Question

B3 (a) Assume that the T = 0 version of the Fermi-Dirac distribution, namely 1 f (E) exp [E E)/(kBT) +1 in the usual notation, with Ep the Fermi energy, applies for T> 0. Sketch, on the same axes, the distribution for T = 0 and for T> 0, marking the Fermi energy and indicating the thermal energy kBT 5 Marks (b) In the Sommerfeld model (free electron quantum gas), each electron occupies (n/L)3 of k-space volume. Remembering that we must count only positive k-states (i.e. ki >0; ky0; k0), show that the density of k-states is g(k) = k2/72 6 Marks (c) The density of energy states g(E) in the Sommerfeld model is 2m$/2 VE 2h3 g(E)= Give an expression for and sketch the density of occupied states at T 0 and at [4 Marks T0 (d)Consider a cube of metal with sides of length L which forms lattice constant a. Assume that there is one atom per lattice site and that each atom simple cubic lattice with a contributes one electron to the free electron Fermi gas. Use the free electron model to find the radius of the Fermi sphere and the Fermi energy 5 Marks

Answer 1

Fermi- Dirac Dignbuhin funcHeh FCE, T) / + (e-u) KT flE T) IKG &T O FCGT) O'k MRet 2p

No-y entrみ とe ト→4> p- tk 『734マル K2 dk オ2 V g/K)= 1 epo 2mF E : 2 4A p(ab E2 de 3ん 2te-de 2. オ 243 (31P JE T-o'k - T> o'k E fermi-radin YF= Fermi - en ry 2 37 m m 13
note,fermi energy is equivalent to mu on page first.thank you