Chapter 10: Molecules, Lasers and Solids

Example 10.1, Page 342

In [1]:
import math

#Variable declaration
m = 2.33e-026;    # Mass of a nitrogen atom, kg
R = 1.1e-010;    # Interatomic separation between two nitrogen atoms, m
h = 6.626e-034;    # Planck's constant, Js
e = 1.6e-019;    # Energy equivalent of 1 eV, J

#Calculations
h_bar = h/(2*math.pi);    # Reduced Planck's constant, Js
I = m*R**2/2;    # Momemt of rotational inertia of nitrogen gas molecule, kg-Sq.m
l = 1;    # Rotational angular momentum quantum number
E_rot = h_bar**2*l*(l+1)/(2*I);    # The energy for lowest rotational state of the nitrogen molecule, J

#Result
print "The energy for lowest rotational state of the nitrogen molecule = %4.2e eV"%(E_rot/e)

The energy for lowest rotational state of the nitrogen molecule = 4.93e-04 eV

Example 10.2, Page 343

In [2]:
import math

#Variable declaration
h = 6.626e-034;    # Planck's constant, Js
e = 1.6e-019;    # Energy equivalent of 1 eV, J
h_bar = h/(2*math.pi);    # Reduced Planck's constant, Js
k = 1.38e-023;    # Boltzmann constant, J/K
u = 1.67e-027;    # Mass equivalent of 1 amu, kg

#Calculations
m1 = 34.97*u;    # Atomic mass of chlorine atom, kg
m2 = 1.008*u;    # Atomic mass of hydrogen atom, kg
mu = m1*m2/(m1 + m2);    # Reduced mass of the HCl system, kg
delta_E = 0.36;    # Spacing between vibrational energy levels of the HCl molecule, eV
omega = delta_E*e/h_bar;    # Angular frequency of vibration, rad/s
kapa = mu*omega**2;    # Effective force constant for HCl molecule, N/m
T = delta_E*e/k;    # Classical temperature associated with the rotational energy spacing, K

#Results
print "The effective force constant for HCl molecule = %3d N/m"%(math.ceil(kapa))
print "The classical temperature associated with the rotational energy spacing = %4d K"%(math.ceil(T))
#answers differ due to rounding errors

The effective force constant for HCl molecule = 489 N/m
The classical temperature associated with the rotational energy spacing = 4174 K

Example 10.4, Page 358

In [3]:
#Variable declaration
e = 1.602e-019;    # Charge on an electron, C
N_A = 6.023e+023;    # Avogadro's number
alpha = 1.7476;    # Madelung constant
E = -764.4e+003;    # Dissociation energy of NaCl molecule, J/mol
V = E/N_A;    # Repulsive potential energy, J
k = 8.988e+009;    # Coulomb's constant, N-Sq.m/C^2
r0 = 0.282e-009;    # Equilibrium separation for nearest neighbour in NaCl, m

#Calculations
rho = r0*(1+r0*V/(k*alpha*e**2));    # Range parameter for NaCl, nm

#Result
print "The range parameter for NaCl = %6.4f nm"%(rho/1e-009)

The range parameter for NaCl = 0.0316 nm

Example 10.5, Page 365

In [4]:
#Variable declaration
e = 1.602e-019;    # Charge on an electron, C
r = 5.29e-011;    # Orbital radius of electron equal to Bohr radius, m
B = 2.0;    # Applied magnetic field, T
m = 9.11e-031;    # Mass of an electron, kg

#Calculations
delta_mu = e**2*r**2*B/(4*m);    # Induced diamagnetic moment in the atom, J/T

#Result
print "The induced diamagnetic moment in the atom = %3.1e J/T"%delta_mu

The induced diamagnetic moment in the atom = 3.9e-29 J/T

Example 10.6, Page 366

In [5]:
import math

#Variable declaration
mu_B = 9.27e-024;    # Bohr's magneton, J/T
B = 0.50;    # Applied magnetic field, T
k = 1.38e-023;    # Boltzmann constant, J/K

#Calculations&Results
T = 10*mu_B*B/k;    # Temperature at which mu*B = 0.1k*T, K
b_muB = mu_B*B/(k*T);
ratio = b_muB/math.tanh(b_muB);    # Ratio of b_muB and tanh(b_muB)
if (ratio - 1) < 0.01:
    print "The value of T = %4.2f K is suitable as a classical temperature."%T
else:
    print "The value of T = %4.2f K is not suitable as a classical temperature."%T

# For higher temperature
T = 100;    # Given temperature
b_muB = mu_B*B/(k*T);
ratio = b_muB/math.tanh(b_muB);    # Ratio of b_muB and tanh(b_muB)
if (ratio - 1) < 0.001:
    print "At the value of T = %4.2f K, the approximation is an excellent one."%T
else:
    print "At the value of T = %4.2f K, the approximation is not an excellent."%T

The value of T = 3.36 K is suitable as a classical temperature.
At the value of T = 100.00 K, the approximation is an excellent one.

Example 10.7, Page 374

In [6]:
#Variable declaration
k = 1.38e-023;    # Boltzmann constant, J/K
e = 1.602e-019;    # Energy equivalent of 1 eV, J
h = 6.62e-034;    # Planck's constant, Js
c = 3.00e+008;    # Speed of light, m/s
T_c = 9.25;    # Critical temperature for niobium, K

#Calculations
E_g = 3.54*k*T_c;    # Energy gap for niobium from BCS theory, J
lamda = h*c/E_g;    # Minimum photon wavelength needed to break the Cooper pair, m

#Results
print "The energy gap for niobium = %4.2f meV"%(E_g/(e*1e-003))
print "The minimum photon wavelength needed to break the Cooper pair = %4.2e m"%lamda

The energy gap for niobium = 2.82 meV
The minimum photon wavelength needed to break the Cooper pair = 4.39e-04 m

Example 10.8, Page 382

In [7]:
import math

#Variable declaration
r = 1e-002;    # Radius of the loop, m
phi0 = 2.068e-015;    # Magnetic flux penetrating to the loop, T-Sq.m

#Calculations
A = math.pi*r**2;    # Area of the loop, Sq.m
B = phi0/A;    # Magnetic field perpendicular to the loop, T

#Result
print "The magnetic field perpendicular to the loop = %4.2e T"%B

The magnetic field perpendicular to the loop = 6.58e-12 T