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Copernicus
2014-Aug-31, 02:40 AM
could someone explain where rydberg energy comes from? Is it part of the proton or electron rest mass? Etc.

Jens
2014-Aug-31, 03:32 AM
Just a simple question, but what do you mean by Rydberg energy? I have found entries for Rydberg constant and equation, but not energy.

Copernicus
2014-Aug-31, 03:40 AM
Just a simple question, but what do you mean by Rydberg energy? I have found entries for Rydberg constant and equation, but not energy.

This constant is often used in atomic physics in the form of the Rydberg unit of energy:
[2]

Rydberg energy = hc(Rinfinity) http://en.wikipedia.org/wiki/Rydberg_constant

Shaula
2014-Aug-31, 04:36 AM
From that page:

The Rydberg unit of energy, symbol Ry, is closely related to the Rydberg constant. It corresponds to the energy of the photon whose wavenumber is the Rydberg constant, i.e. the ionization energy of the hydrogen atom.

Copernicus
2014-Aug-31, 06:20 AM
From that page:

The Rydberg unit of energy, symbol Ry, is closely related to the Rydberg constant. It corresponds to the energy of the photon whose wavenumber is the Rydberg constant, i.e. the ionization energy of the hydrogen atom.

Thank you Shaula! I was just wondering if there was any defintive quantum mechanics reason for why the Rydberg constant and rydberg energy, is what it is?

ben m
2014-Aug-31, 07:22 AM
It's the ionization energy of a hydrogen atom. You figure out what it is by plugging a hydrogen atom into the Schrodinger Equation and solving it. Is that what you're asking?

Copernicus
2014-Aug-31, 07:49 AM
It's the ionization energy of a hydrogen atom. You figure out what it is by plugging a hydrogen atom into the Schrodinger Equation and solving it. Is that what you're asking?

I am wondering if the mixtures of constants that give the rydberg constant, is derivable, or do they happen to just work out like the fine structure constant.

Shaula
2014-Aug-31, 11:49 AM
If you follow the links on the page you referred to you can see how it is derived in the Bohr model: http://en.wikipedia.org/wiki/Bohr_model

If you do, as Ben says, the more correct analysis (this is usually a first year physics problem at undergraduate level - if you search for "Hydrogen Atom Quantum Mechanics Analytical Solution" you will find plenty of worked examples) you get the same factor.

ben m
2014-Aug-31, 07:14 PM
I am wondering if the mixtures of constants that give the rydberg constant, is derivable, or do they happen to just work out like the fine structure constant.

Look at what goes into the atomic-binding-energy solution. It depends on the fact that the electron and proton are attracted to one another, and the (measured) strength of that attraction is down using (measured) quantities e, epsilon-0, and/or alpha depending how you're writing it. And it depends on quantum mechanics, which includes relationships between energy, momentum, and wavelength, and those relationships include h and m_e and c. When you're setting up the equations, those are the constants that go in, and they're still there in the solution.

On the other hand, I don't know what you mean to "just work out like the fine structure constant". The fine structure constant is just a different way of organizing the constants of E&M. The authors of classical E&M wrote force-laws with two unusual numbers, "q" for the amount of charge (in arbirarily-defined Coulombs) and "epsilon_0" to the strength of the force (measured, in funny units). If everyone agrees that "e" is the most commonly-encountered amount of charge, then you can reorganize the equations so they're simpler-looking, and the reorganization groups the arbitrary stuff together into a factor we call "the fine structure constant".

Copernicus
2014-Aug-31, 10:40 PM
Look at what goes into the atomic-binding-energy solution. It depends on the fact that the electron and proton are attracted to one another, and the (measured) strength of that attraction is down using (measured) quantities e, epsilon-0, and/or alpha depending how you're writing it. And it depends on quantum mechanics, which includes relationships between energy, momentum, and wavelength, and those relationships include h and m_e and c. When you're setting up the equations, those are the constants that go in, and they're still there in the solution.

On the other hand, I don't know what you mean to "just work out like the fine structure constant". The fine structure constant is just a different way of organizing the constants of E&M. The authors of classical E&M wrote force-laws with two unusual numbers, "q" for the amount of charge (in arbirarily-defined Coulombs) and "epsilon_0" to the strength of the force (measured, in funny units). If everyone agrees that "e" is the most commonly-encountered amount of charge, then you can reorganize the equations so they're simpler-looking, and the reorganization groups the arbitrary stuff together into a factor we call "the fine structure constant".

Thanks Ben, I do remember going over this in physics class many years ago. It was a great accomplishment for physics.

Copernicus
2014-Sep-01, 09:56 PM
Is the Rydberg constant used empirically for quantum mechanical calculations of properties of other elements besides Hydrogen. I realize that it is not used empirically for hydrogen, but I am not aware that the spectral lines for other elements, other than hydrogen can be calculated exactly using the Bohr model.

antoniseb
2014-Sep-01, 10:02 PM
... I am not aware that the spectral lines for other elements, other than hydrogen can be calculated exactly using the Bohr model.
Singly ionized Helium, doubly ionized Lithium, etc also can be calculated using the same method, but the energies go up linearly with to the number of protons.

EigenState
2014-Sep-01, 10:08 PM
Greetings,


Is the Rydberg constant used empirically for quantum mechanical calculations of properties of other elements besides Hydrogen. I realize that it is not used empirically for hydrogen, but I am not aware that the spectral lines for other elements, other than hydrogen can be calculated exactly using the Bohr model.

The Bohr model is a zero-order approximation of the electronic structure of atoms--even hydrogen--that is predicated only upon the concept of the principal quantum number which of course reflects the radial distribution of the electron. It does not include the physical interactions that lead to fine structure and hyperfine structure.

Best regards,
ES

Copernicus
2014-Sep-01, 10:56 PM
Greetings,



The Bohr model is a zero-order approximation of the electronic structure of atoms--even hydrogen--that is predicated only upon the concept of the principal quantum number which of course reflects the radial distribution of the electron. It does not include the physical interactions that lead to fine structure and hyperfine structure.

Best regards,
ES

This just reminds me of how good my forgetter is. Is there a working equation that accurately predicts the fine structure or hyperfine structure of Hydrogen, Helium or anything else?

ben m
2014-Sep-01, 11:46 PM
Singly ionized Helium, doubly ionized Lithium, etc also can be calculated using the same method, but the energies go up linearly with to the number of protons.

Quadratically, not linearly.


This just reminds me of how good my forgetter is. Is there a working equation that accurately predicts the fine structure or hyperfine structure of Hydrogen, Helium or anything else?

It's still the Schrodinger equation. The Schrodinger Equation is something that allows you to feed it complicated interactions/potentials/etc or simple ones. If you only tell it about one electron, and only to consider an ideal Coulomb's Law potentials, it spits out the vaguely-Bohr-like hydrogen atom. (But it does so in a way that an undergrad can solve with pencil and paper.) If you tell it to do 6 electrons, each with a magnetic moment, around a finite-size nucleus with its own magnetic moment, etc., it'll predict the fine structure and hyperfine structure too, but now you need a computer to solve it numerically. Tell it to do a 100-electron atom and not even a computer can pound through it effectively.

Copernicus
2014-Sep-02, 07:22 AM
Quadratically, not linearly.



It's still the Schrodinger equation. The Schrodinger Equation is something that allows you to feed it complicated interactions/potentials/etc or simple ones. If you only tell it about one electron, and only to consider an ideal Coulomb's Law potentials, it spits out the vaguely-Bohr-like hydrogen atom. (But it does so in a way that an undergrad can solve with pencil and paper.) If you tell it to do 6 electrons, each with a magnetic moment, around a finite-size nucleus with its own magnetic moment, etc., it'll predict the fine structure and hyperfine structure too, but now you need a computer to solve it numerically. Tell it to do a 100-electron atom and not even a computer can pound through it effectively.

Thank you, that is interesting