# chapter 07 : Molecular Physics¶

## Ex7.1 : : Pg: 170¶

In [2]:
from math import sqrt, pi
#Frequency of oscillation of a hydrogen molecule
K = 4.8e+02     # Force constant, N/m
m = 1.67e-027     # Mass of hydrogen atom, kg
mu = m/2     # Reduced mass of the system, kg
v = 1/(2*pi)*sqrt(K/mu)     # Frequency of oscillation of a hydrogen molecule, Hz
print "The frequency of oscillation of a hydrogen molecule = %3.1e Hz"% v

The frequency of oscillation of a hydrogen molecule = 1.2e+14 Hz


## Ex7.2: : Pg: 170¶

In [4]:
from math import sqrt, pi
#bond Length of carbon monoxide
h = 6.626e-034     # Planck's constant, Js
c = 2.997e+010     # Speed of light, cm/s
B = 1.921     # Rotational constant for CO, per cm
nu_bar = 2*B     # Wavenumber of first line in rotation spectra of CO, per cm
mu = 11.384e-027     # Reduced mass of the CO system, per cm
I = 2*h/(8*pi**2*nu_bar*c)     # Moment of inertia of CO molecule about the axis of rotation, kg-m/s
r = sqrt(I/mu)     # Bond length of CO molecule, m
print "The bond length of CO molecule = %5.2f angstrom"% (r/1e-010)

The bond length of CO molecule =  1.13 angstrom


## Ex7.3: : Pg: 171¶

In [5]:
from math import exp
#Intensity ratio of J states for HCL molecule
e = 1.6e-019     # Energy equivalent of 1 eV, J/eV
K = 1.38e-23     # Boltzmann constant, J/K
T = 300     # Absolute room temperature, K
J1 = 0     # Rotational quantum number for ground level
J2 = 10     # Rotational quantum number for 10th level
EJ1 = J1*(J1+1)*1.3e-03     # Energy of ground level of HCL molecule, eV
EJ2 = J2*(J2+1)*1.3e-03     # Energy of 10th level of HCL molecule, eV
# As n10/n0 is propotional to (2J+1)*exp(-(EJ2-EJ1))/KT, so
I_ratio = (2*J2+1)/(2*J1+1)*exp(-(EJ2 - EJ1)/(K*T/e))     # Intensity ratio of J10 and J1 states
print "The intensity ratio of J-states for HCL molecule = %4.2f"% (I_ratio)

The intensity ratio of J-states for HCL molecule = 0.08


## Ex7.4: : Pg: 171¶

In [6]:
from math import sqrt
#CO molecule in lower state
R = 1.13e-010     # Bond length of CO molecule, m
h_red = 1.054e-034     # Reduced Planck's constant, Js
mu = 1.14e-026     # Reduced mass ofthe system, kg
J = 1     # Rotational quantum number for lowest state
I = mu*R**2     # Moment of inertia of CO molecule about the axis of rotation, kg-metre square
EJ = J*(J + 1)*h_red**2/(2*I)     # Energy of the CO molecule in the lowest state, J
omega = sqrt(2*EJ/I)     # Angular velocity of the CO molecule in the lowest state, rad per sec
print "The energy of the CO molecule in the lowest state = %4.2e J" %EJ
print "The angular velocity of the CO molecule in the lowest state = %4.2e rad/sec" %omega

The energy of the CO molecule in the lowest state = 7.63e-23 J
The angular velocity of the CO molecule in the lowest state = 1.02e+12 rad/sec