# 2: Molecular Spectra¶

## Example number 2, Page number 97¶

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

#Variable declaration
lamda_sample=4358;     #wavelength(angstrom)
lamda_raman=4400;      #wavelength(angstrom)

#Calculations
delta_new=(10**8/lamda_sample)-(10**8/lamda_raman);        #raman shift(cm-1)

#Result
print "raman shift is",round(delta_new,2),"cm-1"
print "answer given in the book is wrong"

raman shift is 219.03 cm-1
answer given in the book is wrong


## Example number 3, Page number 98¶

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

#Variable declaration
h=6.62*10**-34;        #planck's constant

#Calculations
E=h**2/(2*math.pi**2);    #energy of diatomic molecule(J)

#Result
print "energy of diatomic molecule is",round(E*10**68,2),"*10**-68 J"
print "answer given in the book is wrong"

energy of diatomic molecule is 2.22 *10**-68 J
answer given in the book is wrong


## Example number 4, Page number 98¶

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

#Variable declaration
lamda0=5000*10**-10;      #wavelength(m)
lamda=5050.5*10**-10;     #wavelength(m)

#Calculations
new0=1/lamda0;       #frequency(m-1)
new=1/lamda;         #frequency(m-1)
delta_new=new0-new;        #raman shift(m-1)
new_as=delta_new+new0;     #frequency of anti-stokes line(m-1)
lamdaas=1*10**10/new_as;          #wavelength of anti-stokes line(angstrom)

#Result
print "raman shift is",round(delta_new*10**-6,2),"*10**6 m-1"
print "wavelength of antistokes line",round(lamdaas,2),"angstrom"
print "answer for wavelength given in the book is wrong"

raman shift is 0.02 *10**6 m-1
wavelength of antistokes line 4950.5 angstrom
answer for wavelength given in the book is wrong


## Example number 5, Page number 99¶

In [11]:
#importing modules
import math
from __future__ import division

#Variable declaration
k=4.8*10**2;        #force constant(N/m)
x=2*10**-10;        #inter nuclear distance(m)
e=1.6*10**-19;      #charge(coulomb)

#Calculations
E=k*x**2/(2*e);     #energy required(eV)

#Result
print "energy required is",int(E),"eV"

energy required is 60 eV


## Example number 6, Page number 99¶

In [19]:
#importing modules
import math
from __future__ import division

#Variable declaration
k=187;        #force constant(N/m)
m=1.14*10**-26;     #reduced mass(kg)
h=6.63*10**-34;     #planck's constant
e=1.6*10**-19;      #charge(coulomb)

#Calculations
new=math.sqrt(k/m)/(2*math.pi);          #frequency of vibration(sec-1)
delta_E=h*new;        #spacing between energy levels(J)
delta_E=delta_E/e;    #spacing between energy levels(eV)

#Result
print "frequency of vibration is",round(new*10**-13,2),"*10**13 sec-1"
print "spacing between energy levels is",round(delta_E*10**2,3),"*10**-2 eV"

frequency of vibration is 2.04 *10**13 sec-1
spacing between energy levels is 8.447 *10**-2 eV


## Example number 7, Page number 100¶

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

#Variable declaration
B=8.5;        #seperation(cm-1)
h=6.62*10**-27;     #planck's constant
c=3*10**10;         #velocity of light(cm/sec)
m1=1;
m2=79;

#Calculations
I=h/(8*math.pi**2*B*c);    #moment inertia of molecule(gm cm**2)
m=m1*m2/(N*(m1+m2));       #reduced mass(gm)
r=10**8*math.sqrt(I/m);          #internuclear distance(angstrom)

#Result
print "internuclear distance is",round(r,2),"angstrom"

internuclear distance is 1.42 angstrom


## Example number 8, Page number 100¶

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda1=4358.3;     #wavelength(angstrom)
lamda2=4768.5;      #wavelength(angstrom)

#Calculations
delta_new=(10**8/lamda1)-(10**8/lamda2);        #vibrational frequency of sample(cm-1)

#Result
print "vibrational frequency of sample is",int(round(delta_new)),"cm-1"

vibrational frequency of sample is 1974 cm-1


## Example number 9, Page number 101¶

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

#Variable declaration
MO=16;
MD=2;
MH=1;
new=3300;     #frequency(cm-1)

#Calculations
mew_OD=MO*MD/(MO+MD);
mew_OH=MO*MH/(MO+MH);
new1=math.sqrt(mew_OD/mew_OH);
new_OD=new/new1;        #frequqncy of OD stretching vibration(cm-1)

#Result
print "frequqncy of OD stretching vibration is",int(new_OD),"cm-1"

frequqncy of OD stretching vibration is 2401 cm-1


## Example number 11, Page number 102¶

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda0=4358;     #wavelength(angstrom)
lamda1=4400;     #wavelength(angstrom)
lamda2=4419;     #wavelength(angstrom)
lamda3=4447;     #wavelength(angstrom)

#Calculations
new0bar=10**8/lamda0;        #wave number of exciting line(cm-1)
rs1=(10**8/lamda0)-(10**8/lamda1);     #raman shift of 4400 line(cm-1)
rs2=(10**8/lamda0)-(10**8/lamda2);     #raman shift of 4419 line(cm-1)
rs3=(10**8/lamda0)-(10**8/lamda3);     #raman shift of 4447 line(cm-1)

#Result
print "raman shift of 4400 line is",round(rs1,2),"cm-1"
print "raman shift of 4419 line is",round(rs2,1),"cm-1"
print "raman shift of 4447 line is",round(rs3,1),"cm-1"

raman shift of 4400 line is 219.03 cm-1
raman shift of 4419 line is 316.8 cm-1
raman shift of 4447 line is 459.2 cm-1


## Example number 12, Page number 102¶

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
new_bar=20.68;          #transition(cm-1)
J=14;

#Calculations
B=new_bar/2;
new=2*B*(J+1);          #frequency(cm-1)
lamda=1/new;            #corresponding wavelength(cm)

#Result
print "corresponding wavelength is",int(lamda*10**4),"*10**-4 cm"

corresponding wavelength is 32 *10**-4 cm


## Example number 13, Page number 103¶

In [17]:
#importing modules
import math
from __future__ import division

#Variable declaration
twoB=4000;        #seperation observed from the series(cm-1)
h=6.62*10**-27;     #planck's constant
c=3*10**10;         #velocity of light(cm/sec)

#Calculations
B=twoB/2;
I=h/(8*math.pi**2*B*c);     #moment of inertia of molecule(gm cm**2)

#Result
print "moment of inertia of molecule is",round(I*10**42,1),"*10**-42 gm cm**2"

moment of inertia of molecule is 1.4 *10**-42 gm cm**2


## Example number 14, Page number 104¶

In [27]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=5461*10**-8;      #wavelength(cm)
new1=608;
new2=846;
new3=995;
new4=1178;
new5=1599;
new6=3064;              #raman shift(cm-1)

#Calculations
newbar=1/lamda;         #wave number(cm-1)
new11=newbar-new1;
new22=newbar-new2;
new33=newbar-new3;
new44=newbar-new4;
new55=newbar-new5;
new66=newbar-new6;
lamda1=10**8/new11;
lamda2=10**8/new22;
lamda3=10**8/new33;
lamda4=10**8/new44;
lamda5=10**8/new55;
lamda6=10**8/new66;        #corresponding wavelength(angstrom)

#Result
print "corresponding wavelengths are",int(lamda1),"angstrom",int(lamda2),"angstrom",int(round(lamda3)),"angstrom",int(lamda4),"angstrom",int(lamda5),"angstrom",int(lamda6),"angstrom"

corresponding wavelengths are 5648 angstrom 5725 angstrom 5775 angstrom 5836 angstrom 5983 angstrom 6558 angstrom


## Example number 15, Page number 105¶

In [20]:
#importing modules
import math
from __future__ import division

#Variable declaration
h=6.63*10**-34;     #planck's constant(J s)
e=1.602*10**-19;    #charge(coulomb)
mew=1.14*10**-26;   #reduced mass(kg)
deltaE=6.63*10**-2*e;     #energy(J)

#Calculations
new=deltaE/h;                 #frequency(sec-1)
k=4*math.pi**2*new**2*mew;    #force constant(N/m)

#Result
print "force constant is",int(k),"N/m"

force constant is 115 N/m