Question

1) a) Calculate the Fermi energy for gold at OK. The density of gold is 19.3 g/cm3, and the molar mass is 197 g/mol. b) The Fermi energy for other temperatures can be approximated as TE? ( kT EF(T)- EF(0) 1- . At what temperature would the Fermi energy of Au 12 E (0) be reduced by 1%? Compare this temperature with the melting point of Au (1337 K). Is it reasonable to assume the Fermi energy is a constant, independent of temperature? 1,011-

Answer 1

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197 > energy 0.99 = 1- 5.33 @ Election concentration N 19. 3 x(6.02 1023) v N 5. 9x 1022 elections/cm3 V N. 5.9x_1028 electrons/m3 V Fermi at o k is E Co) = h2 2/3 Ef Co) = (6.626 x 10-34)2 3_(5.9x1048) 2x (9.11 * 10-31) EF(0)= 8.85 x 10 J in ev Ef (o) 8.85 x 10-49 1-6 X 10 -19 Erro) = 5.53 eV b Given Erle 1-0.01 = 0.99 Erlo from Guiven equation => EF (1) -12 [KI 12 LEF (o) for (N)7% 2me 82 -19 2 1 Ef Co 2 [ 12 KT - W 0.01X12 T2 X 5.53 g KT = 0.61 eV -> T = 0.61 T= 1076 kl. 8.617x 10-5 = 5.3 T TM 7076 133 + Thanks

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