Chem288_2005_PS4 - Spring 2005 Problem Set 4 Handed out...

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Spring 2005 Problem Set 4 Chemistry 288 – Marohn Handed out: Sunday, 20 February 2005 Due: Friday, 25 February 2005 1. Why do I spend my life isolating large amounts of protein? As we shall see later in the semester, nuclear magnetic resonance is the most informative type of spectroscopy, and one of the most powerful tools for determining the structure of proteins and other macromolecules. It is also, unfortunately, one of the least sensitive forms of spectroscopy. This is because the difference in the energy of spin up and spin down states is small compared to kT . The magnetic moment of a proton is μ m = γ ¯ hm (1) where m = 1 / 2 and 1 / 2 for the spin-up and spin-down state of the proton, respectively. In a magnetic field, the energy of the states is E m = μ m B (2) (a) Using Boltzmann statistics, write down an expression for the thermal-average magnetic moment, ( μ ) . (b) Derive an approximate answer for this expression for ( μ ) valid when γ ¯ hB << kT . Your answer should be of the form ( μ ) = c × B . Find the constant c . This is called the Curie law.
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