## Question

###### (14 points) For a certain metal with a face center cubic (FCC) structure, we know its...

(14 points) For a certain metal with a face center cubic (FCC) structure, we know its energy dispersion is E(k) = Ak? +C where A = 7 x 10-39)m² and C = 5.5 x 10-20). We also know that it has energies up to ka = (2472)1/3 filled with electrons where a is the lattice parameter. (a) (5 pt) Find the electron effective mass m* in terms of free electron mass me for electrons in the solid Ans. (1) 1.2 m 0.2 me (iii) 0.87 m. (iv) 0.55 m. 0.07 m. b) 5 pt) Find the number of conduction electrons per atom Z Ans. (1) 1 (ii) 0.5 (iii) 3 (iv) 2 none (©) (4 pt) Calculate the Fermi energy of this solid assuming the lattice parameter a=64 Ans. (1) 1.2 eV (ii) 8.75 eV (iii) 15.75 eV (iv) 0.5 eV 4.99 eV

## Answers

a The given R E(k)= = Ak te o t ? E Effective mass (mt) = Elak? () from equation D, ə - ә a caktc) ak = ZAK e ZE ? (2AK) = 2A (11 ək ӘкSo, Effective mass (mx) == /2A (1.05 x1o34) 20:5)? -39 247xto ima or m² 2x7x10 39 J m2 - 68+39 R Ò. 787 X10 JS/m2 - Box -31 = 0.787x16x9.1X10 Kg 9. XI0 31 mx =0.87 me obtim (iii) is correct. © Fermi energy Ef= ħ 2k2le 2n 2 213 en (1:05x1839) x (2402) 2X0.87X9-1X173T (6X1olo) X1.6x1019 4.59 er Ef ~ 4.99 ev obtion is corre &

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