Number of Quantum Levels & Math Defining Them: Hydrogen

[Dlockwood]

I know of four or five quantum levels of hydrogen. My question is: How many quantum levels are there (of hydrogen) and is there any math that can be used to define these levels and predict other possible levels? I assume that each element has a specific number of quantum levels and that not all elements have the same number of quantum levels. Is that true? Or do quantum levels expand out to infinity. If so, how is this been verified?

If I've asked another stupid, embarrassing question you can email me personally at doug@m16eagle.com. I have another question after this one is answered.

 

[Atheist]

I know of four or five quantum levels of hydrogen. My question is: How many quantum levels are there (of hydrogen) ...

Assuming I understand your question correctly, then the answer is: Infinite.

... and is there any math that can be used to define these levels and predict other possible levels?

You solve the equation for the wave function that seems appropriate to your needs (e.g.: Schroedinger equation for the electron in a central potential) and get an infinite number of solutions. Each corresponding to a certain (not nessecarily unique) energy.

I assume that each element has a specific number of quantum levels and that not all elements have the same number of quantum levels. Is that true?

No, unless some weird things happen when you go over to many-body QM which is neither to be expected nor possible to compute by today´s methods (all methods for many-body QM are approximations).

Or do quantum levels expand out to infinity. If so, how is this been verified?

Yes, see above.

If I've asked another stupid, embarrassing question you can email me personally at doug@m16eagle.com. I have another question after this one is answered.

Your question is in no way stupid or embarrassing. It just shows you think about problems that you don´t know the math or the physical background of.

 

[Dlockwood]

So then, if quantum levels expand out to infinity then when accelerators create 3 million + degree plasmas with the electrons floating in the outer regions, are those electrons really free or are they still 'bonded' to their protons? Is that why they recombine to form hydrogen (the same stuff they started with) after the acceleration is shut down? Why don't they recombine in a more random fashion, like maybe some helium, a few isotopes, you know, stuff like that (not counting the fusion reactions)? Can it be that though the operating dynamics have changed due to very high voltages and very large magnetic fields that we really have just hydrogen with the electrons at a very high quantum level?

 

[zefram_c]

So then, if quantum levels expand out to infinity then when accelerators create 3 million + degree plasmas with the electrons floating in the outer regions, are those electrons really free or are they still 'bonded' to their protons? Is that why they recombine to form hydrogen (the same stuff they started with) after the acceleration is shut down? Why don't they recombine in a more random fashion, like maybe some helium, a few isotopes, you know, stuff like that (not counting the fusion reactions)? Can it be that though the operating dynamics have changed due to very high voltages and very large magnetic fields that we really have just hydrogen with the electrons at a very high quantum level?

I think I see what your misconception is. While there exist an infinity of bound states, they cluster around zero binding energy. If we ignore corrections such as spin-orbit coupling (many orders of magnitude smaller), the energies of the hydrogen atom are given by E(n) = -13.6eV / n^2. So all the higher n states have very small binding energies. In an accelerator, the average energy per electron is much, much greater than 13.6eV so one can use Boltzmann statistics to find virtually all electrons have separated.
To form helium or isotopes, one needs to create new nuclei. This will not happen unless the nuclei themselves are accelerated to high energies. While it is possible for a high-energy electron to smash directly into a nucleus and cause other nuclear particles to come out, this is not the dominant mechanism of energy loss. And in any event, the electrons are not reunited with the protons so they can recombine.

 

[Dlockwood]

I think I see what your misconception is. While there exist an infinity of bound states, they cluster around zero binding energy. If we ignore corrections such as spin-orbit coupling (many orders of magnitude smaller), the energies of the hydrogen atom are given by E(n) = -13.6eV / n^2. So all the higher n states have very small binding energies..

I'm a little confused... is it the higher n states that have very small binding energies while the lower ones cluster around zero binding energy?

 

[quantumdude]

If I've asked another stupid, embarrassing question

Erm...It's not that it's stupid, it's just that you've already asked it before, and it's been answered.

Quanutm level question.

I'm a little confused... is it the higher n states that have very small binding energies while the lower ones cluster around zero binding energy?

No, the ground state is -13.6 eV. It's the higher states that cluster around zero.

 

[Dlockwood]

These answers provoke a related question. Every time I see pictographs of atoms with the core and electrons, they are shown with the electrons being in nice concentric patterns with the electrons evenly spaced and in planar orbits (even on the home page of this forum). What if the electon motion is completely random? What if the eight electrons in n2, for example, don't move in a planar orbit but are completely (or almost) random, collisions being avoided because the repulsive charges outweigh the masses? This would form a charged shell in that n layer that would, in effect, spherically encompass the entire core. Maybe the reason that Heisinburg ? principle applies is because of this chaotic movement. Maybe the math of the electron should be chaos math. What if there are no shells, per se, but just one shell with different quantum energies? That brings me to my third question, next post, maybe.

 

[selfAdjoint]

The electrons, although they are shown in circular planar orbits, are not little bullets that travel in a simple way in circular or any other classical paths. They are both wave and particle and their momentum and position cannot both be known with pure accuracy due to the uncertainty principle. In modern physics, even in chemistry, the question is not what orbit is this electron in, but what energy level.

 

[Dlockwood]

Review

Some of these replies to my posts are quite a dance. I suppose that either they haven't read all my posts or that I have not communicated the concepts that I have tried to bring forward adequately. I'll assume the latter and provide a review here of those concepts.

First, M=E<C. Perhaps in a more readable form, E=M@C. Electrical current says that Einstein's formula cannot be correct. Yea, Yea, I know... Its already been proven. I have found that these 'proofs' are less than adequate (for reasons that would take more time than I have to explain) and if physicists would just do their job and question everything and look at all the variables, I probably would never have made a post to this forum. Why does current travel at near the velocity of light? The only analogy that makes sense is that of Newton's Cradle... The little novelty game with (usually) five balls. The balls in the middle do not hardly move. Apply this concept at the atomic level and its pretty easy to see that the electrons have to 'enter' the wire at (or near) the velocity of light in order for the wave motion to move at the velocity of light, less losses, hence, velocities just below the velocity of light. The only reason for any electron flow at all is because of the expended energy at the other end of the wire. (I understand that someone has 'tagged' electrons in a way that allows them to monitor their movement. Apply this to a closed system using superconductors and you will probably find almost no electron movement, except what is needed to sustain the wave. This would be a good opportunity to establish some basic mathematical standards that would define the basic characteristics of a wave.) This also explains the duality of the electron. Its obvious (to me) that if electron velocity is near the velocity of light then it would take very little energy to push it into a wave. Almost any measuring process would accomplish this. Also, the fact that the electron absorbs and emits light shows the tremendous compatability with radiant energy. Have you ever noticed that all radiant energy in the universe, visible and invisible, natural or synthetic, comes from matter?

Second, I think that our concepts of electron movements are incorrect. But I also think that the disparities between the shell/quantum Bohr/Schrödinger concepts are resolved when the electron movements are viewed as spherical shells or energies surrounding the core. I also think that this concept is vital to an understanding of atomic theory. Most often we tend to relate the movements of planets to the movements of electrons. Everybody admits that this is not a good analogy, but it is still being used and talked down on by the arrogant quantumists who still have not provided an adequate model of electron motion. Part of the planetary analogy is useful. Just put eight planets in the same orbit and see what happens. Things are going to smash up pretty fast. At the atomic level we have a particle with almost no mass but a charge equal to the proton. Put eight of these into n2 and they are going to collide except that the repulsive charges outweigh the masses so they are going to deflect at right angles (for head on collisions) or various oblique angles. These would almost immediately appear as a random spherical movement around the core, hence, a negatively charged sphere (or spheres, depending on the element) will exist around the core.

There are a lot of other things to say here but I'll leave them for others to 'discover'. Again, my apologies for forgetting about the Fraunhofer lines and my thanks for those who helped me re-discover them. You've helped me plug some of my 'gaps' but I still have more. In my third question I will have to address some of the philosophical questions of physics.

Thanks for reading.

Douglas Lockwood

 

[Kane O'Donnell]

If the electrons traveled in any kind of classical orbit, no matter how complex or impressive, they would be constantly radiating electromagnetic radiation and hence would continually lose energy. This does not happen, hence I can sit here and type this response. The orbit model is not just a simplification. It's wrong. It was put forward as one of the earliest models of the atom and has been shown to be inconsistent with experimental results for almost a century now.

Current doesn't flow at near the velocity of light. When you flick the light switch on, an electromagnetic wave propagates from the switch to the light. This wave *does* travel near the speed of light (in fact, it *is* the speed of light in the medium, which is generally slower than in a vacuum) and influences the electrons in it's vicinity.

Besides, what does this have to do with E = mc^2? And what is M = E<C?

No simple picture of atomic structure exists, but models involving classical orbits do not give results that agree with experiment, and this is the ultimate test of a physical theory.

Besides - if you think our theory of electrodynamics is incorrect, you'll have to show where it disagrees with experiment. This will be quite a task. Last I checked, it was accurate to 10 decimal places, with experiment being (you guessed it) accurate to 10 decimal places. QED is the most stringently tested theory in physics. We know it should have limitations (ultimately it should be the low energy limit of more general theories) but in 50 years we have been hard pressed to find experiments that show where the limitations exist. I doubt you're going to provide us with one.

Regards,

Kane O'Donnell

 

[Integral]

Douglas,
Where did you get the idea that electrons in a current carrying wire travel at c? This simply is not true, since much of the rest of your post seems to based on this concept it really does not have much relevance. Why do you push your misunderstandings on to Physics in general? Before you can make any statement about what a Physicists should or should not do, you will need to learn some physics.
Please post your philosophical ideas in the appropriate forum, not here.

 

[Dlockwood]

I'll address the second response first. I did not say that electrons travel through wires at the velocity of light. What I have said is that the reason that wave motion in electrical current moves at C is because the electron, in it's movement around the core, is at C, therefore, like the novilty game called Newton's cradle, when we stimulate electrical current in wires, while the electron barely moves, the motion of the electron at C is transferred through the wire at C. Its a closed looped system. We don't really put electrons in at one end and pull other eletrons out at the other. Think of it this way: Pop the hood on your car and look at the fan belt. Put an imaginary white dot on the belt somewhere where it touches the crankshaft. As you start the engine the white dot begans to move. But the energy is instantly transferred to the water pump, the alternator, the power steering pump and the air conditioner (all at different points on the belt) while the imaginary dot is still on the crankshaft. The dot continues to move in an 'engineered' circuit and eventually returns to the crankshaft. Electrical current is pretty much the same way. We induce the movement at the power station and because it is a poly phase system, the return path is the other wires or the earth.

Addressing the first response: I'm reminded of the proverb that says 'The stone which the builder's rejected, the same is become the chief conerstone.' In their evolutionary vanities scientists have rejected a cornerstone of science that will keep them from ever going to the stars. Its just as well, given the current sad state of the world, but that's another subject. What I have tried to bring forward is that mass does not become infinite as per Einstein. Mass becomes zero at C. That means that if we were to fling the world off into space at the velocity of light, it would have zero mass. It would become radiant energy. It doesn't mean that it ceases to exist as Earth and it doesn't mean that it is infinitely small. It just means that it has changed its state. This is evidenced by the behavior of the electron and electrical current, as previously stated.