13: Bonding In Crystals

Example number 1, Page number 398

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

#Variable declaration
x=9*10**9;              #assume x=1/(4*pi*epsilon0)
e=1.6*10**-19;          #charge(coulomb)
r0=2.5*10**-10;         #radius(m)

#Calculation
U=-e*x/r0;              #potential energy(eV)

#Result
print "potential energy is",U,"eV"

potential energy is -5.76 eV

Example number 2, Page number 398

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

#Variable declaration
x=9*10**9;              #assume x=1/(4*pi*epsilon0)
e=1.6*10**-19;          #charge(coulomb)
U=6.4;                  #potential energy(eV)

#Calculation
r0=-e*x/U;              #equilibrium distance(m)


#Result
print "equilibrium distance is",r0*10**10,"angstrom"

equilibrium distance is -2.25 angstrom

Example number 3, Page number 399

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
x=9*10**9;              #assume x=1/(4*pi*epsilon0)
e=1.6*10**-19;          #charge(coulomb)
alpha=1.76;             #madelung constant
n=0.5;                  #repulsive exponent
r0=4.1*10**-4;          #equilibrium distance(m)

#Calculation
C=18*r0**4/(x*alpha*e**2*(n-1));     #compressibility of the solid

#Result
print "compressibility of the solid is",round(C*10**-14,3),"*10**14"
print "answer given in the book is wrong"

compressibility of the solid is -25.087 *10**14
answer given in the book is wrong

Example number 4, Page number 399

In [15]:
#importing modules
import math
from __future__ import division

#Variable declaration
x=9*10**9;              #assume x=1/(4*pi*epsilon0)
e=1.6*10**-19;          #charge(coulomb)
alpha=1.763;            #madelung constant
n=10.5;                 #repulsive exponent
r0=3.56*10**-10;        #equilibrium distance(m)
IE=3.89;                #ionisation energy(eV)
EA=-3.61;               #electron affinity(eV)

#Calculation
U=-x*alpha*e**2*(1-(1/n))/(e*r0);     #lattice energy(eV)  
E=U+EA+IE;                            #energy needed to form neutral atoms

#Result
print "lattice energy is",round(U,2),"eV"
print "energy needed to form neutral atoms is",round(E,2),"eV"

lattice energy is -6.45 eV
energy needed to form neutral atoms is -6.17 eV

Example number 5, Page number 400

In [18]:
#importing modules
import math
from __future__ import division

#Variable declaration
x=9*10**9;              #assume x=1/(4*pi*epsilon0)
e=1.6*10**-19;          #charge(coulomb)
alpha=1.748;            #madelung constant
n=9;                 #repulsive exponent
r0=2.81*10**-10;        #equilibrium distance(m)

#Calculation
U=-x*alpha*e**2*(1-(1/n))/(e*r0);     #lattice energy(eV)  

#Result
print "lattice energy is",round(U/2,2),"eV"
print "answer given in the book is wrong"

lattice energy is -3.98 eV
answer given in the book is wrong