exam1-2009 - Name _________________________ Exam 1, 2009:...

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Unformatted text preview: Name _________________________ Exam 1, 2009: CHEM/BCMB 4190/6190/8189 1 Exam 1: CHEM/BCMB 4190/6190/8189 (121 points) Thursday, 10 September, 2009 1 ). At thermal equilibrium, the microscopic view of an ensemble of spins in a magnetic field can be illustrated by individual magnetic dipoles precessing about the axis corresponding to the magnetic field ( B ) direction ( z axis), as shown in the figure (panel A). a. In panel B in the figure, what is “ M ” meant to represent. How does it relate to (or arise from) the microscopic view shown in panel A. ( 4 points ) M represents the macroscopic or bulk or net magnetization of the nuclear ensemble. It is simply the sum of the individual magnetic dipoles (i.e. in panel A) of the ensemble. b. In panel B, “ M ” is drawn as a vector, with a direction and magnitude. Please explain the direction of the vector. You should include in your explanation why the orientation is along + z and why there are no net x or y components. ( 4 points ) Microscopically (panel A), at thermal equilibrium, there are more nuclear dipoles aligned with the main ( B ) magnetic field (along +z, ¡ states) than against the field (along –z, ¢ states) because those aligned with the field are lower in energy. Thus, there is a net excess of these ¡ states. When the individual dipoles (vectors) are summed to get M , the net result is a vector pointed along the +z axis. There is no net x or y component because, at thermal equilibrium, the individual dipoles of the ensemble are uniformly distributed about the z axis. c. In panel B, “ M ” is drawn as a vector, with a direction and magnitude. Please explain the magnitude of the vector. Please include in your explanation how the magnitude is established from a microscopic perspective and all contributions to it. ( 6 points ) The magnitude of M depends on the numbers of nuclear dipoles aligned with the main ( B ) magnetic field (along +z, ¡ states) and the numbers of nuclear dipoles aligned against the field (along –z, ¢ states), because the vector M is just a sum of these dipole vectors. These numbers depend on the total number of nuclei in the ensemble (N), the gyromagnetic ratio of the nucleus ( £ ), the strength of the main ( B ) magnetic field, the temperature (T), the spin quantum number (I) and other constants as described in the equation below: A B M = N ¡ 2 ¡ 2 B I(I +1) 3k B T Name _________________________ Exam 1, 2009: CHEM/BCMB 4190/6190/8189 2 2 ). At thermal equilibrium, the microscopic view of an ensemble of spins in a magnetic field can be illustrated by individual magnetic dipoles precessing about the axis corresponding to the magnetic field ( B ) direction ( z axis), as shown in the figure (panel A)....
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This note was uploaded on 11/13/2011 for the course CHEM 4190 taught by Professor Staff during the Fall '08 term at University of Georgia Athens.

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exam1-2009 - Name _________________________ Exam 1, 2009:...

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