8: Statistical physics

Example number 8.2, Page number 164

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
rho=10.5;    #density of silver(g/cc)
M=108;    #atomic weight(g/mole)
NA=6.02*10**23;   #avagadro number(atoms/mole)
h=6.626*10**-34;    #planck's constant(Js)
m=9.1*10**-31;    #mass of electron(kg)
e=1.6*10**-19;   #conversion factor from J to eV

#Calculation
NbyV=rho*NA/M;    #number density of conduction electrons(per cc)
NbyV=NbyV*10**6;   #number density of conduction electrons(per m**3)
EF=(h**2/(8*m))*(3*NbyV/math.pi)**(2/3);   #fermi energy(J)
EF=EF/e;   #fermi energy(eV)
E=3*EF/5;    #mean energy of electron(eV)

#Result
print "number density of conduction electrons is",round(NbyV/10**28,2),"*10**28 per m**3"
print "fermi energy is",round(EF,2),"eV"
print "mean energy of electron is",round(E,2),"eV"

number density of conduction electrons is 5.85 *10**28 per m**3
fermi energy is 5.51 eV
mean energy of electron is 3.31 eV

Example number 8.3, Page number 164

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
T=300;    #temperature(K)
k=1.38*10**-23;   #boltzmann constant(J/K)
EF=5.49;    #fermi energy(eV)
e=1.6*10**-19;   #conversion factor from J to eV
R=1;   #assume

#Calculation
CV=math.pi**2*k*T*R/(2*EF*e);    #electronic contribution of Silver(R)

#Result
print "electronic contribution of Silver is",round(CV,5),"R"

electronic contribution of Silver is 0.02326 R