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