01-26-2008, 07:51 PM
Yes, h is Planck's constant.
Some helpful web pages I found via Google for the equations.
http://hyperphysics.phy-astr.gsu.edu/Hbase/debrog.html
http://en.wikipedia.org/wiki/Bohr_model
[quote Ted King]I thought s-orbitals were limited to one electron pair. But the details of that don't seem to effect the underlying logic of what you are saying.
Oh right. Sorry about that. Yes, s-orbitals have only a pair of electrons. It has been a long time since high-school AP chemistry. (In physics where I got my degree we rarely talked about s, p, d orbitals and the shell model.) The logic is the same for filling p-orbtials and the atom radius shrinking. I didn't want to touch them since it is easier conceptually to think of the spherical s-orbital.
[quote Ted King]
If you don't mind continuing to share your knowledge, does the greater energy of the electrons as their wavelength (and, hence, the radius of the atom) decreases have an effect on the emission and absorption spectra of atoms of elements across the period?
Yes the spectra will change. The spectra measure the differences between electron energy levels since the light emitted or absorbed corresponds to quantized photons as the electrons change positions among these available energy states. Since the energy states themselves go as the atomic number squared, the distance betwee the corresponding states on different atoms should change.
If I extend the formulas presented in the Wikipedia link above, I get that the energy difference (the photon energy) between the n_i (n sub initial) and n_f (n sub final) states is
E_photon = Z^2 * R_E * [ (1/n_f)^2 - (1/n_i)^2]
where Z is the number of protons and R_E is a constant (involving the mass of the electron, speed of light, and so on).
When comparing a transitional line between two different energy levels n_i=1 and n_f=2 for example, two different atoms will have different photon energies because of the Z^2 term. The spectral lines should therefore be different. Since all of the photon energies scale with Z^2, in this model the spectra between atoms will shift by a constant factor.
Note that quantum mechanics and quantum chemistry were not my areas of expertise.
Some helpful web pages I found via Google for the equations.
http://hyperphysics.phy-astr.gsu.edu/Hbase/debrog.html
http://en.wikipedia.org/wiki/Bohr_model
[quote Ted King]I thought s-orbitals were limited to one electron pair. But the details of that don't seem to effect the underlying logic of what you are saying.
Oh right. Sorry about that. Yes, s-orbitals have only a pair of electrons. It has been a long time since high-school AP chemistry. (In physics where I got my degree we rarely talked about s, p, d orbitals and the shell model.) The logic is the same for filling p-orbtials and the atom radius shrinking. I didn't want to touch them since it is easier conceptually to think of the spherical s-orbital.
[quote Ted King]
If you don't mind continuing to share your knowledge, does the greater energy of the electrons as their wavelength (and, hence, the radius of the atom) decreases have an effect on the emission and absorption spectra of atoms of elements across the period?
Yes the spectra will change. The spectra measure the differences between electron energy levels since the light emitted or absorbed corresponds to quantized photons as the electrons change positions among these available energy states. Since the energy states themselves go as the atomic number squared, the distance betwee the corresponding states on different atoms should change.
If I extend the formulas presented in the Wikipedia link above, I get that the energy difference (the photon energy) between the n_i (n sub initial) and n_f (n sub final) states is
E_photon = Z^2 * R_E * [ (1/n_f)^2 - (1/n_i)^2]
where Z is the number of protons and R_E is a constant (involving the mass of the electron, speed of light, and so on).
When comparing a transitional line between two different energy levels n_i=1 and n_f=2 for example, two different atoms will have different photon energies because of the Z^2 term. The spectral lines should therefore be different. Since all of the photon energies scale with Z^2, in this model the spectra between atoms will shift by a constant factor.
Note that quantum mechanics and quantum chemistry were not my areas of expertise.