# Lecture 18 - Magnetic Behavior of an Ideal Fermi Gas Pauli...

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Magnetic Behavior of an Ideal Fermi Gas Pauli Paramagnetism; Alkali metals Pauli 1927 T=0 * magnetic moment B magnetic field (1) * * ( ) (2) * * ( ) | total energy B KE B Parallel B KE B Anti parallel  N = # of electrons in group 1; * KE B   N = # of electrons in group 2; * KE B Spin degeneracy is lifted by magnetic field 3/2 1/2 1/2 0 3 | | 2 ( ) (2 ) no here s V a d m C h g  Magnetic moment *( ) M N N  0 0 ( * ) ( ) ( * ) ( ) FD FD N a B f d N a B f d At T=0 1/2 0 0 3/2 0 ( * ) 1 2 ( * ) 3 F F N C B d CB   B is small so * B the lower limit 0 after a change of variable Similarly 3/2 0 2 ( * ) 3 F N C B 3/2 3/2 3/2 3/2 3/2 3 3/2 3 ) 4 *(2 ) * * 11 3 4 *(2 ) 3 * 3 * 1 1 If B is small 22 3 FF F M N N V m B B h Vm BB h        

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2 3/2 1/2 3 0 2 1 4 lim * (2 ) * 3 F F B MV m B h N   In contrast to classical Langein paramagnetism where 1 ~ (Curie's law) T At low temp 0  constant Pauli Paramagnetism Physical Picture: Langevin result: (Probability that an atom parallel to the magnetic field Probability that it is antiparallel). 11 (if it is small) HH e e H H ee H      For N atoms this gives a net magnetic moment 22 ~ / ~ / N H N H kT N kT    But now at a temp F TT  only ex N of the electrons contribute. This means 2 2 33 ~ ~ / ex F F TH M N H N N H kT T kT  independent of temperature
Fermi Gas : Degenerate Case (Detailed Calculation)             1/2 3/2 3 / 0 3/2 3/2 3 / 0 0 2 2 1 2 2 1 F F F s kT C s kT C T T kT Vd N g m T h e U T g m h e    

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## This note was uploaded on 09/28/2011 for the course PHYSICS 971 taught by Professor Chakabarti during the Spring '10 term at Kansas State University.

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Lecture 18 - Magnetic Behavior of an Ideal Fermi Gas Pauli...

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