Microwave Spectroscopy
or
Rotational Spectroscopy
Applied Chemistry
Course: CHY101
Regions of Electromagnetic Radiation
Frequency ()
Wavelength ()
Radio-waves
Region
Microwaves
Region
Infra-red
Region
Visible
Region
Ultra-violet
Region
X-ray
Region
-ray
Region
Frequency
(HZ)
106 - 1010
1010 - 1012
1012 - 1014
1014 - 1015
1015 - 1016
1016 - 1018
1018- 1020
Wavelength
10m – 1 cm
1 cm – 100µm
100µm – 1µm
700 – 400 nm
400-10 nm
10nm –
100pm
100pm –
1 pm
NMR, ESR
Rotational
Spectroscopy
Vibrational
spectroscopy
Electronic
Spectroscopy
Electronic
Spec.
0.001 – 10
J/mole
Order of some
100 J/mole
Some 104
J/mole
Some 100
kJ/mole
Some 100s
kJ/mole
107- 109
J/mole
109- 1011
J/mole
Energy
UHF TV, cellular,
telephones.
(300 MHz and 3 GHz)
FM Radio, VHF TV.
AM Radio
Microwave ovens,
Police radar, satellite
stations-- (3 to 30 GHz)
Table lamp,
Tube light (400
nm -800 nm or
400–790 THz)
Sun Lamp
X-ray
Electromagnetic Radiation
Electromagnetic Wave
Regions of Electromagnetic Radiation
The interaction of radiation with matter
http://hyperphysics.phy-astr.gsu.edu/hbase/mod3.html
Different types of Energy
Connecting macroscopic thermodynamics to a molecular understanding requires that
we understand how energy is distributed on a molecular level.
ATOMS:
The electrons: Electronic energy. Increase the energy of one (or more)
electrons in the atom.
Nuclear motion: Translational energy. The atom can move around
(translate) in space.
MOLECULES:
The electrons: Electronic energy. Increase the energy of one (or more) electrons in
the molecule.
Nuclear motion:
Translational energy. The entire molecule can translate in space.
Vibrational energy. The nuclei can move relative to one another.
Rotational energy. The entire molecule can rotate in space.
The rotation spectrum of 12C16O at 40 K.
The lines are nearly equally spaced and vary in intensity.
We also will learn why the lines are nearly equally spaced and vary in intensity. Such
spectra can be used to determine bond lengths, and even bond angles in polyatomic
molecules.
Absorption of Electromagnetic Radiation - The Coupling Mechanism
An electromagnetic wave is an oscillating electrical field and interacts only with molecules that
can undergo a change in dipole moment.
The oscillating dipole can be provided by the rotation of a permanent dipole like for example
HCl. This type of interaction leads to microwave spectra
HCl
Fig. The rotation of a polar diatomic molecule, showing the fluctuation in the dipole moment
measured in a particular direction
Microwave Spectroscopy
Incident electromagnetic waves can excite the rotational levels of molecules
provided they have an electric dipole moment. The electromagnetic field exerts a
torque on the molecule.
The spectra for rotational transitions of molecules is typically in the microwave
region of the electromagnetic spectrum.
 Absorption of microwave radiation causes heating due to increased molecular
rotational activity....
Microwave Spectroscopy
Incident electromagnetic waves can excite the rotational levels of molecules provided they
have an electric dipole moment. The electromagnetic field exerts a torque on the molecule.
 Homonuclear diatomic molecules (such as H2, O2, N2 , Cl2) – have zero dipole (non
polar) -- have zero change of dipole during the rotation – hence NO interaction with
radiation -- hence homonuclear diatomic molecules are microwave inactive
 Heteronuclear diatomic molecules (such as HCl, HF, CO) – have permanent
dipolemoment (polar compound) -- change of dipole occurs during the rotation –
hence interaction with radiation takes place – Therefore, heteronuclear diatomic
molecules are microwave active.
RIGID ROTOR
For simplicity, we can consider only rotational motion of rigid diatomic molecule,
A diatomic molecule can rotate around a vertical
axis. The rotational energy is quantized.
Assume a rigid (not elastic) bond
r0 = r1 + r2
For rotation about center of gravity, C :
m1r1 = m2r2
0
= m2 (r0 - r1)
m2r0
r1 
m1  m2
m1r0
r2 
m1  m2
RIGID ROTOR
Moment of inertia about C:
IC = m1r12 + m2r22 = m2r2r1 + m1r1r2 = r1r2 (m1 + m2)
m1m2 2
2
I
r0  μr0
m1  m2
1
1
1


 = reduced mass,
μ m1 m2
A diatomic molecule can rotate around a vertical axis. The rotational energy is quantized. By the
using Schrödinger equation, the rotational energy levels allowed to the rigid diatomic molecule are
given by,
J = Rotational quantum number (J = 0, 1, 2, …)
I = Moment of inertia = mr2
 = reduced mass = m1m2 / (m1 + m2)
r = internuclear distance
Energy is quantized
Planck suggests that radiation (light, energy) can
only come in quantized packets that are of size hν.
Planck, 1900
E  h
Energy (J)
Planck’s constant
h = 6.626 × 10-34 J·s
Frequency (s-1)
Note that we can specify the energy by specifying any one of the following:
1. The frequency, n (units: Hz or s-1):
2. The wavelength, λ, (units: m or cm or mm):
Recall:
  c
3. The wavenumber,
1
Recall: ~ 

~
(units: cm-1 or m-1)
E  h
E
hc

E  hc~
Rotational Spectra of Rigid Diatomic molecule
Rotational Energy Levels for rigid rotor:
Where
Rotational Spectra of Rigid Diatomic molecule
For rigid rotor, J  J + 1,
The allowed rotational energy
levels of a rigid diatomic molecule
Allowed transitions between the energy levels
of a rigid diatomic molecule and the spectrum
Rotational Spectra of Rigid Rotor
Apart from Specific rule, DJ 1, Gross rule- the molecule should
have a permanent electric dipole moment,  . Thus, homonuclear diatomic molecules do
not have a pure rotational spectrum. Heteronuclear diatomic molecules do have
rotational spectra.
Selection Rule:
Dj  1
Dj  1 (absorption)
Dj  1 (emission)
Rotational Energy levels
Microwave Spectroscopy
Incident electromagnetic waves can excite the rotational levels of molecules provided they
have an electric dipole moment. The electromagnetic field exerts a torque on the molecule.
 Homonuclear diatomic molecules (such as H2, O2, N2 , Cl2) – have zero dipole (non
polar) -- have zero change of dipole during the rotation – hence NO interaction with
radiation -- hence homonuclear diatomic molecules are microwave inactive
 Heteronuclear diatomic molecules (such as HCl, HF, CO) – have permanent
dipolemoment (polar compound) -- change of dipole occurs during the rotation –
hence interaction with radiation takes place – Therefore, heteronuclear diatomic
molecules are microwave active.