# Chapter 11 : Free Electron Theory Of Metals¶

## Example number 1 , page number 205¶

In [1]:
#importing module
import math
from __future__ import division

#Variable declaration
k=1.376*10**-23           #Boltzmann's constant in J/K
T=300                     #Temperature
m=9.11*10**-31            #Mass of electron

#Calculations
v=math.sqrt((3*k*T)/m)/10**5

#Result
print"root mean square velocity v= %1.2f*10**5 m/s" %v

root mean square velocity v= 1.17*10**5 m/s


## Example number 2 , page number 205¶

In [2]:
#importing module
import math
from __future__ import division

#Variable declaration
sigma=6.8*10**7        #conductivity
n=8.5*10**28           #number of electrons
m=9.1*10**-31          #Mass of electron
e=1.6*10**-19          #charge on electron
k=1.38*10**-23         #Boltzmann's constant in J/K
T=300                  #temperature in K

#Calculations
lamda=(2*sigma*math.sqrt(3*m*k*T))/(n*e**2)/10**-9

#Result
print"Mean free path for electron= %1.1f*10**-9 m"  %lamda

Mean free path for electron= 6.6*10**-9 m


## Example number 3 , page number 205¶

In [3]:
#importing module
import math
from __future__ import division

#Variable declaration
rho=1.54*10**-8         #resistivity
n=5.8*10**28            #electron density
e=1.602*10**-19         #charge on electron
m=9.1*10**-31           #Mass of electron

#Calculations
tau=m/(n*(e**2)*rho)/10**-14

#Result
print"Relaxation time= %1.2f*10**-14 seconds" %tau

Relaxation time= 3.97*10**-14 seconds


## Example number 4 , page number 206¶

In [4]:
#importing module
import math
from __future__ import division

#Variable declaration
EF=1.1214*10**-18       #fermi energy in J
m=9.11*10**-31          #Mass of electron
h=6.63*10**-34          #planck's constant

#Calculations
n=((8*m*EF)/(h**2))**(3/2)*(math.pi/3)/10**28

#Result
print"No. of free electrons per unit volume= %1.3f*10**28 electrons per meter**3" %n

No. of free electrons per unit volume= 8.395*10**28 electrons per meter**3


## Example number 5 , page number 206¶

In [5]:
#importing module
import math
import numpy as np
from __future__ import division

#Variable declaration
fE=0.01                 #probability
delE=8*10**-20          #ev to J

#Calculations
T=5797/np.log(99)

#Result
print"Temperature= %i" %T,"K"

Temperature= 1261 K