Energy levels, de Broglie

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The Formula for computing E(n) = -(Z^2)/(n^2) * Ei

is fairly straight forward. Am I right in thinking this formula refers to the energy level of the atom with Z number of protons? This formula, what it yields at least, doesn't depend on the number of electrons the atom has?

Also, when trying to find the wavelength of the emitted/absorbed photon, should we use hc/E or h/p ? What makes a wave a de Broglie wave? I have deeper doubts but I don't even know where to start, I hope with more replies it'll become clearer.
 

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jtbell
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The Formula for computing E(n) = -(Z^2)/(n^2) * Ei

is fairly straight forward. Am I right in thinking this formula refers to the energy level of the atom with Z number of protons? This formula, what it yields at least, doesn't depend on the number of electrons the atom has?
This formula works only for hydrogen and for "hydrogen-like" ions, that is, ions with only one electron, e.g. He+, Li++, Be+++, etc. If there's more than one electron, the electrons interact with each other and this affects the energy levels.

Also, when trying to find the wavelength of the emitted/absorbed photon, should we use hc/E or h/p ?
It doesn't make any difference, because for a photon, E = pc. This follows from the general formula for energy, momentum and rest mass:

[tex]E^2 = (pc)^2 + (m_0 c^2)^2[/tex]

with [itex]m_0 = 0[/itex] for a photon.
 
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This formula works only for hydrogen and for "hydrogen-like" ions, that is, ions with only one electron, e.g. He+, Li++, Be+++, etc. If there's more than one electron, the electrons interact with each other and this affects the energy levels.
I suppose for the purpose of my class (and my exam today) this general formula will be enough. Actually, they love to use the energy 13.6 eV in the book, I believe this is the same case that only applies for single electron-atoms.



It doesn't make any difference, because for a photon, E = pc. This follows from the general formula for energy, momentum and rest mass:

[tex]E^2 = (pc)^2 + (m_0 c^2)^2[/tex]

with [itex]m_0 = 0[/itex] for a photon.
That's exactly right..I didn't think it through very well.


What about when they ask for the energy of the photon that is emitted? The wavelength of the emitted/absorbed photon will always equal the Energy needed for the electron to move from one energy level to the next, correct?
 
G01
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What about when they ask for the energy of the photon that is emitted? The wavelength of the emitted/absorbed photon will always equal the Energy needed for the electron to move from one energy level to the next, correct?
The wavelength of an emitted/absorbed photon will be related to the energy decrease/increase of the electron that absorbed it by:

[tex]\Delta E=hc/\lambda[/tex]
 
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