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The attractive Coulomb force between the positive nucleus and the orbiting electron could provide the attractive force which keeps the electron in it’s orbit, much as the planets orbit the sun with gravity providing the centripetal force. 2 Fcentripetal me v0 me02 r r What’s wrong with this picture? Accelerating charges radiate. Could this electromagnetic radiation be the source of the spectral lines? No. This radiation must come at the expense of the kinetic energy of the orbiting electron! It will eventually spiral into the nucleus. The atom would be unstable! Lyman series : n2 (cm) C1 2 2 n 2, 3, 4... n 1 Balmer series : n2 (cm) C2 2 2 n 3, 4, 5... n 2 Paschen series : It also turns out that C1=C2=C3… n2 (cm) C4 2 2 n 4, 5, 6... n 3 But what does all of this mean?? •Classical electromagnetism does not hold for atom sized systems. •Used Planck’s energy quantization ideas to postulate that electrons orbit in fixed, stable, nonradiating states, given by mevr n n 1,2,3... •Used Einstein’s concept of a photon to define the frequency of radiation emitted when an electron jumps from one state to another. The photon energy is just the energy difference between states, i.e., E f Ei hv •Used classical mechanics to calculate the orbit of the electron. Coulomb force keeps electrons in orbit: F ma 2 2 mv e 2 r r 1 KE me v 2 2 e2 U k r But we know that the allowed values of the angular momentum are: mevr n mevr n (Are you wondering why these are the allowed values? You should be.) n v me r 2 ke2 ke2 ke2 E KE U 2r r 2r 1 ke KE me v 2 2 2r 1 n ke2 KE me 2 me r 2r 2 n2 2 rn me ke2 For n=1, this gives the “Bohr radius”: a0 n 1,2,3... 2 2 me ke 0.0529 nm which was in good agreement with experimental values. For other values of n: rn n 2 a0 ke2 1 En 2 n 1, 2, 3,... 2a0 n 13.6 En 2 eV n energy quantization therefore follows from angular momentum conservation. therefore the ionization energy is 13.6 eV. It takes 13.6 eV to liberate an electron in the ground state. At n=infinity, it is removed. This also agreed with experiment. Independent of the orbital angular momentum of the electron, the frequency of a photon emitted is: E f Ei hv Ei E f h ke2 1 1 2a0 h n 2f ni2 ke2 1 1 2 2 c 2a0 hc n f ni 1 1 1 R 2 2 n f ni 1 1. The laser in its nonlasing state 2. The flash tube fires and injects light into the ruby rod. The light excites atoms in the ruby. 4. Some of these photons run in a direction parallel to the ruby's axis, so they bounce back and forth off the mirrors. As they pass through the crystal, they stimulate emission in other atoms. 3. Some of these atoms emit photons. 5. Monochromatic, single-phase, collimated light leaves the ruby through the half-silvered mirror -- laser light! Note that the difference in energies of allowed orbits becomes smaller as n becomes larger. In the limit of large quantum numbers, the frequencies and the intensities of radiation calculated from classical theory must agree with quantum theory. At the beginning of class, I said that Bohr was mostly right…so where did he go wrong? • Failed to account for why some spectral lines are stronger than others. (To determine transition probabilities, you need QUANTUM MECHANICS!) Auugh! • Treats an electron like a miniature planet…but is an electron a particle…or a wave?