Problemsamling

5. The value of the electron contribution Cel = γT to the heat capacity and
the lattice constant for the three alkali metals Na, K and Rb is given
below.
Na K Rb
γ [J/kmol K 2 ] 1.38 2.08 2.41
a [Å] 4.225 5.225 5.585
With the aid of a suitable diagram, calculate the effective
thermal mass of the three metals.
6. Consider a two-dimensional free electron gas with a density N/A in a
quadratic lattice with lattice constant a. Derive an expression for the density
of states.
7. An aluminium wire is 0.5 m long and has a cross sectional surface area of
1.00 mm 2 . A voltage of 13.5 mV is required to drive a current of 1.0 A
between the ends of the wire. Determine the relaxation time using the free
electron model and the average mean free path for the electrons in
aluminium, as well as their drift velocity in this case. Aluminium is a
trivalent metal.
8. What is the separation between neighbouring levels at the Fermi surface
for (a) 10 cm 3 , (b) 10 µm 3 and (c) 100 Å 3 of Al particles in the free electron
model?
9. Let an imaginary two dimensional metal crystallise in a simple quadratic
lattice and assume that the free electron model is applicable.
(a) Show that the kinetic energy of the electron is twice the size when
it lies at the corner of the first Brillouin zone as it is when in the
middle of the zone boundary.
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