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

1. Dec 13, 2008

### 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

Last edited: Dec 13, 2008
2. Dec 13, 2008

### DeShark

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.

3. Dec 13, 2008

### malawi_glenn

Dec6-08, 09:03 PM

4. Dec 14, 2008

### DeShark

That's not true. Feynmann 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.

5. Dec 14, 2008

### malawi_glenn

ah ok, I see! Sorry!

6. Dec 15, 2008

### edguy99

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 seperate 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 seperate 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 dont 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.

7. Dec 16, 2008

### epenguin

8. Dec 16, 2008

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.

Last edited: Dec 16, 2008
9. Dec 16, 2008

### feynmann

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

10. Dec 16, 2008

### 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?

11. Dec 16, 2008

### edguy99

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:

12. Dec 16, 2008

### DeShark

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.

13. Dec 16, 2008

### 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.

14. Dec 16, 2008

### DeShark

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.

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.

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.

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.

15. Dec 16, 2008

### 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.

16. Dec 16, 2008

### DeShark

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.[/QUOTE]

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.

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.

17. Dec 16, 2008

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

18. Dec 16, 2008

### edguy99

The proton-proton repulsion force keeps them apart.

19. Dec 17, 2008

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 ?

Last edited: Dec 17, 2008
20. Dec 17, 2008

### malawi_glenn

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.