On Fri, Mar 30, 2012 at 1:08 AM, <[email protected]> wrote: > In reply to Xavier Luminous's message of Thu, 29 Mar 2012 23:56:53 +0200: > Hi, > [snip] >>On Thu, Mar 29, 2012 at 10:22 PM, <[email protected]> wrote: >>> In reply to Xavier Luminous's message of Thu, 29 Mar 2012 16:28:25 +0200: >>> Hi, >>> [snip] >>>>This Bohr model picture of the atom is incorrect. Electrons do not >>>>orbit the nucleus of an atom, so there's no centrifugal force >>>>component (though they are bound via quantum mechanical principles). >>>> >>>>-X >>> Prove that the Bohr model is not a special solution to the Schrödinger >>> equation. >> >>Here's an example for starters. An electron has a charge, and an >>accelerating charge will emit a photon. If an object travels in a >>circular path, it is accelerating. If the Bohr model was correct, the >>electrons would emit a burst of photons as they orbited, losing energy >>and quickly crashing into the nucleus. But of course this doesn't >>happen, which is one reason why the Bohr model is incorrect and you >>can't say that electrons orbit an atom. > > The reason this doesn't happen is not because the Bohr model is impossible. > The > reason is that a smaller orbit than the "ground state" would require a change > in > angular momentum of the electron that is less than the angular momentum of a > photon, hence a photon can't be formed to carry away the difference in angular > momentum that shrinkage below the ground state would require. Which in turn > neatly explains why photon emission stops upon achieving the ground state.
The picture that electrons orbit an atom makes no sense whatsoever. Your description works for simple atoms, but fails to account for may effects. Here's a good list from Wikipedia of things the Bohr model has problems with: - Much of the spectra of larger atoms. At best, it can make predictions about the K-alpha and some L-alpha X-ray emission spectra for larger atoms, if two additional ad hoc assumptions are made (see Moseley's law above). Emission spectra for atoms with a single outer-shell electron (atoms in the lithium group) can also be approximately predicted. Also, if the empiric electron-nuclear screening factors for many atoms are known, many other spectral lines can be deduced from the information, in similar atoms of differing elements, via the Ritz-Rydberg combination principles (see Rydberg formula). All these techniques essentially make use of Bohr's Newtonian energy-potential picture of the atom. - The relative intensities of spectral lines; although in some simple cases, Bohr's formula or modifications of it, was able to provide reasonable estimates (for example, calculations by Kramers for the Stark effect). - The existence of fine structure and hyperfine structure in spectral lines, which are known to be due to a variety of relativistic and subtle effects, as well as complications from electron spin. - The Zeeman effect - changes in spectral lines due to external magnetic fields; these are also due to more complicated quantum principles interacting with electron spin and orbital magnetic fields. - The model also violates the uncertainty principle in that it considers electrons to have known orbits and definite radius, two things which can not be directly known at once. - Doublets and Triplets: Appear in the spectra of some atoms: Very close pairs of lines. Bohr’s model cannot say why some energy levels should be very close together. - Multi-electron Atoms: don’t have energy levels predicted by the model. It doesn’t work for (neutral) helium. (Off the top of my head this doesn't explain the exclusion principle either.) In short, quantum mechanics makes up for all the shortcomings of this description and we should really abandon thinking of atoms as electrons orbiting a nucleus. > In short this argument doesn't constitute the requested proof. Hopefully the above list is sufficient. If you'd like me to elaborate on any one of them, and their experimental confirmations I'd be glad to. If you're interested you should check out an intro to quantum book like Griffiths... it explains this stuff in really easy to understand language. >> >>The other easy thing is that the Bohr model doesn't predict the >>electron cloud density: p- and s-orbitals, etc. > > Note that I didn't say that the Bohr model was "the" solution. I only > requested > that you show that it couldn't be a *particular* solution. IOW I'm asking that > you show that it can *never* happen. You're correct that the Bohr model can be a particular solution to explain some atomic features. My problem with it is that it makes you think of electrons as classical particles instead of quantum mechanical objects. This thinking, IMHO, should be eliminated. > BTW exactly how is electron cloud density measured? (IOW how do you know that > QM > predictions thereof are correct?) You take pictures! Here are two, hopefully they're not paywalled. http://www.chymist.com/Imaging%20atomic%20orbitals.pdf http://arxiv.org/pdf/cond-mat/0107195 A little bird told me while writing this that you can look at the diffraction of ultrashort pulses and reconstruct other orbitals, but I didn't look for a paper. >>Again, electrons don't orbit an atom. > > (Usually) EVER! :) -X > [snip] > Regards, > > Robin van Spaandonk > > http://rvanspaa.freehostia.com/project.html >
