from __future__ import division
import math
# Python Code Ex14.1 Polarization of water molecule: Page-456 (2010)
#Variable declaration
NA = 6.023e+23; # Avogadro's number
p = 6e-030; # Dipole moment of water molecule, C-m
r = 1e-03; # Radius of water molecule, m
M = 18e-03; # Molecular weight of water, kg
d = 1e+03; # Density of water, kg per metre cube
#Calculation
V = M/d; # Volume of water, metre cube
# Now M/d metre cube volume will contain NA = 6.023e+023 water molecules,
#so that 4*%math.pi/3*(r**3) metre cube volume will contain
N = NA*d*4*math.pi*r**3/(M*3); # Number of water molecules per metre cube
P = N*p; # Polarization of water molecules, coulomb per metre square
#Results
print"\nThe polarization of water molecules ="
print round((P*10**10),2)*10**-10,"coulomb per metre square"
from __future__ import division
import math
# Python Code Ex14.2 Calculating dielectric constant from
# electric polarizability of the atom: Page-464 (2010)
#Variable declaration
# Electric polarizability of the Kr-atom, farad-metre square
alpha_Kr = 2.18e-040;
NA = 6.023e+023; # Avogadro's number
# Electrical permittivity of free space,
# coulomb square per newton per metre square
epsilon_0 = 8.85e-012;
#Calculation
N = NA/(22.4e-03);# Number of Kr atoms per metre cube
# Relative electrical permittivity of Kr specimen
epsilon_r = N*alpha_Kr/epsilon_0 + 1;
#Result
print"\nThe diectric constant of Kr specimen =", round(epsilon_r,5)
from __future__ import division
import math
# Python Code Ex14.3 Calculating electric polarizability of
#a molecule from its susceptibility: Page-464 (2010)
#Variable declaration
NA = 6.023e+023; # Avogadro's number
# Electrical permittivity of free space, coulomb square per newton per metre
epsilon_0 = 8.85e-012;
chi = 0.985e-03; # Electrical susceptibility of carbon-dioxide molecule
rho = 1.977; # Density of carbon-dioxide, kg per metre cube
M = 44e-03; # Molecular weight of CO2, kg
#Calculation
N = NA*rho/M; # Number of molecules per unit volume, per metre cube
# Total electric polarizability of carbon-dioxide, farad-metre square
alpha = epsilon_0*chi/N;
#Result
print"\nThe total electric polarizability of carbon-dioxide ="
print round((alpha*10**40),2)*10**-40,"farad-metre square"
from __future__ import division
import math
# Python Code Ex14.4 Calculating electric polarizability
#of Oxygen atom: Page-465 (2010)
#Variable declaration
e = 1.602e-019; # Charge on an electron, coulomb
p = 0.5e-022; # Dipole moment of oxygen atom, C-m
# Distnace of the centre of negative charge cloud from the nucleus, m
d = 4e-017;
# Electrical permittivity of free space, coulomb square per newton per metre
epsilon_0 = 8.85e-012;
#Calculation
# In equilibrium, Coulomb interaction = Lorentz force
# i.e. 8*e*E = (8*e)*(8*e)/(4*%math.pi*epsilon_0*d**2)
# Solving for E
# The strength of local electric field, volt per metre
E = 8*e/(4*math.pi*epsilon_0*d**2);
# As p = alpha*E, solving for alpha
alpha = p/E; # Atomic polarizability of oxygen, farad-metre square
#Result
print"\nThe atomic polarizability of oxygen = "
print round((alpha*10**48),2)*10**-48,"farad-metre square"
from __future__ import division
import math
# Python Code Ex14.5 Dipolar polarization of HCl molecule: Page-470 (2010)
#Variable declaration
k = 1.38e-023; # Boltzmann constant, J/mol/K
T = 300; # Temperature of the HCl vapour, kelvin
N = 1e+027; # Number of HCL molecuels per unit volume, per metre cube
# Electric field strength to which the HCL vapour is subjected, volt/m
E = 1e+06;
p = 3.46e-030; # The dipole moment of HCl molecule,C-m
#Calculation
# Dipolar polarizability of HCl molecule, farad-metre square
alpha_d = p**2/(3*k*T);
# As P = N*p = N*alpha_d*E
#Orientational or Dipolar polarization of HCl molecule,coulomb per metre square
P = N*alpha_d*E;
E_M = p*E; # Magnetic energy stored in the dipole-field system, joule
E_Th = k*T; # Thermal energy of the HCl molecule, joule
a = E_M/E_Th; # Ratio of magnetic energy to the thermal energy
#Result
print"\nThe orientational polarization of molecules in HCl vapour ="
print round((P*10**7),2)*10**-7,"coulomb per metre square"
print"\nThe ratio of magnetic energy to the thermal energy ="
print round(a,6)," << 1"
from __future__ import division
import math
#Python Code Ex14.6 Effect of molecular deformation on polarizability:Page-471
#Variable declaration
# Polarizability of ammonia molecule at 309 K, farad-metre square
alpha_309 = 2.42e-039;
# Polarizability of ammonia molecule at 448 K, farad-metre square
alpha_448 = 1.74e-039;
k = 1.38e-023; # Boltzmann constant, J/mol/K
T1 = 309; # First temperature of the experiment, kelvin
T2 = 448; # Second temperature of the experiment, kelvin
#Calculation
# As alpha = alpha_i + alpha_d = alpha_i + p**2/(3*k*T) = alpha_i + bta/T
# where bta = p**2/(3*k)
# Thus alpha_309 = alpha_i + bta/309 and alpha_448 = alpha_i + bta/448
# Solving for bta
# bta(1/309-1/448) = alpha_309 - alpha_448
# bta = p**2/(3*k), farad-kelvin metre square
bta= ( alpha_309 - alpha_448)/(1/309 - 1/448);
# Solving for alpha_i
# Polarizability due to permanent dipole moment, farad-metre square
alpha_i = alpha_309 - bta/309;
# Polarizability due to deformation of molecules = bta/T, bta = p**2/(3*k)
alpha_d_309 = bta/T1# Orientational polarizability at 309 K, farad-metre square
alpha_d_448 = bta/T2#Orientational polarizability at 448 K, farad-metre square
#Result
print"\nThe polarizability due to permanent dipole moment ="
print round((alpha_i*10**40),2)*10**-40," farad-metre square"
print"\nThe orientational polarization of ammonia at 309 K ="
print round((alpha_d_309*10**39),2)*10**-39,"farad-metre square"
print"\nThe orientational polarization of ammonia at 448 K ="
print round((alpha_d_448*10**39),2)*10**-39," farad-metre square"