Lecture Date: January 22nd, 2013

Introduction to Spectroscopy

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

Figures from NASA (www.nasa.gov)

The electromagnetic spectrum

Each color you see is a specific (narrow) range of frequencies in this spectrum

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

components– E = electric field– B = magnetic field

Wave properties:– Wavelength (frequency)– Amplitude– Phase

1 2 3 4 5

-1

-0.5

0.5

1

1 2 3 4 5

-1

-0.5

0.5

1

Long wavelength(low frequency)

Short wavelength(high frequency)

c = the speed of light (~3.00 x 108 m/s) = the frequency in cycles/second (Hz) = the wavelength in meters/cycle

c

Note – this figure shows polarized radiation!

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:

ii

c n

c = the speed of light (~3.00 x 108 m/s) i = the velocity of the radiation in the medium in m/sni = 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:

1

2

2

1

2

1

sinsin

vv

nn

1 = the velocity of the radiation in medium 1 in m/sn1 = 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

2

Medium 1

Medium 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

Diffraction gratings:– Widely used in

spectroscopic instruments to separate frequencies (can be made precisely)

sin2d n

http://www.astro.virginia.edu/research/observatories/40inch/fobos/images/grating.jpg

Bragg diffraction – multiple slit Fraunhofer diffraction:– Important for instrument design, crystallography

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)

Mie scattering: applies to large particles, involves scattering in different directions.

– Practical use in particle size analysis

4

1

scattering

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 “cross-corelated” 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 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

hE

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

E = h

Higher energy

Lower energy

Absorption Emission

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 energy-driven 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):

A forbidden transition is usually still possible, but often is weaker than allowed transitions

1J

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”:

tE

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:

– 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

px x 21

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.