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120A_PS6 - Chemistry 120A Problem Set 6(due 1 Problems 6-43...

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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 textbook’s 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, μ 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 ˆ z , is E mag = - μ 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 . With this formula in mind, you will consider the Hamiltonian for a hydrogen atom perturbed by an electric field and use first order degenerate
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