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ZapperZ
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#12
Dec3-05, 07:23 AM
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Quote Quote by McQueen
Bohr’s theory ( or the old quantum theory as it is now called ) suffered from internal contradictions : in order to determine the radius of the orbit , it was necessary to make use of relations of different kinds- the classical relation
[tex] m\frac {e^2}{r^2_n}[/tex] and the quantum relation
[tex]mv_nr_n=n\hbar[/tex] . The Heisenberg Uncertainty relation
[tex] \Delta\p_x\Delta\x \geq \hbar[/tex] illustrates why the electron does not spiral into the nucleus. If the electron is localized at a definite point x , then its momentum will have an arbitrarily large uncertainty. If on the contrary the electron is in a state with a definite value of [tex]{p_x}[/tex] then it cannot be localized exactly. This also illustrates the fact that the electron is not one of the constituents of the nucleus. What strikes me however is that no-one has yet referred to the virtual transitions of electrons from orbit to orbit through the process of self interaction (i.e the absorption and emission ) of virtual photons. This is the result of another Heisenberg Uncertainty relation which can be stated as
[tex] \Delta{E}\Delta{t}\geq\hbar[/tex]. Thus an electron can move from [tex]E_1\longrightarrow{E_2}\longrightarrow{E_1}[/tex] if it satisfies the relation :
[tex]\frac{\hbar}{\Delta}{t}\geq ({E_2}{-} {E_1})[/tex]. This theory of virtual transitions through the absorption and emission of virtual photons is a continuous process.The statement that the electron occupies level [tex]E_1[/tex] should be understood specifically as incessant transitions from the original state to others with an inevitable return every time to the starting level. Virtual transitions don’t require an expenditure of energy. It is only when the electron absorbs a real photon that an actual transition is considered to have been made.
I'm not sure why you are addressing PM's comment using the outdated Bohr's model. Why aren't you using the standard QM approach that we teach to every physics undergraduate students? Is there something wrong with that?

Secondly, I don't need to cause a "real" transition only when "electron absorbs a real photon". I can bombard an atom with electrons and cause such an excitation. Your fluorescent light bulb works this way. What this means is that how you excite an atom is irrelevant. If you can sneeze at it to cause a transition, then that works too. I also don't think you should be using "virtual transition" as an explanation for this, especially since you are still using the Bohr model. Keep in mind the rules against over speculative posting.

Zz.