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# LectureQ8 - H133 Spring 2004 1 Chapter 8 Spectra • In...

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Unformatted text preview: 4/20/2004 H133 Spring 2004 1 Chapter 8: Spectra • In this Chapter we want to study the phenomena of atomic spectra. There are several topics that we will cover: Spontaneous Emission of Photons. Spectral Lines Absorption Lines Physics of spin • Some of these topics we being studies experimentally before, during, (and after) the development of quantum mechanics. These phenomena are difficult to explain with classical physics and were part of the body of evidence that pointed the way toward quantum mechanics. Special Note: Professor Heinz will be lecturing on this chapter. He may not necessarily follow these notes. I provide them for completeness. 4/20/2004 H133 Spring 2004 2 Energy-Level Diagrams • When considering spectral lines (and absorption lines) it is use to have a picture of the energy levels of the atom or bound system that you are considering. • These are very simple diagrams but they contain useful information. We depict them as a two-dimensional diagram • The vertical axis is the energy. We place a horizontal line at each energy-level of our bound system. The horizontal direction has no meaning. • Let’s make energy diagrams for the three bound systems that we have looked at in the last chapter • (1) Electon in a Box Let’s take L=0.50 nm We saw in the last chapter the energy levels are: E 3 E 2 E 1 E E 1 = 1.5 eV ( ) eV 5 . 1 nm) 5 . ( )c eV/c 000 , 511 ( 8 nm)- eV 1240 ( 8 8 1,2,3,.... n 8 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 = = = = = = = = L mc hc mL h E E n mL h n E n E 2 = 6.0 eV E 3 = 13.5 eV 4/20/2004 H133 Spring 2004 3 Energy Level Diagrams • (2) Simple harmonic Oscillator: Take ω such that In the last chapter we saw that the energy levels for a simple harmonic oscillator is • (3) Bohr’s Model of hydrogen Remember, one of the things the Bohr model did reasonable well was predict the energy levels of H. These levels are: eV . 4 = ω 4/20/2004 H133 Spring 2004 4 Spontaneous Emission • There is an interesting phenomena that this called “spontaneous emission”. Photon emitted from an atom as an electron makes a transition from one energy-level to another. • Recall what we said in the last chapter If the quanta has a definite energy value it must be in a state which is an energy eigenvector. Energy Eigenvectors do not change with time This was a consequence of the time-evolution rule • The electric field of an electron can be thought of as the electric field due to a charge density which is given by the wave function. A static charge density cannot radiate EM waves (photons)…and thus lose energy. • These points seem to indicate that an electron at one energy-level should not spontaneously make a transition to a lower energy-level What’s going on?...
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LectureQ8 - H133 Spring 2004 1 Chapter 8 Spectra • In...

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