Chapter 5:Principles of Quantum Mechanics

Example 5.1, Page number 5.12

In [1]:
#Varaible declaration
c = 3*10**8        #velocity of air(m/s)
m = 1.67*10**-27   #mass of proton(kg)
h = 6.626*10**-34  #Planck's constant(J x sec)

#Calculation
v = c/10.   #velocity of proton(m/s)
lamda = h/(m*v)

#Result
print "The de Brogile wavelength is",round((lamda/1E-14),3),"*10^-14 m"

The de Brogile wavelength is 1.323 *10^-14 m

Example 5.2, Page number 5.12

In [2]:
import math

#Varaible declaration
V = 400  #potential(V)

#Calculation
lamda = 12.26/math.sqrt(V)

#Result
print "The de Brogile wavelength is",lamda,"A"

The de Brogile wavelength is 0.613 A

Example 5.3, Page number 5.12

In [3]:
import math

#Varaible declaration
E = 0.025          #kinetic energy of neutron(eV)
m = 1.674*10**-27  #mass of neutron(kg)
h = 6.626*10**-34  #Planck's constant(J x sec)

#Calculations
E_j = E*1.6*10**-19 #converting eV to joules
lamda = h/math.sqrt(2*m*E_j)

#Result
print "The de Brogile wavelength is",round((lamda/1E-11),3),"*10^-11 m"

The de Brogile wavelength is 18.106 *10^-11 m

Example 5.4, Page number 5.13

In [4]:
import math

#Varaible declaration
V = 1600  #potential(V)

#Calculation
lamda = 12.26/math.sqrt(V)

#Result
print "The de Brogile wavelength is",lamda,"A"

The de Brogile wavelength is 0.3065 A

Example 5.5, Page number 5.21

In [19]:
#Varaible declaration
h = 6.626*10**-34  #Planck's constant(J x sec)
m = 9.1*10**-31    #mass of electron(kg)
L = 0.1*10**-9     #length of each side of box(m)
#For lowest energy level,
nx = 1
ny = 1
nz = 1

#Calculations
E1 = (((h**2)*(nx**2+ny**2+nz**2))/(8*m*L**2))/(1.6*10**-19)

#Result
print "The lowest energy of electron is",round(E1,2),"eV"

The lowest energy of electron is 113.08 eV

Example 5.6, Page number 5.22

In [18]:
#Variable declaration
h = 6.626*10**-34  #Planck's constant(J x sec)
m = 9.1*10**-31    #mass of electron(kg)
L = 0.1*10**-9     #length of each side of box(m)
#For level next to lowest energy level,
nx = 1
ny = 1
nz = 2

#Calculations
E1 = (((h**2)*(nx**2+ny**2+nz**2))/(8*m*L**2))/(1.6*10**-19)

#Result
print "The lowest energy of electron is",round(E1,2),"eV"

The lowest energy of electron is 226.15 eV

Example 5.7, Page number 5.23

In [17]:
#Variable declaration
h = 6.626*10**-34  #Planck's constant(J x sec)
m = 9.1*10**-31    #mass of electron(kg)
E = 2000.          #energy of electron(eV)

#Calculations
Ej = E*1.6*10**-19 #converting eV to joules
lamda = h/math.sqrt(2*m*Ej)

#Result
print "The de Brogile wavelength is",round((lamda/1E-9),4),"nm"

The de Brogile wavelength is 0.0275 nm

Example 5.8, Page number 5.23

In [16]:
#Variable declaration
h = 6.626*10**-34  #Planck's constant(J x sec)
m = 9.1*10**-31    #mass of electron(kg)
L = 4*10**-10      #length of each side of box(m)
#For minimum energy 
n = 1

#Calculations
E1 = ((h**2)*(n**2))/(8*m*L**2)

#Result
print "Minimum energy =",round((E1/1E-18),3),"*10^-18 J"

Minimum energy = 0.377 *10^-18 J

Example 5.9, Page number 5.24

In [21]:
#Variable declaration
h = 6.626*10**-34  #Planck's constant(J x sec)
m = 9.1*10**-31    #mass of electron(kg)
L = 1*10**-10      #length of each side of box(m)
n1 = 10            #For energy in ground state
n2 = 2             #For energy in first excited state
n3 = 3             #For energy in second excited state

#Calculations
E1 = ((h**2)*(n1**2))/(8*m*L**2)
E2 = ((h**2)*(n2**2))/(8*m*L**2)
E3 = ((h**2)*(n3**2))/(8*m*L**2)

#Results
print "Energy in ground state =",round((E1/1E-17),4),"*10^17 J (Calculation mistake in textbook)"
print "Energy in first excited state =",round((E2/1E-17),4),"*10^17 J"
print "Energy in second excited state =",round((E3/1E-17),4),"*10^17 J"

Energy in ground state = 60.3075 *10^17 J (Calculation mistake in textbook)
Energy in first excited state = 2.4123 *10^17 J
Energy in second excited state = 5.4277 *10^17 J

Example 5.10, Page number 5.24

In [22]:
#Variable declaration
h = 6.626*10**-34    #Planck's constant(J x sec)
m = 9.1*10**-31      #mass of electron(kg)
lamda = 1.66*10**-10 #wavelength(m)

#Calculations
v = h/(m*lamda)
KE = (m*v**2)/(2*1.6*10**-19) #in joules

#Result
print "Velocity of electron =",round((v/1E+7),4),"*10^7 m"
print "Kinetic energy of electron =",round(KE,2),"eV"

Velocity of electron = 0.4386 *10^7 m
Kinetic energy of electron = 54.71 eV

Example 5.11, Page number 5.25

In [23]:
import math

#Varaible declaration
V = 15*10**3  #potential(V)

#Calculation
lamda = 12.26/math.sqrt(V)

#Result
print "The de Brogile wavelength is",round(lamda,2),"A"

The de Brogile wavelength is 0.1 A

Example 5.12, Page number 5.25

In [24]:
import math

#Varaible declaration
V = 344    #potential(V)
theta = 60 #glancing angle(degrees)

#Calculation
lamda = 12.26/math.sqrt(V)
#For first reflection 
n = 1
d = (n*lamda)/(2*math.sin(math.radians(theta)))

#Result
print "The interatomic spacing of the crystal is",round(d,4),"A"

The interatomic spacing of the crystal is 0.3816 A