulombic minimum. To do this, it sits in the ground state.

 

[malawi_glenn]

You have ALREADY aksed this

Dec6-08, 09:03 PM

 

[DeShark]

You have ALREADY aksed this

Dec6-08, 09:03 PM

That's not true. Feynman has already asked for a layman's description of why there are discreet energy levels, but not why there is a non-zero ground state energy. The two questions are different, yet similar.

 

[malawi_glenn]

ah ok, I see! Sorry!

 

[edguy99]

I'm looking for a simple physical explanation of the lowest energy level in atoms, so I can provide a brief explanation to interested laypeople (not to mention just to help myself understand better). Does anybody want to take a crack at it? Or am I asking for the impossible?

Since electron can't crash into the proton if it has a lowest energy level, with just a .
So the Bohr's model of electron orbiting the proton explains the stability of atoms.
But the problem with Bohr's model is that we know there is No orbiting angular momentum in the ground state of hydrogen atom, so Bohr's model is wrong in this case and we can't use it to explain the stability of hydrogen atom

I think in its simpliest form, consider the ionization energy of the last electron in a one electron, one proton model. In Hydrogen, the closer the electron is to the proton the harder is to pull it away, up until a very important number. Once the electron is within 53 picometers of the hydrogen proton, the amount of force required to separate the electron from the proton stays at 13.6 evolts no mater how close the electron gets to the proton in a classical sense. It doesn't seem to matter where the electron is, the important thing is that it takes 13.6 evolts of energy to pull it out.

That same distance is important in all elements, as the energies to separate the last electron from a helium, lithium, beryllium, ... atom, although higher then hydrogen, all stop rising at that same distance, what people call the Bohr radius. Inside this shell, the electrons don't need to do anything, they may well have no orbiting angular momentum. The only thing we know for sure is that there is a limit to the electrons orbital angular momentum. If the electron is going to fast, it will spin away from the proton.

 

[epenguin]

You have ALREADY aksed this

Dec6-08, 09:03 PM

Already asked https://www.physicsforums.com/showthread.php?t=277593 but was it answered?

I think we got sidetracked on the Bohr model.

 

[thaddeus]

The question is getting better tho ..

How about this .. the question is actually better described in terms of what forces maintain the "orbital zone" whereby (for instance) a hydrogen ion exists with only one electron .. h+This lowest energy level reference we have been making is quite a mysterious metaphor because what the 'lowest energy level' actually is can vary ... but the structural quality of the h+ ion is constant .

Also Hydrogen is far more likely found in as H-H (hydrogen gas .. H2) , so although we can discuss a single hydrogen ion , left to its own devices hydrogen has 2 electrons in the first shell - and this is arguably the lowest energy form of Hydrogen .

The dipole (pull) attraction of the electron towards the nucleus of the atomic structure is fairly well accounted for , but the force that maintains the divide (the push) that keeps them separate is not so well described at all to my knowledge ..

Nor for that matter is the Force in general that sets the float levels , or measured distances , for spans and separations any of the orbital shells levels.

 

[feynmann]

I guess it all comes down to the commutation relation between position and momentum. i.e. the Heisenberg uncertainty principle. For the electron to be in a state of lowest energy, it would have to be described by the dirac delta function centred in the nucleus. But this would cause an uncertainty in momentum and thus the electron would have more kinetic energy. My physical intuition says that the electron wants to find the midway point between this extra "uncertainty" kinetic energy and the coulombic minimum. To do this, it sits in the ground state.

Is calling for Heisenber's principle about the stability of atoms is just utterly confusing?

Calling for Heisenber's principle about the stability of atoms is not irrelevant, it's just utterly confusing. I've always considered that innapropriate, but maybe I'm missing the physics behind.

The way I see it, it can be justified in the following manner. Radiation reaction will cause canonical commutators for a harmonic oscillator to decay to zero unless coupling to the fluctuating vacuum is included. Commutator in that case are consistently preserved indeed. In a sort of fluctuation-dissipation relation, one can impose that "spontaneous emission" is exactly canceled by "spontaneous absorption" in the ground state, thus cancelling out radiation reaction. If you do that, you find that the cancellation gives you Bohr's quantization condition for the ground state (for excited states, you have different conditions on the "spontanenous emission vs absorption", corresponding to the necessity of vacuum fluctuations for transitions to occur).

Anyway, I don't think anybody takes those very seriously. This is how some physicists have interpreted Bohr's condition back in the early XXth century. But it's out of proportion to introduce that when calculating say Hydrogen's level, at the very beginning of QM.

 

[malawi_glenn]

why is HUP good to use when dealing with "Laymen terms" ?? Why is not things like "differential equations have discrete spectra" or anything else which is related to the REAL fact WHY you have discrete lying energy levels AND a lowerst one, a good laymen explanation?

Where do you use HUP when evaluating the energy levels of atoms?

 

[edguy99]

The question is getting better tho ..
Also Hydrogen is far more likely found in as H-H (hydrogen gas .. H2) , so although we can discuss a single hydrogen ion , left to its own devices hydrogen has 2 electrons in the first shell - and this is arguably the lowest energy form of Hydrogen .

The dipole (pull) attraction of the electron towards the nucleus of the atomic structure is fairly well accounted for , but the force that maintains the divide (the push) that keeps them separate is not so well described at all to my knowledge ...

The balance of these forces must produce the stable forms of hydrogen. The Ortho Hydrogen (most common form of hydrogen) must have a H-H bond length of 74pm and a certain amount of ability to vibrate in and out without breaking:

 

[DeShark]

why is HUP good to use when dealing with "Laymen terms" ?? Why is not things like "differential equations have discrete spectra" or anything else which is related to the REAL fact WHY you have discrete lying energy levels AND a lowerst one, a good laymen explanation?

Where do you use HUP when evaluating the energy levels of atoms?

Well, it's embedded into the whole thing isn't it? The fact that the system is described by a wave equation means that you have the same uncertainty principle that you have between omega and k in the classical waves. Since their quantum mechanical analogues are momentum and position, then the HUP transfers accordingly. So the HUP gives you the wave picture or the wave picture gives you the HUP. The two things are pretty much the same. But I can explain the HUP to my grandmother; explaining solutions of differential equations with boundary conditions and discrete excitations is somewhat more difficult.

 

[malawi_glenn]

ah so your grandmother knows what "fact that the system is described by a wave equation means that you have the same uncertainty principle that you have between omega and k in the classical waves. Since their quantum mechanical analogues are momentum and position, then the HUP transfers accordingly"?? ;-)

"how is the HUP found" layman is asking -> You give him the answer that it comes from the commutator relation of x and p... You will always in QM "explained" for laymen come back to the pure math.

Iam quite against explaining things "in laymen terms" since it is not acurate.

Now comming back to using HUP as explaining WHY atom have lowest energy level.

Objections:

Why has lowest energy state dirac delta function? "For the electron to be in a state of lowest energy, it would have to be described by the dirac delta function centred in the nucleus." Why is not the state "almost" delta function same? When deriving energy levels of hydrogen atom you never use radius at all... As you see, there is a problem of this argument.

edguy99, which is using a classical picture of the electron orbiting around the nucleus and then is arguing that at the bohr radius it takes 13.6eV to remove it. And that electrons can have such high angular momenta that they will leave the atom. Highly non quantum mechanical description I would say.

 

[DeShark]

ah so your grandmother knows what "fact that the system is described by a wave equation means that you have the same uncertainty principle that you have between omega and k in the classical waves. Since their quantum mechanical analogues are momentum and position, then the HUP transfers accordingly"?? ;-)

Not exactly... but I could tell her she can't put an electron in a tiny box without it gaining a lot of momentum. From this, I could explain that the electron wants to get to the center of the coulomb potential (which is like those black hole coin machines you get at supermarkets sometimes), but it can't because it picks up too much momentum. Therefore, it has a minimum energy that it can reach. This is zero-point energy explained to my grandmother. Try getting her to understand about differential equations and I think you'll fail.

"how is the HUP found" layman is asking -> You give him the answer that it comes from the commutator relation of x and p... You will always in QM "explained" for laymen come back to the pure math.

It doesn't have to be found. Tell them it's a fundamental assumption which works. Nature wants it that way. Whatever. Some thing *have* to come from nature. Tell them it's about this or that symmetry in space and time.

Iam quite against explaining things "in laymen terms" since it is not acurate.

I'm against explaining things in "pure maths", because the maths is there to describe nature. I can make up a bunch of axioms and "derive" all sorts of wonderful creatures. Are any of them physically relevant? Probably not. The physically relevant mathematical descriptions are founded upon some basic principles. You don't need maths to explain interference. Spinning arrows work just as well. When two particles with spinning arrows (or phase) are aligned, the probability (the length of the arrow squared) adds up and you're twice as likely to find the particle there. or whatever. This is the underlying picture of how things work. Talking about infinite dimensional hilbert spaces helps, but only to those who understand maths well enough. And that's all it is: a helping aid to facilitate calculation. In my opinion.

Why has lowest energy state dirac delta function?

Because that would minimise the energy due to the coulomb potential, making the Energy lower. But that's counteracted by the momentum term, which can't be zero because of the HUP.

 

[malawi_glenn]

i) Why can't you not put an electron in a tiny box without letting it get momentum, one would ask.

ii) Then I could just say that the physical law that governs the "quantum motion" of the electron in the atom is such that discrete levels are the ones coming out. An unexplained / unmotivated HUP is not better than this.

iii) Math is the language of physics, hence you can't go around the math.

iv) Show it, mathematically that it does mimize the columb potential and where it enters the Shrödinger Eq for hydrogentic Atoms. The energy eigenvalues are connected to a wavefunction which is a SOLUTION to the shcrödinger eqiaton. You don't put in a funtion in the shrödinger equation and find out what energy it corresponds to.

 

[DeShark]

i) Why can't you not put an electron in a tiny box without letting it get momentum, one would ask.

It's a basic fact of nature would be my reply.

ii) Then I could just say that the physical law that governs the "quantum motion" of the electron in the atom is such that discrete levels are the ones coming out. An unexplained / unmotivated HUP is not better than this.

So how do you explain that energy is only quantised for bound electrons? You've got one rule for half the time and another rule for the other half. This is worse, since you don't know when the rule is applicable.[/QUOTE]

iii) Math is the language of physics, hence you can't go around the math.

That's like saying that maths is the language to describe finding the shortest route and any attempt to find the shortest route without the maths will be a failure. Maths can be used in many circumstances to help out, but often it's quicker and simpler just to get in the car and go than to carefully plan it out every step of the way. In this case maths just gets in the way. Sure, if finding routes is your job, you'll be in a sore place without some sort of route finding algorithm, but the main points of route finding should be known by everyone. I think even non-physicists need to know about physics, why we do it, why they pay their taxes for things like CERN, etc.

iv) Show it, mathematically that it does mimize the columb potential and where it enters the Shrödinger Eq for hydrogentic Atoms. The energy eigenvalues are connected to a wavefunction which is a SOLUTION to the shcrödinger eqiaton. You don't put in a funtion in the shrödinger equation and find out what energy it corresponds to.

Ok fair point. But show mathematically where you get the potential corresponding to the interaction between an electron and a proton. My point is that the potential is *made up* so that the observations work. Often I feel like physicists are going round in circles and don't know what they're showing. Some things need to be taken as basic facts from which everything else is derived. Maxwell's equations did it for electromagnetism, Newton's law did it for mechanics. The Schroedinger equation does not explain all the commutation relations, all the interaction terms, etc. There are too many parameters (in my opinion) for the theory to be a good one. It seems to me (And maybe it's because I'm not that well acquainted with QM) that most of the stuff is plucked out of the air because it works.

 

[thaddeus]

The balance of these forces must produce the stable forms of hydrogen. The Ortho Hydrogen (most common form of hydrogen) must have a H-H bond length of 74pm and a certain amount of ability to vibrate in and out without breaking:

What is the Force that stops the Bond distance from reducing less than around 74pm ?

 

[edguy99]

What is the Force that stops the Bond distance from reducing less than around 74pm ?

The proton-proton repulsion force keeps them apart.

 

[thaddeus]

The proton-proton repulsion force keeps them apart.

My apologies .. i stumbled several times over how to word my question and posted it knowing it wasnt particularly clear .

In the diagram posted above of the Hydrogen Bond isotypes there is an example of Ortho H2 demonstrating the Two Nuclei with the electrons drawn into the space between ..
Now that is a simplistic diagram yet very good at its job of explaining the primary relationship

As we can see it is the Electrons mediate the two (2) Hydrogen nuclei
- so it is in reality a proton-electron repulsion force in action there , and not a proton-proton repulsion .

The single h+ (ion) is now a very good example of this proton-electron "repulsion force".

The Electron is attracted towards the Nuclei due to the dipole moment of positive and negative forces , closer and closer .. and then at a certain point (e.g. @ hydrogen bond = 74pm) the ionic attraction ceases to bring the electron any closer to the nuclei .. at this point another force comes into dominance .

This force is set as required to maintain the single electron in the 1st orbital shell and no lower ..

What is this force that buffers the electron from the Proton ?

 

[malawi_glenn]

It's a basic fact of nature would be my reply.

So how do you explain that energy is only quantised for bound electrons? You've got one rule for half the time and another rule for the other half. This is worse, since you don't know when the rule is applicable.

The shcrödinger eq for free electrons gives cont. energy.

That's like saying that maths is the language to describe finding the shortest route and any attempt to find the shortest route without the maths will be a failure. Maths can be used in many circumstances to help out, but often it's quicker and simpler just to get in the car and go than to carefully plan it out every step of the way. In this case maths just gets in the way. Sure, if finding routes is your job, you'll be in a sore place without some sort of route finding algorithm, but the main points of route finding should be known by everyone. I think even non-physicists need to know about physics, why we do it, why they pay their taxes for things like CERN, etc.


Try to explain WHY HUP works with no math, one must resign and say things like "it is a basic fact of nature"




Ok fair point. But show mathematically where you get the potential corresponding to the interaction between an electron and a proton. My point is that the potential is *made up* so that the observations work. Often I feel like physicists are going round in circles and don't know what they're showing. Some things need to be taken as basic facts from which everything else is derived. Maxwell's equations did it for electromagnetism, Newton's law did it for mechanics. The Schroedinger equation does not explain all the commutation relations, all the interaction terms, etc. There are too many parameters (in my opinion) for the theory to be a good one. It seems to me (And maybe it's because I'm not that well acquainted with QM) that most of the stuff is plucked out of the air because it works.[/QUOTE]


it is not the same thing, potential etc are there from first principles of physics, wheres your modifications are ad hoc.

 

[DeShark]

The shcrödinger eq for free electrons gives cont. energy.

You said that the fact that the energy levels are quantised could be taken as the basic fact instead of the HUP. So that my response was that the energy isn't always quantised. Now you're taking the Schrödinger equation as the basic, but you still need to find out the interaction energies.

Try to explain WHY HUP works with no math, one must resign and say things like "it is a basic fact of nature"

Explaining why the HUP works with maths will fall back to the Schrödinger equation being a wave equation and the "bandwidth" relation giving the HUP. I suppose taking the Schrödinger equation as fundamental is better in this respect since it gives both the HUP and the quantisation of energy (given the correct potential). But it doesn't explain why only two electrons are found in the first energy level. Additionally, it could be asked "Why is the Schrödinger equation the correct equation to use?" and in this Mathematics will get you nowhere. Your picture using maths is more succinct and easy to deal with, I'm happy to admit, but just because the description fits the facts does not make it better than the facts themselves. The facts are numerous and ad hoc. The theory just has a nice picture to consolidate them. In essence, I think what I'm driving at is that nobody can give a description as to why there is a ground state of energy. With or without maths. The fact is that it's there and any theory should be able to calculate the levels. Quantum theory does this as well as we can measure. But it explains nothing, neither to the layperson, nor to the physicist.

 

[malawi_glenn]

The shcrödinger eq IS the basics when talking about dynamis, the HUP is not :) Therefor my suggestion is that laymen terms should boil down to the Shcrödinger equation, which is the CORRECT answer. By imposing false "layman solutions/explanations" you are not telling the truth.

No HUP as nothing to do with Schrödinger eq, it is a syntetic relation you are doing now.

Why only two electrons in first level comes from Pauli principle which has no classical analogy. So there it really boils down to math.

Shrödinger eq is the QM mirror image of Newtons laws one can say. Of course the axioms and definitions can't be derived mathematically, defintions are definitions. What I argued against you was that you said that the lowest energy level should be described by a dirac delta function, but that is not true or even the correct way how to find energy levels of systems.

 

[Alfi]

The Ortho Hydrogen (most common form of hydrogen) must have a H-H bond length of 74pm

Just a layman here :)
When I see a measurement of 74pm ( Pico Meters ? ) I wonder. Is this anything to do with a wavelength?

Sorry to interrupt. just curious.

 

[edguy99]

Just a layman here :)
When I see a measurement of 74pm ( Pico Meters ? ) I wonder. Is this anything to do with a wavelength?

Sorry to interrupt. just curious.

Not really a wavelength, 74 picometers (10^−12 meters) is the traditionally accepted distance between the centers of the 2 hydrogen protons (depected here as shells) in a common form of hydrogen called Orthohydrogen and it is the simplest example of a covalent bond in chemistry. The shells are drawn with a radius of 53picometers (called the bohr radius).

To thaddeus: Does the proton - proton repulsion (coulomb) force play any roll when adding up all the forces involved? At a distance of around 74 picometers, this seems a reasonably large force that would tend to push the protons apart.

 

[thaddeus]

eddy ,

Im sure it has a great deal to do with it ..

There is an acceptable balance between the pushes and the glue ..

 

[Dadface]

A simple explanation was wanted so let me have a crack at it[being a bit simple myself]Bohr quantised angular momenta in order to explain the hydrogen spectrum.He couldn't really justify his analysis other than it worked[reasonably well].Later, when De Broglie showed that particles move like waves some sort of justification was provided-electron waves in orbit link up with themselves,rather like a snake eating its own tail.There are an integral number of waves in each orbit,one in the ground state two in the first excited state and so on.

 

[feynmann]

A simple explanation was wanted so let me have a crack at it[being a bit simple myself]Bohr quantised angular momenta in order to explain the hydrogen spectrum.He couldn't really justify his analysis other than it worked[reasonably well].Later, when De Broglie showed that particles move like waves some sort of justification was provided-electron waves in orbit link up with themselves,rather like a snake eating its own tail.There are an integral number of waves in each orbit,one in the ground state two in the first excited state and so on.

So what you are saying is that there is one wave in the ground state.
But I still don't understand why this ground state can not get arbitrarily close to the proton
In other word, why this one wave ground state is located at Bohr radius of atom
It could be at half of Bohr radius, what prevent this to happen?

 

[Dadface]

Bohr was inspired by the fact that mvr the angular momentum of a rotating point particle has the same units as h [plancks constant].He applied it to the electron in the hydrogen atom fiddled about with it and showed that the hydrogen spectrum could be explained if mvr was quantised and took only integral values of h divided by 2pi.The smallest value of mvr=1times h divided by 2pi,and this relates to the ground state.In the first excited state mvr equals 2h divided by 2 pi and so on.Bohrs model has since been improved and superseded but his main findings still apply.In short it is quantum theory that fixes the radii but why quantum theory is as it is no one knows and that's just one of the things that makes physics interesting.

 

[Dadface]

Bohr was inspired by the fact that mvr the angular momentum of a rotating point particle has the same units as h [plancks constant].He applied it to the electron in the hydrogen atom fiddled about with it and showed that the hydrogen spectrum could be explained if mvr was quantised and took only integral values of h divided by 2pi.The smallest value of mvr=1times h divided by 2pi,and this relates to the ground state.In the first excited state mvr equals 2h divided by 2 pi and so on.Bohrs model has since been improved and superseded but his main findings still apply.In short it is quantum theory that fixes the radii but why quantum theory is as it is no one knows and that's just one of the things that makes physics interesting.[/QUOTE]

 

[tim_lou]

It seems that so far, no one has actually tried to answer the original question of why there is a lowest energy state...

I'll try to crack it here,

So, feynmann basically got it right, saying that it explains the stability of atom.

Basically, in the quantum world, things fluctuate, an electron in an atom can move to different states by emitting light particles (photons)--energy must be conserved though. So, imagine I have an atom, and there isn't a lowest energy state, then by the above, the electron will just keep emitting photons and move to a yet lower energy state. We know that this doesn't happen in nature, so physicists actually require a sensible theory to contain a lowest energy state. This is what turns out to be the case for the quantum mechanical model of hydrogen.

Of course, you can work out some math and show that a lowest energy state must exist given some suitable conditions. I don't think this is the answer OP wants though. In real life, the way physicists answer this question is to work backward. They ask, how can I make it so that there is a lowest possible energy state? then they find out that quantum mechanics allows this and so they accept this model.

I kinda dodge around the question there but I hope this clears some things up.