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CHEM 21112
Atomic and Molecular
Spectroscopy
References:
1. Fundamentals of Molecular Spectroscopy
by C.N. Banwell
2. Physical Chemistry by P.W. Atkins
Dr. Sujeewa De Silva
Sub topics
• Light and matter
• Polarizability and molar polarization
• Molecular Spectroscopy
Vibrational spectroscopy
Rotational spectroscopy
• Raman spectroscopy
• Electronic Spectroscopy
Spectroscopy, in general
-is the study of light interaction with matter
Interactions between light and matter determine
the appearance of everything around us
Light & Matter can interact in a number of different ways:
• Matter can transmit light (glass, water).
• Matter can reflect or scatter light.
• Matter can gain energy by absorbing light.
• Matter can lose energy by emitting light.
Movie screen scatters light from the projector
in all directions
Interactions between light and matter determine the appearance of
everything around us
Absorb radiation
Black surface
Reflects radiation
White surface
Transmit all radiation
Colourless surface
Wavelength (nm)
Colour
Absorbed
Colour
Observed
380 – 420
Violet
Green-Yellow
420 - 440
Violet-Blue
Yellow
440 – 470
Blue
Orange
470 – 500
Blue-Green
Red
500 – 520
Green
Purple
520 – 550
Yellow-Green Violet
550 – 580
Yellow
Violet-Blue
580 – 620
Orange
Blue
620 – 680
Red
Blue-Green
680 - 780
Purple
Green
CuSO4
solution
Emit blue
radiation
Absorb red/orange light
The Bunsen burner is used for elemental analysis.
Li
Na
K
e- can have only specific (quantized) energy values
• Energy levels or "shells― exist for electrons
in atoms and molecules.
Evidences:
Observations of light emitted by the elements is
one evidence for the existence of shells, subshells
and energy levels. (Flame Test)
The brilliant colors of fireworks result from jumps of
electrons from one shell to another of mixture of
metal atoms in explosive powder.
Bohr’s Model of the Atom
(1913)
1. e- can have only specific
(quantized) energy values
2. light is emitted as e- moves
from higher energy level to a
lower energy level
n (principal quantum number) = 1,2,3,…
RH (Rydberg constant) = 2.18 x 10-18J
The Bohr Model of the Atom
excited state
The atom is less stable in an excited
state and so it will release the extra
energy to return to the ground state
ground state
Electromagnetic Radiation (EMR)
Electromagnetic radiation
• Electromagnetic radiation is an energy wave that
is composed of an electric field component and
a magnetic field component.
 When radiation in the visible region falls on the human eye, it is the
interaction of the electric component with the retina which results in
detection.
 It is also the electric character of electromagnetic radiation which is most
commonly involved in spectroscopy.
The Effect of Radiation on Atoms and Molecules
• Atoms can absorb and emit energy in only discrete
chunks (called quanta)
 Suggested by Max Planck (1858-1947)
• All EMR / light behave as packets of energy called
photons.
A photon is a particle of EMR
 Albert Einstein (1879—1955)
e- can have only specific (quantized) energy values
• EMR is a stream of photons, each
traveling in a wave-like pattern, moving at
the speed of light and carrying some
amount of energy
Wavelength and Amplitude
07_02.JPG
Wavelength x Frequency = Speed

m
x

=
1
s
c
c = 
m
s
c is defined to be the rate of travel of all electromagnetic energy
in a vacuum and is a constant value—speed of light.
c = 3.00 x 10 8 m s-1
This speed c differs from one medium to another, but not enough to
distort our calculations significantly.
Electromagnetic energy
• Einstein found a very simple relationship between the
energy of a light wave E (photon) and its frequency 
Energy of light (E) = h × 
h - Planck's constant'' = 6.626 × 10-34 Js
c =  or` = c/  orh` = c/
hc
E  hν 
 hcν
λ
1
ν 
λ
hc
E  hν 
λ
• Bluer light has shorter λ, higher frequency, and more
energy.
• Redder light has longer λ, lower frequency, and less
energy.
hc
E  hν 
λ
What is a Spectrum?
A spectrum is the distribution of photon energies coming from a
light source:
- Shows how many photons of each energy are emitted by the
light source?
• Spectra are observed by passing light through a spectrograph:
- Breaks the light into its component wavelengths and spreads
them apart (dispersion).
Absorption
Emission
• White light pass through a monochromator and
then though the sample
• Detector records the intensity of transmitted light
as a function of frequency
Atomic spectrum
- less interaction between atoms in the gas
phase
-absorb specific wavelengths
Molecular spectrum
- Molecular interactions and collision leads
to distribution of energy,
- absorb a range of wavelengths
• Beer-Lambert Law
• The Beer-Lambert law is the linear relationship between
absorbance and concentration of an absorber of
electromagnetic radiation.
• The general Beer-Lambert law:
A = ελ x b x c
A
b
c
ελ
-
is the measured absorbance
is the path length
is the analyte concentration
wavelength-dependent molar absorptivity coefficient
• where I - is the intensity of transmitted radiation
I0 - is the intensity of incident radiation
Experimental measurements are usually made in
terms of transmittance (T)
T = I / I0
A = log10 (I0 / I ) = ελ b c
The relation between A and T is:
A = - log10 (I / I0 ) = - log10 (T) = ελ b c
Absorbance
Beer-Lambert Law
Concentration
Deviation from Bear Lambert law
Low c
High c
The Beer-Lambert law assumes that
all molecules contribute to the
absorption and that no absorbing
molecule is in the shadow of another
Some important terms
• Dipole moment:
• There is a net charge separation due to different
electronegativities of the atoms of a molecule
+δH
•
Cl-δ
Molecular Dipole Moments (m)
Molecular Dipole Moments are the vector sum of the individual bond
Dipole moments. They depend on the magnitude and direction of the
bond dipoles.
NH3
H2O
H
H N
H
H
:
m  1.5 D
H
CO2
:
O
:
1.9 D
..
..
:O =C = O :
0.0 D
CH3Cl
H
H
H
C Cl
1.87 D
Potential energy
When two charges q1 and q2 in a polar molecule,
are separated by a distance r in a vacuum, the
potential energy (v) of their interactions can be
given by
q1
r
q2
q1 q 2
v
4  0 r
Electric force lines produced by an electric dipole
Effect of external electric field
• The electrons and nuclei of molecule are mobile to a
limited degree.
• For that reason, when a polar or non-polar molecule is
placed in an electric field a small displacement of the
charge will take place.
• As a result, a dipole would be introduced in the molecule,
in addition to the permanent one that may exist.
DP = µp+ µi
Polarizability and Molar Polarization
• Polarizability is the relative tendency of the electron
cloud of an atom to be distorted from its normal shape
by the presence by an external electric field (or near by
ions or dipole)
• It is experimentally measured as the ratio of induced
dipole moment (µ ind ) to the electric field E which
induces it:
•
α = µ ind / E
•
The units of α are C2 m2 V–1
• Polarizabilities(α) in different directions along the bond, called ‘longitudinal polarizability’
•
and
perpendicular to the bond, called ‘transverse polarizability’
• The molar polarization or induced polarization is given by
(Debye equation)
 r 1 M
•
p
•
•
•
•
•
•
•
r  2


Where,
P is the molar polarization
M is the molar mass of the sample
ρ is the mass density of the sample
εr is the relative permittivity where εr = ε/ε0
ε is permittivity of the medium
ε0 is vacuum permittivity
Molecular Spectroscopy
• The free motion of molecules in the gas
phase can be divided into 3 components
•
1) Translational
•
2) Vibrational &
•
3) Rotational
• Translation : The motion of the molecular
•
center of mass
• Rotation: The molecular motion around the
center of mass while all inter-atomic distances
and angles remain constant
• Vibration: Relative motion of atoms with respect
to each other
• Rotational and vibrational energy levels
are quantized (have specific values for a
molecule) E
3
E2
E1
• Translational motions of molecules are
not quantized
•
- no discrete spectral lines associated
•
with this motions
•
- no translational spectroscopy
Quantized energy levels - have certain, particular, discrete energy values
Molecular absorption processes
~10-18 J
• Electronic transitions
• UV and visible wavelengths
• Molecular vibrations
• Thermal infrared wavelengths
Increasing energy
• Molecular rotations
• Microwave and far-IR wavelengths
~10-23 J
• Each of these processes is quantized
• Translational kinetic energy of molecules is unquantized
Rotational spectroscopy
Rotational spectroscopy
• Pure rational spectra of molecules are caused by the
interaction of molecules with microwave radiation of
EMR.
• The range of rotational frequencies is about
8 x 1010 - 4 x 1011 Hz
 ~ 0.75 - 3.75 mm
- nuclear transitions between the rotational energy
levels are considered
+
-
- +
- +
+
Dipole
moment
along z
axis
Diatomic Molecule with a oscillating dipole moment can absorb
electromagnetic radiation via their rotational motion.
Eg: CO, NO, and HCl
+
- +
-
• The rotation of a diatomic molecule is best described in
terms of its angular velocity (ω), about the center of
gravity of the molecule.
Figure 40-16 goes here.
A diatomic molecule can rotate
around a vertical axis..
An important quantity
for describing the
energy of rotation is the
moment of inertia( I )
mi – is the mass of the atom at distance ri
The moment of inertial about
the center of mass is
From the center of mass definition
For a diatomic molecule
Rigid rotors
 describe the molecules that do not distort under the
stress of rotation.
 the potential energy change may be set to zero since
there is no change in bond length during the rotation.
q1q2
v 
4 0 r
The energy levels obtained from solving schrödinger
equation are given by:
•
•
•
•
Ej– energy of the Jth rotational energy level/J
J – is the rotational quantum number
I – moment of inertia of the molecule/ Kgm2
h – Plank’s constant /JS
• The constant factors, rotational constant (B), are given
the symbols
cm-1
cm-1
2B
• Question 1:
• The first rotational line of CO occur at 3.84235 cm-1 (J=0 to
J=1). Calculate the bond length of a CO molecule.
•
h = 6.626 × 10-34 Js
•
c= 2.99792 x 108 ms-1
•
•
2B = 3.84235 cm-1
•
B = 1.92118 X 102 m-1
•
•
 h 
B 2 
 8 IC 
6.626 x10 34 JS
B 2
8 I x 2.99793 x108 ms 1
34
2 1
6.626 x10 Kgm s
I 2
8
1
8 x 2.99793 x10 B ms
6.626 x10 34 kgm
I 2
8 x 2.99793 x108 x1.92118 x10 2 m 1
I  14.5695 x10  47 kgm2
I  mr
2
 mc mo  2
r
I  
 mc  mo 
mC
• mc = 12.0X10-3 kg / 6.023 x 1023
• mo = 16.0X10-3 kg / 6.023 x 1023
r = 1.131Ǻ
mO
• Question 2:
• The rotational spectrum of HI shows a series of lines
separated by 12.8 cm-1. Calculate the inter atomic
distance of HI. (H = 1.007 g and I = 114.80 g)
Answer = 1.63 Ǻ
• Question 3:
• The first rotational line of 12CO is occurred at 3.84235 cm-1
and that of 13CO is occurred at 3.67337 cm-1.
• Calculate the mass of 13C.
•
• Assumption: r
12
CO
• Answer = 13.0007g
=r
13
CO
Rotational spectrum of non-rigid rotor
• High energy rotations do not obey the rigid rotor
model.
• Because molecular bond/ inter-atomic distance is
not completely fixed; the bond between the atoms
stretches out as molecule rotates faster.
• - hence change the moment of inertia (I)
• - higher values of the rotational quantum numbers.
• - This effect can be accounted by introducing a
•
correction factor known as the centrifugal
•
distortion constant (D)
•
Units of D - cm-1
• The energy levels of the non-rigid molecule is defined
as
2
4
h
h
2
2
Ej  2 J ( J 1)
J
(
J

1
)
Joule
4 2
8 I
32 I re k
•
•
•
•
•
•
EJ – energy of the Jth rotational quantum level/J
J – is the rotational quantum number
I – moment of inertia of the molecule/ Kgm2
h – Plank’s constant /JS
re – is the equilibrium bond length/m
k – is force constant of the bond/ Nm-1
j
h
h3
2
2

J
(
J

1
)

J
(
J

1
)
8 2 IC
32 4 I 2 re kC
cm-1
j
h
h3
2
2

J
(
J

1
)

J
(
J

1
)
8 2 IC
32 4 I 2 re kC
• Simplification can be achieved by using the rotational
constant (B) and defining the centrifugal distortion D.
•
3
h
D
4 2
32 I re kc
•
B = h / 8π2IC
•
εJ = EJ / hc = BJ(J+1) –DJ2(J+1)2 cm-1
• εJ is a symbol which express energy in frequency
units
• Normally D has a value much less than B.
eg: HCl has B = 10.395 cm-1 and D = 0.0004 cm-1.
D is large when a bond is easily stretched
B= h / 8π2IC
B ∞ 1/ r2