Rot.spectra

1
Microwave Spectroscopy
or Rotational Spectroscopy
Applied Chemistry
Course CHY101
2
Regions of Electromagnetic Radiation
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.
Energy 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
Table lamp, Tube light (400 nm -800 nm or
400790 THz)
UHF TV, cellular, telephones. (300 MHz and 3 GHz)
Sun Lamp
X-ray
FM Radio, VHF TV. AM Radio
Microwave ovens, Police radar, satellite
stations-- (3 to 30 GHz)
3
Electromagnetic Radiation
4
Electromagnetic Wave
5
Regions of Electromagnetic Radiation
6
The interaction of radiation with matter
http//hyperphysics.phy-astr.gsu.edu/hbase/mod3.ht
ml
7
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.
8
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.
9
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
10
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....

11
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.
IMPORTANT

• 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.

12
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 m2 (r0 -
r1)
13
RIGID ROTOR
Moment of inertia about C IC m1r12 m2r22
m2r2r1 m1r1r2 r1r2 (m1 m2)  
? reduced mass,
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

14
Energy is quantized
Planck suggests that radiation (light, energy)
can only come in quantized packets that are of
size h?.
Plancks constant
h 6.626 10-34 Js
Energy (J)
Planck, 1900
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, ?, (units m or cm or mm)
Recall
3. The wavenumber,
(units cm-1 or m-1)
Recall
15
Rotational Spectra of Rigid Diatomic molecule
Rotational Energy Levels for rigid rotor
Where
16
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
17
Rotational Spectra of Rigid Rotor
Selection Rule Apart from Specific rule, DJ
?1, Gross rule- the molecule should have a
permanent electric dipole moment, m . Thus,
homonuclear diatomic molecules do not have a pure
rotational spectrum. Heteronuclear diatomic
molecules do have rotational spectra.
18
Rotational Energy levels
19
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.
IMPORTANT

• 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.