p42_015 - f equal 0 . 01, we evaluate the expression for T...

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15. The Fermi-Dirac occupation probability is given by P FD =1 / ( e E/kT +1 ) , and the Boltzmann occu- pation probability is given by P B = e E/kT .Le t f be the fractional di±erence. Then f = P B P FD P B = e E/kT 1 e E/kT +1 e E/kT . Using a common denominator and a little algebra yields f = e E/kT e E/kT +1 . The solution for e E/kT is e E/kT = f 1 f . We take the natural logarithm of both sides and solve for T . The result is T = E k ln ³ f 1 f ´ .
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Unformatted text preview: f equal 0 . 01, we evaluate the expression for T : T = (1 . 00 eV)(1 . 60 10 19 J / eV) (1 . 38 10 23 J / K) ln . 010 1 . 010 = 2 . 5 10 3 K . (b) We set f equal to 0 . 10 and evaluate the expression for T : T = (1 . 00 eV)(1 . 60 10 19 J / eV) (1 . 38 10 23 J / K) ln . 10 1 . 10 = 5 . 3 10 3 K ....
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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