Chapter 10: Energy Bands in Solids

Example 10.1, Page 323

In [1]:
from math import log

#Variable declaration
#E=Ef+1% of Ef
k=1.38*1e-23;#boltzman constant
e=1.6*1e-19;#charge of electron
E=0.0555;

#calculations
#0.1=1/[(exp((E*e)/(k*T)))+1]
T=(E*e)/(k*log(9));#Temprature

#Result
print 'Temprature = %.f K'%T
#Incorrect answer in the textbook

Temprature = 293 K

Example 10.2, Page 324

In [2]:
from math import exp

#Variable declaration
sx=0.01 #in ev. where x=E-Ef
x1=sx*1.6*1e-19 #converting it in joule
T=200 #in kelvin

#calculation
Fe=1/(1+exp(x1/(1.38*1e-23*T)));#The value of F(E) 

#Result
print 'The value of F(E) = %.2f'%Fe

The value of F(E) = 0.36

Example 10.3, Page 327

In [3]:
#Variable declaration
density=7.13*1e3  #in kg/m^3
M=65.4
N=6.023*1e26 #avogedro number

#Calculations
n=(2*density*N)/M
n1=n**(2./3);
Ef=3.65*1e-19*n1; #in eV
Ef1=(3./5)*Ef #in eV

#Results
print 'fermi energy = %.1f eV'%Ef
print 'Mean energy at T=0K is %.f eV'%Ef1
#Incorrect answers in the textbook

fermi energy = 9.4 eV
Mean energy at T=0K is 6 eV

Example 10.4, Page 328

In [4]:
#Variable declaration
Ef=5.51 #in eV

#calculation
E=(3./5)*Ef;#The average energy of a free electron in silver at 0k

#Result
print 'The average energy of a free electron in silver at 0k = %.3f eV'%E

The average energy of a free electron in silver at 0k = 3.306 eV