c120a_lecture29_s07 - Chem 120A Spin 04/04/07 Spring 2007...

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Unformatted text preview: Chem 120A Spin 04/04/07 Spring 2007 Lecture 29 READING: Ratner/Schatz Ch.8 Atkins/Friedman Ch. 7.1 - 7.7 1 What is spin? Elementary particles and composite particles carry an intrinsic angular momentum called spin. For our pur- poses, the most important particles are electrons and protons. They each contain a little angular momentum vector that can point up | > or down | > . The quantum mechanical spin state of an electron or proton is thus | > = c 1 | > + c 2 | > . Aside: There are many different binary notations for spin up and spin down. Some include: spin up vextendsingle vextendsingle )big vextendsingle vextendsingle )big spin down vextendsingle vextendsingle )big vextendsingle vextendsingle 1 )big The spin angular momentum is intrinsic and signals the presence of an intrinsic magnetic moment. Uhlen- beck and Goudsmit introduced the concept of spin in 1925 to explain the behavior of hydrogen atoms in a magnetic field. When they placed hydrogen in a magnetic field, they saw new transitions in the energy levels, which appeared as if each of orginal energy levels were being split into two new ones, one with slightly higher energy and one with slightly lower energy. (see Figure 5). This is now often referred to as the Zeeman effect or Zeeman splitting. Figure 1: The energy levels of Hydrogen split in the presence of a magnetic field ( B negationslash = 0) producing new electronic transitons. The extra energy levels can be explained if an electron has an intrinsic magnetic moment, vector , since a mag- netic moment in a magnetic field, vector B has an energy E = vector vector B . In the context of QM, new energy levels can Chem 120A, Spring 2007, Lecture 29 1 derive from vector being oriented parallel or anti-parallel to vector B . Classically, a magnetic moment vector comes from a loop of current Figure 2: A charge moving, q , moving at a velocity, vector v in a loop of radius, vector r , produces a magnetic moment, vector . The right-hand rule determines the direction of the magnetic moment The energy E = vector vector B comes from the Lorentz force F = vector I vector B of a current in a B-field. The lowest energy and thereby the place where the system wants to go, is obtained when the magnetic moment and B-field line up....
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This note was uploaded on 02/19/2010 for the course CHEM 120A taught by Professor Whaley during the Spring '07 term at University of California, Berkeley.

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c120a_lecture29_s07 - Chem 120A Spin 04/04/07 Spring 2007...

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