el out in vacuum and hence oelow 170 nm.

Hence
the region below 170 work has to be carried
ultraviolet region. Fig. 5.3 shows a nm is called the vacuum
Qty& vacuum spectrograph.The light s
from the slit S falls on the
grating G and the diffraction spectrum
received on the photographic plate is Fig. 5.3.
R
Application of ultraviolet spectroscopy
(i) All elements singly
or multiply ionised have spectra in the
All molecules produce ultraviolet region below 200 nm.
absorption spectra and many organic substances
both emission and absorption of biochemical interest have
spectra in the region. Their structures have been
of vacuum ultraviolet spectroscopy. revealed by the study
(ii) Electron transmission
in solids are of importance in solid state
spectrumin the region 30 to 10 nm physics. Studies of ultraviolet
are useful in the theoretical explanationof the phenomenonof
photoconductivity, fluorescence and
phosphorescence and the transmission and absorption bands of
dielectrics.
(iii) Observations of emission
spectra in the vacuum ultravroletregion have been useful in
astrophysics in explaining unusual types
of stellar spectra. By such studies, surface temperaturesof
hot stars has been determined.
5.4.Rayleigh's Scattering
Rayleigh showed theoretically that the
intensity of scattered light is inversely proportional to
the fourth power of the wavelength i.e., I —1 This is known as Rayleigh's law of scattering. I is
4
also proportional to the square of the volume of the particle. The blue colour of the sky is due to the
greaterscattering of short wavelengths by the dust suspensionsin the atmosphereor by the air
molecules. This type of scattering simply produces separation of wavelengths originally present in
the incident light. No wavelength can be present in the scatteredlight which is not present in the
incident light i. e, no new wavelength is created. For this reason, Rayleigh scattering is called coherent
scattering.

8AMAN EFFEC
5.5.Discovery
While studying the scattering of light, Raman found that when a beam of monochromaticlight
waspassed through organic liquids such as benzene, toluene, etc., the scattered light contained other
frequenciesin addition to that of the incident light. This is known as Raman effect.
The original arrangement used by Raman was simple in design. A round-bottomedglass flask
was filled with pure dust-free benzene. The liquid was strongly illuminated by the mercury blue line
 132 Optics and
Spectrosco
of wavelength 435.8 nm. The scattered light was examined through a
spectroscope in a
perpendicular to that of the incident beam. It was observed that the spectrum contained, indirection
addition
to the original wavelength (435.8 nm), some lines which had wavelengths longer as
well as shorter
than the original wavelength. These lines of modified wavelengths are known as Raman lines
lines having wavelengths greater than that of the incident wavelength are called Stokes lines The
those having shorter wavelengths are called anti-stokes lines. The Stokes lines are found to be
intense tinn the anti-stokes lines. Most of the Raman lines are strongly polarised. more
The 'displacement of the modified spectral lines from the exciting line, when measured
wavenumbers, depends only on the scattering substanceand is independent of the wavenumberin
the exciting radiation. The Raman spectrum is thus characteristic of the scattering substance. of
Raman effect is quite different from Rayleigh scattering. In Rayleigh or coherent scattering, there
is no change in wavelength. But in Raman scattering, the scattered light contains modified Wavelengths
as well as the original wavelengths. For this reason, Raman effect is also called incoherent scattering
and is consid as the optical analogue of the Compton effect.
5.6. Experimental Study of Raman Effect
The apparatus siown in Fig. 5.4 first developed by Wood, is used for studying Raman effect
in
liquids. It consists of aglass tube AB containing the pure experimental liquid free from dust
and air
bubbles. ne tube is closed at one end by an optically plane glass plate Wand at the other
end it is
drawn into a horn (H) and blackened on the outside.
Light from a mercury arc Sis passed through a filterFwhich allows only monochromatic
radiation
ofX—435.8 nm to pass through it. The
tube is surroundedby a water-jacket
(J) through which water is circulated
to precent overheating ofthe liquid. A w
semi-cylindrical aluminium reflector
R is used to increase the intensity
of illumination. The scattered light
coming out of W is condensed
on the slit of a Spectrograph.The
spectrograph must have a large light
gathering power and the prism must Spectrograph
s
have a large resolving power. A short
Fig. 5.4.
focus camera is used to photograph
the spectrum.
Original line •—- 435.8 nm
On developing thephotographicplate,itexhibitsanumber
Antistokes' line Stokes' line
ofstokes' lines, a few anti-stokes lines and a strong unmodified
line (Fig. 5.5).
Characteristics of Raman lines :
(J) The Stokes lines are always more intense than anti-
stokes' lines.
(2) The Raman lines are symme@icallydisplaced about
the parent line. Fig. 5.5.
(3) The frequency difference betweer the modified and parent line represents the frequency Of
the corresponding infrared absorption lil

5.7. Quantum Theory of Raman Effect

Raman effect is due to the interaction between a light photon and a molecule of the scatterer•
Suppose a photon of frequency, VI is incident on a molecule and there is a collision between the two•
Spectroscopy 133

m = mass of the molecule, VIand

v'2its velocitiesbefore and after impact, E I and E 2 the intrinsic
•esof the molecule before and
en after collision. Let v2 be the frequency of the scattered photon.
App • g the principle of conservation of energy,

E2 + + hV2= El + —mvj + hVl h.

We ay assume that the K.E. of the
molecule is unaltered during the process. Hence,
E2 + hV2 = El + hV1or V2—VI = ...(2)
h h
Three cases may arise :
(1) When there is no change in the energy
of the molecule, El = 4. Then VI v2. This represents
the unmodified line.
(2) If E El , then, v2 < VI. This representsthe Stokes line. It means that the molecule has
absorbedsome energy from the incident photon. Consequently the scattered photon has lower energy
or longer wavelength.
(3) If E < El , then, v2 > VI. This represents the antistokes line. It means that the molecule was
previouslyin the excited state and it handed over some of its intrinsic energy to the incident photon.
Thescattered photon thus has greater energy or shorter wavelength.
Since the molecules possess quantised energy levels, we can write,
El -E 2 = nhvc ...(3)
wheren = 1, 2, 3... etc., and the characteristic frequency of the molecule.
In the simplest case n = 1, Eq. (2) reduces to
v2=v1 ± v
Eq. (4) shows that the frequency difference VI —v2 between the incident and scattered photon
correspondsto the characteristic frequency Vcof the molecule.
Raman effect and fluorescence. Raman effect and fluorescence resemble each other in that the
incidentlight in both the cases suffers a change of wavelength and lines of new wavelengths appear
in the spectrum of either. But the Raman effect is quite different from fluorescence. We compare the
twophenomena in the table.

Raman Spectra Fluorescence Spectra

1. Spectral lines have frequencies greater The frequencies of the lines in the fluorescent
and lesser than the incident frequency. spectrum are always less than the incident frequency.
2. The frequency shifts of the Raman Frequencies ofthe fluorescent lines are determined
lines are determined by the scatterer by the nature of the scatterer,
rather than the frequencies themselves.
3. Raman lines are strongly polarised. Lines are not polarised.

5.8.Applications
(l) Raman effect and molecular structure. A qualitative identificationof Raman spectrum
in the evaluation of the wavelength of the lines, their intensities,and state of polarisation.
COnsists
Investigationof bond angles, bond stiffness, and other structural confirmation require Raman data
in addition to infrared studies.
(i) Diatomic molecules. From the analysis of Raman spectra of a diatomic molecule, we can
havean idea about the nature ofthe chemical bond existing between the atoms. In a diatomic molecule,
 134 Optics and Spectroscopy

the frequency of vibration of the atoms is given by v = — where F is the restoring force,per
27t g
unit displacement and is the reduced mass of the molecule. It is seen that a molecule in whi h the
force binding the atoms is great should have higher characteristic frequency than one in w ch the
force is weak. This force depends upon the nature of interatomic bonds. In covalent m ecules
polarisability is considerably changed by the nuclear oscillations due to the nuclei. This ap reciable
change ih polarisability gives rise to intense Raman lines. In electrovalent molecules, t binding
electrons definitely change over from one nucleus to the other in the formation of the leculeso
that the polarisability of the molecule is little affected by nuclear oscillations and henc no Raman
lines will appear.
(ii) Triatomic molecule. Dealing with triatomic molecules (of type AB2), the uestions to
be decided are : Whether each molecule is linear or not and, if linear, whether it i symmetrical
(B - A -B) or asymmetrical ( B - B - A). From the number and intensity of the observed lines in the
Raman effect in conjunction with infrared data, it is possible to draw important conclusions about
molecular structure, Theory leads to the following rule, known as the rule of mutual exclusion.It
states thatfor molecides with a centre of symmetry, transitions that are allowed in the infrared are
forbidden in Raman spectra and vice versa. The rule does not imply that all transitions forbidden
in one must occur in the other ; i.e., some transitions may be forbidden in both. On the other hand,
certain transitions can occur both in the infrared and in the Raman spectra in the case of molecules
without a centre of symmetry.
Examples : (a) C02 has two very strong bands in its infrared absorption spectrum at 66800 and
234900 m-l while only one strong band in its Raman spectrum at 138900m-l . None of these bands
occur both in Raman and infrared spectra. Hence, it follows from the rule of mutual exclusion,
that
C02 molecule has a centre of symmetry. This implies that the molecule is linear and symmetric
and
hence it should be represented by O —C —O.
(b) Nitrous oxide (N20) has three absorption bands at 222400, 128500 and
58900 m-l of which
the first two appear in the Raman spectrum. Thus the molecule cannot have a
centre of symmetry
though linear. Hence the molecule has the unsymmetrical structure N - N - O .
In a similar manner, the bent symmetric structure of a water molecule
o
represented by Fig. 5.6 is revealed by Raman Effect. Thus the study ofRaman
spectra of different substances enables one to classify them according to
their molecular structure. 1200
(2) Raman effect in crystals is complimentary to X-ray crystal study
and provides information about the binding forces in crystals. Fig. 5.6.
(3) Various chemical effects like strength ofchemical bonds,
electrolytic dissociation, hydrolysis,
etc., have been understood through Raman effect. Specific heat capacities
of solids, brilliance of
metals and their molecular structure have been explained by Raman effect.

5.9. Nuclear Magnetic Resonance

Introduction : Spectroscopy may be defined as the interaction between
matter and electromagnetic
radiation, such that energy is absorbed or emitted according to the
relation AE = hv.
Here, A E = energy difference between the initial and final states of
matter,
v = frequency of the electromagnetic radiation.
Nuclear Magnetic Resonance (NIIIR)is a branch ofspectroscopy in
which radio frequency waves
induce transitions between magnetic energy levels of nuclei of a
molecule. The magnetic energy
levels are created by keeping the nuclei in a magnetic field.
Without the magnetic field, the spin states ofnuclei are degenerate, i.e.,
possess the same energy
and energy level transition is not possible. When a magnetic field is applied,
there is splitting up Of
nuclear energy levels. Radio frequency radiation can cause transitions between
these energy levels•