HW#2_594I

HW#2_594I - ECE594I, Prof. Brown, Fall Quarter 2009...

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ECE594I, Prof. Brown, Fall Quarter 2009 1 Homework Problems #2: THz Propagation Phenomenology 1. Vapor State: Molecular Rotational Transitions. Along with water, the Earth’s atmosphere can hold many trace molecules of interest for global warming, and homeland security, many of which have measurable resonances in the THz or millimeter-wave regions. (a) A molecule of interest for the “greenhouse effect” and global warming is nitrous oxide, N 2 O. Using the rigid rotor model to estimate the resonance frequencies between 100 GHz and 1.0 THz (b) A molecule of interest for homeland security is phosgene, COCl 2 which is a planar molecule having the structure shown in the figure below. It can be shown for any four- atom planar molecule that the moment of inertia about the axis perpendicular to the plane is given by 4 3 2 1 2 34 4 3 2 24 4 2 2 23 3 2 2 14 4 1 2 13 3 1 2 12 2 1 m m m m d m m d m m d m m d m m d m m d m m I + + + + + + + + = where d ij is the distance between the i and j atoms. Use this to predict the lowest rotational
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HW#2_594I - ECE594I, Prof. Brown, Fall Quarter 2009...

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