ch41-p030 - 30. The probability that a state with energy E...

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30. The probability that a state with energy E is occupied at temperature T is given by PE e EE k T F () / = + 1 1 where k is the Boltzmann constant and 23 4 2 2/3 28 3 2/3 19 31 0.121 0.121(6.626 10 J s) (1.70 10 m ) 3.855 10 J 9.11 10 kg F e h En m −− ×⋅ == × = × × is the Fermi energy. Now, 19 19 20 4.00 10 J 3.855 10 J 1.45 10 J F EE −= × × = × and 20 23 1.45 10 J 5.2536 (1.38 10 J / K)(200K) F kT × × , so 3 5.2536 1 ( ) 5.20 10 . 1 e × + Next, for the density of states associated with the conduction electrons of a metal, Eq. 41- 5 gives ( ) 3/2 31 3/2 1/2 19 33 4 3 56 3/2 3 3 19 46 3 8 2 8 2 (9.109 10 kg) ( ) 4.00 10 J (6.626 10 J s) 1.062 10 kg / J s 4.00 10 J 6.717 10 / m J m NE E h ππ × × × where we have used 1 kg =1 J·s
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This note was uploaded on 05/19/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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