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McQueen
#11
Dec3-05, 06:08 AM
P: 265
Quote Quote by Physicsmonkey
Your first question is answered by quantum theory. The "orbits" of the electron in Hydrogen are quantized. The only way an electron can change its energy is by jumping between levels and emitting light. Once the electron sits in the ground state of atom, the lowest energy state, it can't go down anymore because of quantum effects. For more complicated atoms, all the discrete states up to a certain energy are filled, and the atom is stable because of the Pauli exclusion principle which tells you that no two electrons can be in the same quantum state.
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.