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)
```

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
```

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)
```

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
```

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
```

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
```

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
```