Chapter 7: Elecron theory of Solids

Example 7.1, page no-160

In [4]:
# Mobility ofelectrons

import math
#variable declaration
rho=1.73*10**-8                      # Resistivity of copper
z=63.5                               # atomic weight of copper
d=8.92*10**3                         # density of copper
avg=6.023*10**26                     # Avogadro's number
e=1.6*10**-19                        # charge of an electron
m=9.11*10**-31                       # mass of an electron

#variable declaration
n=avg*d/z
sig=1/rho
tau=sig*m/(n*e**2)
mu=sig/(n*e)

#Result
print("Mobility of electrons in copper is %.2f *10^-3 m^2/V-s"%(mu*10**3))

Mobility of electrons in copper is 4.27 *10^-3 m^2/V-s

Example 7.2, page no-161

In [23]:
# Resistivity of copper

import math
#variable declaration
r=1.85*10**-10                      # radius of the sodium atom
t=3*10**-14                         # mean free time of sodium atom
m=9.11*10**-31                      # mass of electron
e=1.6*10**-19                       # charge of an atom
n= 2.0                              # No of atoms per unit cell

#calculations
a=r*(4.0/math.sqrt(3.0))  
a= math.floor(a*10**12)/10**12       
ne=n/a**3
ne= math.ceil(ne*10**-26)/10**-26
rho=m/(ne*t*e**2)

#Result
print("Resistivity of copper is %.3f*10^-8 Ohm-m"%(rho*10**8))

Resistivity of copper is 4.616*10^-8 Ohm-m

Example 7.3, page no-161

In [25]:
# Electrical resistivity of sodium

import math
#variable declaration
t=3.1*10**14                       # mean free time of electron
m=9.11*10**-31                     # mass of an electron
e=1.6*10**-19                      # charge of an electron 
n=25.33*10**27                     # no of electrons per unit volume

#calculations
rho=m/(n*t*e**2)

#Result
print("The electric resistivity of sodium at 0°C is %.3f*10^-36 Ohm-m"%(rho*10**36))

The electric resistivity of sodium at 0°C is 4.532*10^-36 Ohm-m

Example 7.4, page no-162

In [27]:
# mobility of the electron

import math
#variable declaration
t=3.4*10**-14                     # relaxation time of conduction electrons
m=9.11*10**-31                    # mass of electron
e=1.6*10**-19                     # charge of electron
n=5.8*10**28                      # no of force electrons per unit volume

#calculations
rho=m/(n*t*e**2)
print("\nThe electric resistivity of material is %.3f*10^-8 Ohm-m"%(rho*10**8))
mu=e*t/m
print("\nThe mobility of the electron in a metal is %.2f*10^-3 m^2/v-s"%(mu*10**3))

The electric resistivity of material is 1.805*10^-8 Ohm-m

The mobility of the electron in a metal is 5.97*10^-3 m^2/v-s

Example 7.5, page no-163

In [28]:
# drift velocity

import math
#variable declaration
rho=1.54*10**-8                   # resistivity of silver
E=100                             # electric field along the wire
n=5.8*10**28                      # carrier concentration of electron
e=1.6*10**-19                     # charge on electron

#calculation
mu=1/(rho*n*e)
vd=mu*E

#Result
print("\nMobility of electron in silvetr is %.4f*10^-3 m^2/v-s\n\nThe drift velocity of the electron in silver is %.5f m/s "%(mu*10**3,vd))

Mobility of electron in silvetr is 6.9973*10^-3 m^2/v-s

The drift velocity of the electron in silver is 0.69973 m/s

Example 7.6, page no-163

In [32]:
# mobility ofelectron

import math
#variable declaration
d=10.5*10**3                      # density of silver
sig=6.8*10**7                     # conductivity of silver
wt=107.9                          # atomic weight of silver
e=1.609*10**-19                   # charge of electron
avg=6.023*10**26                  # avogadro's number

#calculations
n=avg*d/wt
mu=sig/(n*e)

#Result
print("The mobility of electron is %.2f *10^-2 m^2.V/s"%(mu*10**2))

The mobility of electron is 0.72 *10^-2 m^2.V/s

Example 7.7, page no-164

In [33]:
#Lorentz number

import math
#variable declaration
sig=5.87*10**7                    # electrical conductivity of  copper
k=390.0                           # thermal conductivity of copper
T=293.0                           # temperature

#calculation
L=k/(sig*T)

#Result
print("The Lorentz number is %.3f *10^-8 W.Ohm/K^2"%(L*10**8))

The Lorentz number is 2.268 *10^-8 W.Ohm/K^2

Example 7.8, page no-164

In [36]:
#Lorentz number
import math

#variable declaration
t=1*10**-14                        # relaxation time
T=300                              # temperature
m=9.1*10**-31                      # mass of electron
e=1.6*10**-19                      # charge of electron
n=6*10**28                         # electron concentration

#calculations
sig=(n*t*e**2)/m
k=1.38*10**-23
k1=n*math.pi**2*k**2*T*t/(3*m)
L=k1/(sig*T)

#Result
print("\nThe electrical conductivity is %.4f * 10^7/ohm-m"%(sig*10**-7))
print("\n\nThermal conductivity is %.2f W/m-k"%k1)
print("\n\nThe Lorentz number is %.4f *10^-8 W.Ohm/k^2"%(L*10**8))

The electrical conductivity is 1.6879 * 10^7/ohm-m


Thermal conductivity is 123.93 W/m-k


The Lorentz number is 2.4474 *10^-8 W.Ohm/k^2

Example 7.9, page no-165

In [38]:
# Electrical conductivity

import math

#variable declaration
d=8900                            # Density of copper
cu=63.5                           # Atomic weight of Cu
t=10**-14                         # Relaxation time
avg=6.022*10**23                  # Avogadro's number
m=9.1*10**-31                     # mass of electron
e=1.6*10**-19                     # charge of electron

#Calculations
n=avg*d*1000/cu
sig=(n*t*e**2)/m
print("The electrical conductivity is %.3f *10^7 /Ohm-m"%(sig*10**-7))

The electrical conductivity is 2.374 *10^7 /Ohm-m

Example 7.10, page no-166

In [51]:
# Drift velocity of electrons
import math

#variable declaration
rho=1.6*10**-8                     # resistivity of the silver piece
e=1.603*10**-19                    # charge of an electron
fe=5.5*e                           # energy of the silver
avg=6.023*10**23                   # avogadro's number
d=1.05*10**4                       # density of silver
wt=107.9*10**-3                    # atomic weight of silver
m=9.1*10**-31                      # mass of electron
c=3*10**8                          # speed of light

#calculations
sig=1/rho
n=avg*d/wt
t=sig*m/(n*e**2)
lam=c*t
vd=sig*100/(n*e)

#Result
print("\nThe conductivity of silver piece is %.2f*10^7 per Ohm-m\n\nThe relaxation time is %.2f*10^-14 s"%(sig*10**-7,t*10**14))
print("\nThe drift velocity of electrons in the silver piece is %.2f m/s"%(math.floor(vd*100)/100))

The conductivity of silver piece is 6.25*10^7 per Ohm-m

The relaxation time is 3.78*10^-14 s

The drift velocity of electrons in the silver piece is 0.66 m/s

Example 7.11, page no-167

In [52]:
# resistivityy of the copper

import math
#variable declaration
r1=1.7*10**-8                    # resistivity of copper at T1
t2=300.0                         # temperature(T1)
t1=700.0+273                     # temperature(T2)

#calculation
r2=r1*math.sqrt((t1/t2))
print("The resistivityy of the copper wire is %.4f*10^-8 Ohm-m"%(r2*10**8))

The resistivityy of the copper wire is 3.0616*10^-8 Ohm-m

Example 7.12, page no-168

In [55]:
# Relaxation time, Drift velocity, Fermi velocity, mean free path

import math
#variable declarations
rho=1.54*10**-8                      # Resistivity 
e=1.6*10**-19                        # charge of electron
ef=5.5*e                             # Fermi energy
n=5.8*10**28                         # concentration of electrons
m=9.1*10**-31                        # mass of electron 

#(i)
t=m/(rho*n*e**2)
mu=e*t/m
print("\n(i)\nThe relaxation time is %.2f*10^-14 s\nThe mobility of the electrons is %.4f *10^-3 m^2/V-s"%(t*10**14,mu*10**3))

#(ii)
vd=e*t*100/m
print("\n\n(ii)\nthe drift velocity of elctron is %.5f m/s"%vd)

#(iii)
vf=math.sqrt(2*ef/m)
print("\n\n(iii)\nFermi velocity is %.2f*10^6 m/s"%(vf*10**-6))

#(iv)
lam=vf*t
print("\n\n(iv)\nThe mean free path is %.3f*10^-8 m"%(lam*10**8))

(i)
The relaxation time is 3.98*10^-14 s
The mobility of the electrons is 6.9973 *10^-3 m^2/V-s


(ii)
the drift velocity of elctron is 0.69973 m/s


(iii)
Fermi velocity is 1.39*10^6 m/s


(iv)
The mean free path is 5.535*10^-8 m