Orbital Harmonics

[Xittenn]

I keep coming back to the same brick wall on these matters, that prevents me from thinking beyond the initial value problem.

 

Beginning with the Bohr Model, we have the attractive force between the nucleus and the electron. A stable orbit is achieved if the centrifugal force balances with this Coulombic attraction. Under wave-particle duality we have the need for harmonic orbitals. The length of the orbital must have a value of an integral number of the electrons wavelengths or it will interfere destructively with itself and the amplitude will decrease to zero.

 

i) Do we ever observe non-harmonic orbiting? -- or -- Are non-harmonic orbitals never achieved?

 

ii) Is it the harmonic oscillation that ensures the stable orbit? -- or -- Are harmonic oscillations the only way in which electronic orbitals manifest themselves?

 

iii) Will the Ultra-Violet catastrophe occur when a non-harmonic orbit is achieved? -- or -- Do we never see the UV Catastrophe under any conditions at all?

 

Understood, the Bohr model fails to predict all features of the set of phenomena as is presented by the theories of Quantum Mechanics. I am however, having a rather difficult time getting passed this early idea and I quickly lose interest in the pages following as my thoughts keep nagging me to get this part right first. I guess what I'm saying is, are classical pathways still taken and the events so short as to be described as non-existent? Is harmonic either achieved, or the reactants roll back down the hill as the activation energy is not satisfied as to make the products, or the products themselves collapse?

 

I've been stuck on this for a very long time. I keep going over it and I get to a point and think that I must be missing something. For the most part I've blamed math, but now I know the math, at least the math required to do the work in the book I'm currently reviewing the concepts in. These questions though are completely left unanswered, and it seems that I'm just supposed to take it in and not ask questions.

[swansont]

You're right that the Bohr model is deprecated, but the surviving concepts in QM include the quantization of energy and angular momentum, which appear in the solutions of the Schrödinger equation. States in which the the system does not have the allowed value are not observed. Since there is no classical trajectory, you really can't look at this in terms of harmonics anymore and besides, that's one of the things the Bohr model gets wrong: the S state has zero angular momentum, rather than one unit it predicts. "Stable orbits" become allowed states (eigenstates of the Hamiltonian operator). If a photon is incident on an atom and the energy does not match an allowed transition the photon can still interact and be delayed, but it will not result in an excitation or any kind of energy or momentum transfer — this is the quantum model of why light slows down in a medium.

 

The ultraviolet catastrophe is a separate issue of classical mechanics related to the equipartition of energy and energy modes in a cavity.

http://en.wikipedia.org/wiki/Ultraviolet_catastrophe

[Xittenn]

Thank you! I will read on then and try to put the pieces together.

[questionposter]

You're right that the Bohr model is deprecated, but the surviving concepts in QM include the quantization of energy and angular momentum, which appear in the solutions of the Schrödinger equation. States in which the the system does not have the allowed value are not observed. Since there is no classical trajectory, you really can't look at this in terms of harmonics anymore and besides, that's one of the things the Bohr model gets wrong: the S state has zero angular momentum, rather than one unit it predicts. "Stable orbits" become allowed states (eigenstates of the Hamiltonian operator). If a photon is incident on an atom and the energy does not match an allowed transition the photon can still interact and be delayed, but it will not result in an excitation or any kind of energy or momentum transfer — this is the quantum model of why light slows down in a medium.

 

The ultraviolet catastrophe is a separate issue of classical mechanics related to the equipartition of energy and energy modes in a cavity.

http://en.wikipedia....let_catastrophe

 

Wait, so, shouldn't the weakest light possible for matter to generate be by the ground state of an atom of normal matter? Because there was one link you gave me which somehow mixed the bhor model and cloud model together and it stated that the electrons on heavier nuclei were closer to the nucleus than that of hydrogen, but I asked a chemist I know and they said that it's not correct, and that the problem comes from measuring negative joules. I don't get how we have radio waves and only have few things to pick them up while everything else cant if every atom's electron energy levels are the same distance from any nucleus.

Edited November 10, 2011 by questionposter

[swansont]

Wait, so, shouldn't the weakest light possible for matter to generate be by the ground state of an atom of normal matter? Because there was one link you gave me which somehow mixed the bhor model and cloud model together and it stated that the electrons on heavier nuclei were closer to the nucleus than that of hydrogen, but I asked a chemist I know and they said that it's not correct, and that the problem comes from measuring negative joules. I don't get how we have radio waves and only have few things to pick them up while everything else cant if every atom's electron energy levels are the same distance from any nucleus.

 

The inner electrons in an atom are the most tightly bound, but the outermost ones are not — the inner electrons screen the nuclear charge. So if you compared them to the ionization energy of Hydrogen — 13.6 eV, for an electron in the 1S state — you would find that the 1S electron takes a lot more energy to ionize, but the outermost electron takes less energy. Usually just a few eV.

 

Broadcast radio waves typically don't come from from atomic transitions. They come from the radiation that results from acceleration of free charges.

[questionposter]

The inner electrons in an atom are the most tightly bound, but the outermost ones are not — the inner electrons screen the nuclear charge. So if you compared them to the ionization energy of Hydrogen — 13.6 eV, for an electron in the 1S state — you would find that the 1S electron takes a lot more energy to ionize, but the outermost electron takes less energy. Usually just a few eV.

 

Broadcast radio waves typically don't come from from atomic transitions. They come from the radiation that results from acceleration of free charges.

 

So the amount of energy needed to go the the next energy level lessens as you travel further away from the nucleus? Does it lesson the same for each nucleus? I don't get how these more energetic photons come about then, because aren't those photons suppose to be the result of high energy electrons accepting a photon then going back? And also, how can cell-phones pick up such low energy radio-waves then if atoms can't generate that low energy of a photon? Would a denser or heavier element be able to pick up radio waves and a lighter element wouldn't?

Edited November 11, 2011 by questionposter

[swansont]

So the amount of energy needed to go the the next energy level lessens as you travel further away from the nucleus? Does it lesson the same for each nucleus? I don't get how these more energetic photons come about then, because aren't those photons suppose to be the result of high energy electrons accepting a photon then going back? And also, how can cell-phones pick up such low energy radio-waves then if atoms can't generate that low energy of a photon? Would a denser or heavier element be able to pick up radio waves and a lighter element wouldn't?

 

Different elements and even individual isotopes each have their own structure. "further away from the nucleus" is a misnomer because we have orbitals, not orbits but lower states are more tightly bound and typically require more energy to ionize or excite. Atomic transitions are only one of several ways of getting photons — you can have nuclear transitions and interactions including pair annihilation, and Bremsstrahlung. And there's also the whole array of transitions in molecular and solid-state systems.

 

Antenna operation is not something one would describe with atomic absorption models. A single atom is not absorbing the photon.