Download Introduction to Spectroscopy

Introduction to Spectroscopy
Lecture Date: January 22nd, 2013
What is Spectroscopy?


The study of the interaction between radiation and
matter
“Analytical spectroscopy”, as defined in this class,
covers applications of spectroscopy to chemical
analysis
History of Analytical Spectroscopy

1666: Isaac Newton (England) shows that white light
can be dispersed into constituent colors, and coins the
term “spectrum”
– Newton also produced the first “spectroscope” based on lenses,
a prism, and a screen



1800: W. Herschel and J. W. Ritter show that infrared
(IR) and ultraviolet (UV) light are part of the spectrum
1814: Joseph Fraunhofer noticed that the sun’s
spectrum contains a number of dark lines, developed
the diffraction grating
1859: G. Kirchoff obtains spectra of the elements,
explains the sun’s spectrum
The Visible Spectrum of the Sun
(Black lines are absorption by elements in the cooler outer region of the star)
Figure from National Optical Astronomy Observatory/Association of Universities for Research in Astronomy/National Science Foundation, http://www.noao.edu/image_gallery/html/im0600.html
History of Analytical Spectroscopy

1870: J. C. Maxwell formalizes and combines the laws
of electricity and magnetism
 1900 to present: More than 25 Nobel prizes awarded to
spectroscopists, including:
– 1902: H. A. Lorentz and P. Zeeman
– 1919: J. Stark
– 1933: P. A. M. Dirac and E. Schrodinger
– 1945: W. Pauli
….
– 1999: A. Zewail
Introduction to Spectroscopy
 The electromagnetic

spectrum
Each color you see is a
specific (narrow) range of
frequencies in this
spectrum
Figures from NASA (www.nasa.gov)
The Electromagnetic Spectrum
 Modern life (not just analytical spectroscopy) revolves
around the EM spectrum!
Properties of Electromagnetic Radiation
 Wave/particle duality
 Perpendicular E and B
Note – this figure
shows polarized
radiation!
components
– E = electric field
– B = magnetic field
 Wave properties:
– Wavelength (frequency)
– Amplitude
– Phase
1
0.5
Long wavelength
(low frequency)
1
2
3
4
5
1
2
3
4
5
-0.5
-1
 
c

1
0.5
Short wavelength
(high frequency)
-0.5
c = the speed of light (~3.00 x 108 m/s)
 = the frequency in cycles/second (Hz)
 = the wavelength in meters/cycle
-1
Interference of Radiation
 Monochromatic: radiation containing a single frequency
 Polychromatic: radiation containing multiple frequencies


Constructive interference:
when two waves reinforce
each other
Destructive interference: when
two waves cancel each other
The Interaction of Radiation and Matter

Electromagnetic radiation travels fastest in a vacuum
 When not travelling in a vacuum, radiation and matter
can interact in a number of ways

Some key processes (for spectroscopy):
–
–
–
–
Diffraction
Refraction
Scattering
Polarization
– Absorption
Transmission of Radiation

The velocity at which radiation travels (or propagates)
through a medium is dependent on the medium itself
 When radiation travels through a medium and does not
undergo a frequency change, it cannot be undergoing a
permanent energy transfer
 However, radiation can still interact with the medium
– Radiation, an EM field, polarizes the electron clouds of
atoms in the medium
– Polarization is a temporary deformation of the electron
clouds
Transmission and Refraction
 The refractive index (ni) of a medium is given by:
ni 
c
i
c = the speed of light (~3.00 x 108 m/s)
i = the velocity of the radiation in the medium in m/s
ni = the refractive index at the frequency i
 Refractive index measures the degree of interaction
between the radiation and the medium
– Liquids: ni ~ 1.3 to 1.8
– Solids: ni ~ 1.3 to 2.5
 Refractive index can be used to identify pure liquid
substances
Refraction
 When radiation passes through an interface between two
media with different refractive indices, it can abruptly
change direction
 Snell’s law:
sin 1
n1 v2


sin  2
n2 v1
1 = the velocity of the radiation in medium 1 in m/s
n1 = the refractive index in medium 1


Snell’s law is a consequence
of the change in velocity in
the media
Reflection always occurs at
an interface. Its extent
depends on the refractive
indices of the media
1
Medium 1
Medium 2
2
Diffraction
 Fraunhofer diffraction:
– Also known as far-field diffraction, parallel beam
diffraction
– Important in optical microscopy
 Fresnel diffraction
– Also known as near-field diffraction
Diffraction

Bragg diffraction – multiple slit Fraunhofer diffraction:
– Important for instrument design, crystallography
n  2d sin 
 Diffraction gratings:
– Widely used in
spectroscopic instruments
to separate frequencies
(can be made precisely)
http://www.astro.virginia.edu/research/observatories/40inch/fobos/images/grating.jpg
Scattering
 Rayleigh scattering (an elastic process):
– Scattering of small amounts of radiation by molecules
and atoms (whose size is near to the wavelength of
the radiation)
scattering 
1

4
 Mie scattering: applies to large particles, involves
scattering in different directions.
– Practical use in particle size analysis
Polarization

Polarization of EM radiation – a simple classical picture:
Figure from Sears, et al., “University Physics”, 7th Ed., 1988
Coherent Radiation
 Coherent radiation fulfils two
conditions: (1) it has the
same frequency or set of
frequencies, and (2) it has a
well-defined and constant
phase relationship
– Coherent radiation is “crosscorelated” in that the
properties of one beam can
be used to predict those of the
other beam
 Examples of coherent
radiation:
– Lasers
– Microwave sources (masers)
Coherent radiation: different
frequencies (colors) with a defined
phase relationship interfere to produce
a pulse
Diagram from wikipedia.org (public domain)
Incoherent Radiation
 Produced by “random”


emission, e.g. individual
atoms in a large sample
emitting photons
Actually is coherent, but just
to a tiny (undetectable)
extent
Also known as “continuous”
radiation
 Examples of incoherent
radiation:
– Incandescent light bulbs
– Filament sources
– Deuterium lamps
Incoherent radiation: different
frequencies (colors) combined to
produce continuous radiation with
varying phase, frequency and
amplitude
Diagram from wikipedia.org (public domain)
More Properties of Electromagnetic Radiation
 Wave and particle behavior: photons behave as both
waves and particles
– Quantum mechanics developed around the concept of
the photon, the elementary unit of radiation
 Planck’s law:
E  h
 E is the energy of the photon in joules
 h is Planck's constant (6.624 x 10-34 joule seconds)
  is the frequency of the radiation
Absorption and Emission
 Absorption is a process accompanied by an energy
change
– involves energy transfer of EM radiation to a
substance, usually at specific frequencies
corresponding to natural atomic or molecular energies
 Emission occurs when matter releases energy in the form
of radiation (photons
Higher energy
Absorption
Lower energy
Emission
E = h
Energy Levels

Several types of quantum-mechanical energy levels
occur in nature:
– Electronic
– Rotational
– Vibrational (including phonons and heat)
– Nuclear spin (other nuclear energy levels usually need
high energies to access)
 For each of these, a discrete quantum state and energydriven transitions between these states can be studied
(as opposed to a continuous range of energies)
Selection Rules
 Selection rules:
 Simple rules that are derived from transition moment
integrals (usually via symmetry arguments) that
express which energy level transitions are allowed

Example (for rotational energy levels of a rigid linear
rotor such as a diatomic molecule):
J  1

A forbidden transition is usually still possible, but often is
weaker than allowed transitions
The Uncertainty of Measurements
 Because the lifetimes of quantum states can persist for
short periods, it can be difficult to measure their energies
accurately
 This is usually stated in the form of an “energy-time
uncertainty”:
Et  
The Uncertainty Principle
 The uncertainty principle:
it is not possible to know both
the location and the momentum of a particle exactly – a
fundamental limit on all measurements
 In Heisenberg’s terms, the act of measuring a particle’s
position affects its momentum, and vice versa
 In equation form:
xpx  12 
– In other words, if you know the position of a particle to within x,
then you can specify its momentum along x to px
– As the uncertainty in x increases (x ), that of px decreases (x
), and vice versa
Spectra and Spectrometers
 Spectra are usually plotted as frequency vs. amplitude
– Instead of frequency, wavelength or energy can also
be used
– The choice of x- and y-axes is often dependent on the
particular technique, its history, etc…
– In most techniques, a key parameter is the
frequency/energy/wavelength resolution
 Spectrometers:
instruments that measure the interaction
of radiation with matter, so the properties of such
interactions can be studied
Spectroscopy in Analytical Chemistry
 Widely used approach for characterizing systems ranging
from chemical physics to biology, from individual atoms to
the largest molecules
 Some of the most common techniques are:
– UV-Visible spectroscopy
–
–
–
–
Fluorescence spectroscopy
IR spectroscopy
Raman spectroscopy
X-ray spectroscopy
– NMR spectroscopy
– EPR spectroscopy
Further Reading
P. W. Atkins and R. S. Friedman, Molecular Quantum
Mechanics, 3rd Ed. Oxford University Press, New York
(2003).
R. P. Feynman, R. B. Leighton, M. Sands, The Feynman
Lectures on Physics, Addison-Wesley, Reading, MA
(1977).
M. Fox, Optical Properties of Solids, Oxford University
Press, New York (2010).
Physics textbooks often contain good discussions of basic
spectroscopic phenomena.