What is spectroscopy?Spectroscopy is the study of the interaction ofelectromagnetic radiation with matter.

Electromagnetic radiation refers to various forms oflight, including X-rays, UV and visible light, infra-redradiation, microwaves and radio waves.

Atoms and molecules are composed of electrically chargednuclei and electrons, and may interact with the oscillatingelectric and magnetic fields of light, absorbing theenergy carried by the light.

However, molecules do not interact with all wavelengths(i.e., energies) of light - the molecules only interact withlight that has the right amount of energy to promote themolecule from one discrete energy level to another (this isreferred to as a spectroscopic transition).

More specifically: Spectroscopy may be defined as theinteraction between matter and electromagnetic radiationsuch that energy is absorbed or emitted according to theBohr frequency condition, E = hL

Generally, spectroscopy is basically an experimentalsubject and is concerned with the absorption, emission orscattering of electromagnetic radiation by atoms andmolecules.

Photons of varying energies pass through materials ifthey do not bridge the gap between any pairs ofquantized energy levels.

If photons are of the correct energy, they are absorbedby the material - this absorption causes a transition,whereby energy is made available to promote particlesor states up to higher energy states.

In the related processof emission, energyis released when anexcited statestructure falls to alower energy state

Spectroscopic Transitions

An example: 127I79Br

7.961 × 10-21 J

2.662 × 10-21 J

)E = 5.299 × 10-21 J

The diatomic molecule 127I79Br vibrates in its lowest vibrationalstate (ground state) with an energy of 2.662 × 10-21 J. The nextlowest vibrational energy level available to the molecule is at7.961 × 10-21 J. If far-infrared light of energy 5.299 × 10-21 J isshone on the molecule, the molecule in the ground state ispromoted to its first excited vibrational state -light of any otherenergy does not have any influence!

270 cm-1260255 265

The representativevibrational spectrumhas a peak (which is notinfintely sharp!) centredat 266.8 cm-1

= 5.299 × 10-21 J

What is a spectrometer?

Consider the example of white light and the magnesiumcomplex in chlorophyll:

Eye and brain make a spectroscope which sorts out thevarious wavelengths of light emerging from the object - thebrain “sees” different colours

Narrow range: 400 nm - 700 nm

More sophisticated equipment is required to probe matterwith light!

GREEN

A spectrometer is a device for exciting, dispersingand/or detecting different frequencies and intensities ofEM radiation.

Early Spectroscopy

spectroscopist visible lightspectrum

dispersingelement

(spectrometer)

EM radiationsource

Sir Isaac Newton, 1667

Josef Fraunhofer, 1814Designed a spectroscope which enabled the first high resolutionacquisition of a visible light photograph of the sun: “...saw an almostcountless number of lines which are darker than the rest of the colouredimage; some appeared to be almost perfectly black. I have convincedmyself that these lines are due to the nature of the sun and not an opticalillusion.” - he formed the basis for astrophysical spectroscopy

Early Chemical AnalysisAn emission spectrum from Comet Winnecke wasrecorded by William Huggins in 1868

The dark lines arise from absorption of sunlight, butthere was no explanation for the bright lines

Huggins examined the emission spectrum of sparkedethylene (C2H4) and found the exact same sets of bands,leading him to conclude that some of the cometary matterarises from the presence of double-bonded carbon atoms(C2). This was the first example of chemical analysis byspectroscopy, and interestingly arises from aninvestigation in the field of astronomy.

Spectroscopy entered a new era with the discovery byGustav Kirchoff and Robert Bunsen that substances emitdifferent light spectra when burnt. The discovery led tothe development of a system of fingerprints that could berecorded and compared. The ability to analyse light fromthe sun and other planets was also noted ultimatelyleading to the discovery of Helium by Norman Lockyer.

Modern Chemical AnalysisAnother example from astronomy: astronomers useinfra-red spectroscopy (and other techniques) toobserve the Orion Nebula, and found signalscorresponding to polyaromatic hydrocarbons (PAH’s)believed to be contained within the interstellar dust.

Opticalphotograph of the“HorseheadNebula”

Comparison of IRdata obtained fromthe Orion Nebula, andIR spectra ofcoronene obtained inthe laboratory

See http://cosmos.colorado.edu/astr1120/l9S1.htm

Applications of SpectroscopyAstronomy:# Measurement of temperature of space, stars and other

cosmic entities# Determination of chemical composition of stars, planets

and their atmospheres

Chemistry:# Analytical chemistry, elemental analysis# Synthetic chemistry (NMR, IR, UV, etc.)# Correlation of molecular structure to bulk physical

properties of matter# Reaction kinetics and chemical equilibria

Environmental:# Atmospheric studies (ozone layer, etc.)# Toxic emissions from vehicles, factories, etc.

Medicine:# Magnetic resonance imaging (MRI)# Optical scans, PET, CAT# Diagnostics with IR sources and detectors

Physics:# Atomic clock# Accurate determination of atomic and molecular

structure# New experiments in teleportation

MatterMatter and light are intimately interwoven in nature-divided by a very fine line

Matter is composed of electrons and nuclei

Physical Properties:

masslargely due to the nuclei; thermal properties

electric chargeatoms and molecules are bound together byelectrostatic interactions

magnetismnucleus interacts with magnetic fields;little consequence for atomic or molecularstructure

spinleast “tangible” property; closest classicalanalogy: electrons and nuclei are spinning likelittle planets

Light: Wave-like natureLight: Electromagnetic (EM) Radiation has a dual nature:Wave and Particle

I. Wave Behaviour of Lightc = 8< c = 2.9979 × 108 m s-1

Interference: Two waves produced near one another willinterfere constructively or destructively. Waves bendaround obstacles in their paths.

When it hits an aperature, it is diffracted

When an EM wave hits an interface, it is reflected orrefracted

one slit two slits

Light: Particle-like nature

II. Particle Nature of LightMax Planck (1858-1947) & Albert Einstein (1879 -1955): Light is particle-like, and exists in quantizedenergy packets known as photons (Planck - 1900)

E = h< h = 6.6262 × 10-34 J s

Photoelectric Effect (1888)Heinrich Hertz (1857 - 1894)

# Below frequency <0, no electrons emitted# At frequencies > <0, KE proportional to < - <0# Number of electrons proportional to intensity# Electrons emitted even with very low intensity light, and

almost instantaneously (< 10-9 s)

Matter and Light

Matter and light blur together in form and function:

# Light conveys electromagnetic force from point topoint and instant to instant, interacting withminuscule charges that constitute matter

# Light arises from charge in motion

# Light sets charge in motion

All of chemistry (i.e., every event outside of thenucleus of the atom) is related directly to someelectromagnetic influence (we will not considergravity, or weak and strong nuclear forces)

Five senses: touch, hearing, taste, smell, sightAll chemical and electromagnetic!

To see matter is to illuminate matter

Spectroscopy: Special “sight” for observing theatomic and molecular structure of matter

Electromagnetic WavesComposed of orthogonal electric (E) and magnetic (B)fields, the electromagnetic wave oscillates in space andtime, rising and falling in amplitude, and varying infrequency (with a fixed speed of light)

EM radiation (light) can be described by a plane wave:

E(r,t) ' E0 cos(k @r & Tt % N0)

E(r,t) ' Re(E0 e i(k @ r & Tt % N0))or

The wave propagates through space in the direction k, andE is an electric field (V m-1) which is perpendicular to k. The wave has an angular frequency T = 2Bv = 2B/T, where< is the frequency and T = 1/< is the period.

E0 is the amplitude of the wave, the wavevector k has amagnitude *k* = k = 2B/8, and the wave has a phase givenby k·r - Tt + N0, where N0 is an initial arbitrary phase.

Electromagnetic Waves, 2

E0

E

B

k

EM waves carry energy in the direction of propagation. Theenergy density stored by electric fields and magnetic fields aregiven by 0E = ½gE2 and 0B = ½B2/µ, respectively. Both play arole in transport of energy. The rate of energy transport perunit area is given by the Poynting vector

S '1µ0

E × B

Since E and B are perpendicular, the magnitude is given byS = EB/µ0. A condition of the solution for a plane wave isBm = Em/c; thus, the average intensity for a plane wave is

S '1

cµ0

E 2m sin(kx & Tt) '

1cµ0

E 2m

2

Electromagnetic Waves, 3Wavelength and frequency are related by 8< = c. In a vacuum,c = c0; generally, c = c0/n where n is the index of refraction ofthe medium through which the light is propagating. Thus:

The oscillating EM wave can be defined spatially and/ortemporally. If the wave is along a spatial axis defined by z,and examined at one instant in time, t = 0, then for anarbitrary phase N0 = 0:

80

n< '

c0

nHistorically, it was only possible to measure 8 accurately inthe visible and IR regions of the spectrum, and then correct forn to give 80. Thus, this lead to the reporting of wavenumbers, , which have units of reciprocal centimeters (cm-1)and are still commonly reported today, despite the prevalenceof SI units (m-1 are not used!)

< ' 1/80

The EM wave can be observed at a single point, z = 0, as afunction of time

E ' E0 cos(kz) ' E0 cos 2Bz8

E ' E0 cos(Tt) ' E0 cos(2B<t)

EM waves are transverse waves. If a wave propagates along z,then there are two orthogonal (independent) transversedirections, x and y. Thus, light can be polarized, since E maybe along x, y or anywhere in the xy-plane. Thus,

E ' Ex i % Ey j

This rough progression of thought lead to thinking aboutthe dual nature of light, with both particle- and wave-likecharacteristics:

1. Many physicists ca. 1900 believed that most majorproblems had been or could be solved by the classicalphysics of Newton and Maxwell.

2. Several outstanding problems remained which couldnot be rationalized by classical physics:# blackbody radiation (UV catastrophe)# heat capacities of solids at low temperatures# photoelectric effect# atomic spectra (we will discuss this further!)

3. Max Planck proposed that energy is quantized, orhas discrete values determined by E = nhL.

4. Albert Einstein explains the photoelectric effect (andheat capacities of solids) using the idea of quantizedenergy. He proposes that light has a dual nature,possessing both wave- and particle-like behaviour.

5. Louis de Broglie proposes that both light and matterpossess wave- and particle-like properties, and that thecharacteristic wavelength can be calculated for anymoving object, with 8 = h/p

Physics circa 1900

Black Body RadiationObjects which are heated emit electromagnetic radiation. As the temperature of an iron block increases, it glows redand eventually emits white light (said to be “white hot”).

A black body is an ideal emitter ofEM radiation, which absorbs allfrequencies of EM radiation

Inside a cavity, radiation is continuallyabsorbed and re-emitted by the walls(not reflected). The radiation whichleaks out of the small pinhole of theblack box has been absorbed andemitted continually, and is in thermalequilibrium with the walls.

As the temperature is increased, theenergy density (i.e., g = E/V)increases, and the peak of energyoutput shifts to shorter wavelengths(i.e., from red to blue).

This phenomenon was treatedunsuccessfully with classical physicsby a number of physicists, includingWilhelm Wien, Josef Stefan andLudwig Boltzmann

Ultra-Violet CatastropheLord Rayleigh, with some help from James Jean, proposedthat the EM field was a collection of oscillators of allpossible frequencies L = c/8, and their average energy atroom temperature was kT. The Rayleigh-Jeans Law is:

dg ' Dd8 D '8BkT84

The law was successful for longer wavelengths of radiation(including IR and some visible EMR), but failed for shorterwavelengths of radiation. The law predicted thatoscillators of very short wavelengths (e.g., X-rays, UV) areexcited, even at low temperatures, implying that coolobjects glow in the dark - this of course is absurd.

where D is the proportionality between energy density andd8 (over that infinitesimal range of wavelengths).

Fast oscillators emitshort wavelengthradiation

Slower oscillators emitlonger wavelengthradiation

Quantization of EnergyMax Planck accounted for black body radiation byproposing that each electromagnetic oscillator is restrictedto discrete values, and cannot be continuously variedarbitrarily (for RJ Law, all possible energies are allowed).

Quantization of energy therefore refers to the limitationof energies to discrete values (contrary to classical physics,where all energies across a continuum are possible).

Planck accounted for the relationship between energy andfrequency with his famous equation:

E ' nh< n ' 0, 1, 2, ...where h = 6.6260755 × 10-34 J s.On this basis, he derived the Planck distribution:

dg ' Dd8 D '8Bhc85

1e hc /8kT

& 1

This expression is similar to the RJ Lawat low frequencies, but as the frequency(energy) increases, the energy densityapproaches zero, in agreement withexperimental observations. For long 8,hc/8kT / hL/kT « 1, and therefore:

e hc /8kT& 1 ' 1 %

hc8kT

% ... & 1 . hc8kT

Photoelectric EffectIt was well known from classical experiments that light hadwave-like behaviour and properties - however, there was anexperiment conducted by Heinrich Hertz and later byPhilipp Lenard (1862-1947)

Electrons were ejected from the metal plate (emitter)when light of the appropriate frequency hits the metal, andare received at a second plate (collector), with the currentmeasured at A.

Classically: More intense light beams should deliverenough energy to the electrons on the surface to eject them.

Observation: Light must be above some thresholdfrequency in order for the electrons to be ejected.

The voltage could easily be varied in this electricalapparatus in order to enhance or retard the movementof the electrons between these plates. The energymust be > qV0 to strike the plate - so photoelectronenergies could be measured accurately

Particle Character of LightObservations of the photoelectric effect:1. No electrons are ejected unless the frequency is higher

than some threshold frequency (i.e., EM radiation has aparticular energy), regardless of the light intensity

2. The kinetic energy of the ejected electrons is linearlycorrelated to the frequency of the applied radiation, butindepedent of the intensity of the radiation

3. As long as the frequency of the EM radiation is higherthan the threshold, the number of electrons ejected fromthe metal varies linearly with the intensity of the light

12

mev2

' hL & M

Einstein again: The first law of thermodynamics requiresthat in order for an electron to be ejected from the metal:

where M is the work function of the metal (energy neededto remove the e- from the metal) (i.e., hL > M for ejection!)

Wave/Particle DualityEinstein’s proposal of photons and the “corpuscular”nature of light were not immediately accepted, though theydid explain the photoelectric effect exactly. He eventuallywent on to propose that light could be explained by “afusion of wave and particle theories”. Not many peoplebelieved in the photon part of things at this time.

In 1924, Louis de Broglie (1892 - 1987) made anastounding proposal which immediately caught Einstein’sattention: “Propagation of a wave is associated with themotion of a particle of any sort...photon, electron, proton orother.” In other words, he proposed that light and matterboth have wave-like and particle-like characteristics.

electron

group velocityof wave packetphase velocity

of wave packet

de Broglie suggested that waves always accompaniedparticle in their motion through space and time, always inphase with the “internal process” of the particle. Thephase velocity is the speed at which the wave crest movesand the group velocity is the speed of the reinforcementregions when many waves are superimposed. Theseregions display all of the properites of a particle (p, U, etc.)

de Broglie Wavelengthde Broglie started with Einstein’s famous equation for theenergy content of anything

E = mc2 = (mc)(c)Since mc is just mass times speed, this is equivalent tomomentum of the photon, p = mv. And, since c = L8

E = (p)(c) = (p)(L8)

From the suggestions of quantization of energy fromPlanck and Einstein, i.e., E = hL, we can write

hL = (p)(L8)

Which after some simple algebra rearranges to

8 = h/pThus, if the wavelength of light is decreased, themomentum of the individual light photons is increased. This means that as the mass or the velocity of a particleincreases, the momentum increases, and the wavelengthdecreases - so most macroscopic objects have very smallwavelengths which cannot be observed.

However, if the particle is small enough, it should bepossible to detect the wave-like behaviour of particles.

Most physicists at the time regarded this idea as completelypreposterous. Einstein believed it though, and said “deBroglie has lifted the great veil...”

Experimental Proof of Particle Wavesde Broglie remarked at his Ph.D. defence that “matterwaves might be observable in crystal diffractionexperiments, like those carried out with X-rays”

In 1925, experiments with electrondiffraction conducted by G.P.Thomson (1892-1975), (whose fatherJ.J. Thomson coincidentallydiscovered the particle-like nature ofelectrons 30 years earlier) andDavisson and Germer showed thatelectrons scatter off of crystals ofpure metals, producing diffractionpatterns akin to those of light waves.de Broglie had one more idea, which became crucial forexplaining atomic structure. He thought that when anelectron moves in an atom, the associated wave isstationary standing wave - and only certain discretefrequencies can produce this standing wave

The Electromagnetic Spectrum

Spectroscopy in all EM rangesI. (-rays (< 0.01 nm)

Associated with nuclear processes

II. X-rays (20 nm to 0.1 nm) [eV]Dislodge core electrons which are bound tightly nearthe nucleus: X-ray photoelectron, X-ray fluorescenceand Auger Spectroscopy

III. UV/Visible Light (700 nm - 4 nm) [nm or Å]Excitation of weakly bound valence electrons -thoseresponsible largely for chemical bondingsub-divisions: visible (780 - 400 nm), near-UV (400 -200 nm), vacuum-UV (200-10 nm)

IV. Infra-Red Radition (100,000 - 700 nm) [cm-1]Vibrational excitation in molecules - this too isquantized: Ev = (v+1/2)hL0 [cm-1]sub-divisions: far-IR (33-333 cm-1), mid-IR (333-3333cm-1) and near-IR (3333 - 13000 cm-1)

V. Microwaves (0.01 - 20 cm) [GHz]

Rotational excitation in molecules - quantized as EJ =BJ(J+1); also: EPR spectroscopy -flip of an electron’sspin

VI. Radiofrequency Waves (20 cm - 3 km) [MHz]NMR spectroscopy - especially in the FM region:nuclear spin flips