120A_PS6 - Chemistry 120A Problem Set 6 (due March 17,...

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Unformatted text preview: Chemistry 120A Problem Set 6 (due March 17, 2010) 1. Problems 6-43, 6-44 and 6-45 in McQuarrie and Simon. These problems lead you through the textbooks treatment of orbital magnetization in the hydrogen atom. You might find them helpful as background for Problem 2 below. 2. The orbital motion of the electron in a hydrogen atom produces a magnetic moment in the z-direction, z =- ( e/ 2 m e c ) L z , where- e and m e are, respectively, the charge and mass of an electron, c is the speed of light, and L z is the differential operator giving the z-component of the angular momentum. The energy of a magnetic moment in a static magnetic field, ~ B = B z , is E mag =- z B . Use first order perturbation theory for the energy and calculate the expectation values for the energy when the hydrogen atom is in the states ( n,,m )=(2,1,1), (2,1,0), and (2,1,-1). Compare your results with the magnetic energies discussed in lecture. 3. The instantaneous dipole moment of a hydrogen atom is ~ =- e~ r , where ~ r is the position of the electron relative to that of the nucleus. The energy of a dipole in an electric field, ~ E , is E elec =- ~ ~ E ....
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This note was uploaded on 03/17/2010 for the course CHEM ?? taught by Professor Davidchandler during the Spring '10 term at University of California, Berkeley.

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120A_PS6 - Chemistry 120A Problem Set 6 (due March 17,...

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