Show that the chemical potential
*
m
*
*
*
(
*
T
*
)
of a free electron gas in two dimensions is given by
*
m
*
*
*
(
*
T
*
)
=
*
k
_{
B
}
T
*
ln [exp(

where
*
n
*
is the density of electrons per unit
area. In the limit that
*
T
*
= 0, show that
*
m
*
(0) gives the correct
*
E
_{
F
}
*
calculated in question 1(c).