1: Bonding in Solids

Example number 1.1, Page number 1.4

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

#Variable declaration
IE_1 = 502     #first ionisation energy(kJ/mol)
EA_B = -335    #electron affinity for B atom(kJ/mol)
e = 1.602*10**-19
r = 0.3      #inter ionic seperation(nm)
epsilon0 = 8.85*10**-12      #permittivity of free space(C/N-m)

#Calculation
r = r*10**-9      #inter ionic seperation(m)
N = 6.022*10**23*10**-3
E = (-e**2*N)/(4*math.pi*epsilon0*r)      #electrostatic attraction energy(kJ/mol)
dE = IE_1+EA_B+E;     #net change in energy per mole

#Result
print "electrostatic attraction energy is",int(E),"kJ/mol"
print "net change in energy is",int(dE),"kJ/mol"
print "A+B- molecule will be stable"
print "answer for net change,dE given in the book is wrong"

electrostatic attraction energy is -463 kJ/mol
net change in energy is -296 kJ/mol
A+B- molecule will be stable
answer for net change,dE given in the book is wrong

Example number 1.2, Page number 1.5

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

#Variable declaration
IP_K = 4.1     #IP of K(eV)
EA_Cl = 3.6     #EA of Cl(eV)
e = 1.602*10**-19
epsilon0 = 8.85*10**-12 

#Calculation
delta_E = IP_K - EA_Cl      #energy required(eV)
#if their total energy is 0, delta_E = Ec
Ec = delta_E
R = e/(4*math.pi*epsilon0*Ec)      #seperation between ion pair(m)
R = R*10**9          #seperation between ion pair(nm)
R = math.ceil(R*10**3)/10**3;   #rounding off to 3 decimals

#Result
print "energy required to form K+Cl- ion pair is",delta_E,"eV"
print "seperation between ion pair is",R,"nm"

energy required to form K+Cl- ion pair is 0.5 eV
seperation between ion pair is 2.881 nm

Example number 1.3, Page number 1.6

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

#Variable declaration
e = 1.602*10**-19
EA = 3.65     #electron affinity of Cl(eV)
IP = 5.14     #ionisation energy of Na(eV)
epsilon0 = 8.85*10**-12
r0 = 236      #equilibrium distance(pm)

#Calculation
r0 = r0*10**-12      #equilibrium distance(m)
V = (-e**2)/(4*math.pi*epsilon0*r0)       ##potential energy(J)
V = V/e       #potential energy(eV)
Ue = V
BE = -Ue - IP + EA       #bond energy(eV)
BE = math.ceil(BE*10**3)/10**3;   #rounding off to 3 decimals

#Result
print "bond energy for NaCl molecule is",BE,"eV"

bond energy for NaCl molecule is 4.614 eV

Example number 1.4, Page number 1.19

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
e = 1.602*(10**-19)
epsilon0 = 8.85*(10**-12)
r0 = 0.281     #equilibrium seperation(nm)
A = 1.748     #Madelung constant
n = 9    #born repulsive exponent

#Calculation
r0 = r0*10**-9     #equilibrium seperation(m)
CE = (A*e**2)*(1-(1/n))/(4*math.pi*epsilon0*r0)    #cohesive energy(J)
CE = CE/e       #cohesive energy(eV)
CE = math.ceil(CE*10**3)/10**3;   #rounding off to 3 decimals

#Result
print "cohesive energy of NaCl is",CE,"eV"

cohesive energy of NaCl is 7.966 eV