Electromagnetic Radiation

Electronic Vector

Magnetic Vector at 90 deg


Wavelength (l) crest to crest distance 10-9 NM ==> 100 Km

Speed (c) speed of light

vacuum 3.00 x 108 m/sec

slower in all other media - slowed by electronic interactions

h = Refractive index = speed in vac > 1

speed in medium

function of wavelength

light of different energy moves at different rates in medium other than vacuum.

sigma wave number = waves/cm = cm-1 = 1/ Lambda in vacuum

Frequency ( sigma ) = waves passing fixed point/sec.

period (p) time per wave crest nu = 1/p

all are related nu = c



E = hnu = hc/8 = hcsigma


Intensity and power

P = energy/sec/area

I = energy/sec/unit solid area (steridians)


Properties of Waves


Constructive (in phase) Interference


Destructive (out of phase) Interference

Electromagnetic spectrum

0.01D 0.10D 10 nm 200 nm 340 nm 800 nm 2.5 : 25 : .04 cm 25 cm
0.10D 100D 200 nm 400nm 800 nm 2.5 : 25 : .04 cm 25 cm 1000Km


Interaction of matter and Electromagnetic Radiation

All can interact with matter in a wide variety of ways.

Most interaction depends on size of particle relative to wavelength.

Particles < 1/2 Lambda are transparent.

Electronic vector Interactions

X-rays - - ionize atoms eject inner shell e-

UV-VIS - energy charges in valence e-

IR - molecular vibrations

microwave - molecular rotations

Magnetic vector Interactions ( in magnetic field)

microwave - electron spin changes

radio wave - nuclear spin changes


Spectroscopy - 1 or more courses required to cover in any detail

Open peephole on what is there to be known.

Show energy levels in diagrammatic form


        _____3s ____ 3p ____ 3d

E      ____ 2s ____ 2p

         ____1s                    describe transitions

Emission occurs when e- state drops. Studied for atoms.

Absorption occurs when photon of exactly the energy of the transition strikes the atoms. Studied for molecules (hard to exited enough to emit.)

Molecular spectroscopy uses molecular rather than atomic orbitals in diagram. S , P , N

CAChe can calculate them and show relative energies.



Quantitative aspects of Absorption

Beer's Law Beer-Lambert Law (Harry Gray's version)


Log relationship between

distance light travels in an absorbing medium

and concentration

if each thin segment (dx) absorbs some fraction of all of incident light (Px)

dP = -k Px C dx

k= cross section area of absorbing region of molecule (0rbital or conjugated system)

PX = Probability of transition occurring (0 => 1 )

C = Concentration

-dP/Px = kC dx

Integrate over entire path length b

log(P0/P) = k/2.303 Cb = , bC or (abC)

P = Transmittance (T)


log 1 = -log T = A Absorbance - A is dimensionless


A = abc C in gm/l

A= e bc C in moles/l

bC = cm*mol/1000cm3 = mol/1000cm2

a units cm2/gm       e  unit = cm2/mol



Light must be monochromatic


Enter at a right angle.

Extensions - Multicomponent Systems

A 1 = , 1bC1 + , 2bC2 + , 3bC3 +.....

Total abs. = sum of absorbencies of individual absorbing species.

Measure at several wavelengths solve simultaneous equations. Calc. conc. of all species.

HP instrument 6 or 7 component mixture solves 125 simultaneous eq. Each wavelength in region.

Best possible accuracy.

Deviations from Beers Law - Accuracy


1. Non-monochromatic light

value of , or a not constant across bandwidth of spectrometer.



Negative deviation at high conc.

Beers Law

Negative Deviation

Concentration error and lower sensitivity.

Need more standards.

Wide slits give lower A values - Value measured on ST320 or Spec 20 will be less than for HP diode array which may be less than PE 330

Stray light

a) Reflections

b) Higher orders

c) slit diffraction

Chemical Deviations

Equilibria - acid base pH control

Activity coef.


Solvent effects


Diagnostic Tool for Deviations

Plot A vs path length.

Beers Law - straight line

Stray Light - negative deviation


Instrumentation for Optical Spectroscopy.


Spectrometer - Record light through sample at given wavelength.

Spectronic 20, HP Diode Array Spectrometer

Spectrophotometer - Ratio of 2 beams PE 330

A. Sources of Radiation

1. Black body radiators - Tungsten lamp 2870oK - 1.5 micron peak

Quartz - Iodide - 3600oK more UV & VIS

2. Discharge Lamps

H2 or D2 165 to 360 Nm.

D2 lasts longer and brighter than H2.

B. Detectors

1. Eye - Colorimetry

No numerical Readout Most sensitive to Green

2. Photovoltaic Cells

No power supply needed


Response like eye

3. phototube

Photo emissive surface

Work function - photon energy

needed to eject e-'s photo cathodes designed for various regions of the spectrum.

each photon produces 1 or more e-

some thermal e- also produced

shot noise

dark current function of temp.

4. Solid State Detectors - Photodiodes and change couple devices.

Photodiodes - pn junction conduct in reverse direction due to photon flux.

Linear photodiode Arrays

512 diodes - detect 512 wavelengths at once - complete spectrum not scanned. HP Spectrometer

Good visibility sensitivity

Rapid response

high linearity

C. Monochromators

1. Filters

Glass 30-50 nm band width

5-20% T at max.

2. Prisms - Dk2A

3. Gratings - parallel lines on glass

Practical considerations

A. Cells

Glass or Plastic Vis only

Quartz UV-VIS-NIR $60-100 each

Flat parallel windows best

Cylindrical cells must always be in the same position

(mark on spec 20 cells)

B. Solvents - must be transparent

UV cutoff

Solvent UV Cutoff
Acetone 330
Acetonitrile 210
Benzene 280
Carbon disulfide 380
Chloroform 245
Dichloromethane 233
Ether 220
Ethyl Acetate 260
Hexane 210
Methanol 210
Water 200







Errors in concentration due to errors in Transmittance

Assume error is a constant value of Transmittance (T)

A=abC A= -log T

C = - log(T)/ab

take derivative of C with respect to T

dC/dT = -0.4343/T(ab)

Want relative concentration error dC/C so divide by

C= -log(T)/ab

ab term cancels

dC/C has a minimum at T=0.368 (36.8%)

Use this equation to calculate the relative error in concentration (dC/C) for a given relative error in Transmittance (dT/T).

Problem assignment will help you explore this topic for yourself.


Applications of Spectrophotometry

Direct determination of a chromophoric compound - anything that absorbs strongly.

Absorbances range from 0 to 500,000 , wide range of sensitivities.

1. use tabulated absorbance

2. measure absorbance from a single standard

3. prepare calibration curve

Form a chromophore with non-absorbing species

1. metals react with ligands to form colored complexes - large number of analytical methods developed to use this

2. organic derivatives - 2,4-dinitrophenyl hydrozones

azo coupling (acid rain nitrate detn.)

vanillate ion in lab


1. Direct Use of Beer’s Law – Least Precise and Accurate (one point calibration) assumes blank=0.00

2. Using a Standard Curve

Known concentrations vs Abs. – Least Squares


3. Standard Addition Method



Useful if matrix of sample has background absorbance which cannot be accounted for in a blank or calibration curve.


Three approaches to Std. Add.

1. Add micro amounts of standard and ignore dilution.

2. Add standard and correct for dilution.

3. Dilute unknown and standard additions to constant volume.






Graphical treatment of std. addition












4. Spectrophotometric titration












E. Use of Spectrophotometry to study reaction stoichiometry - metal complexes, enzyme substrate complexes, etc.

1. Job’s Method _ Continuous variation method. Use where ratio is close to 1:1

Total moles of two reactants constant. Plot Mole ratio vs A

2. Mole-Ratio method - use where ratio is large

Like a titration. Treat constant molar conc. of metal with varying molar amounts of ligand. (Plot A vs Moles ligand)



3. Slope Ratio Method- use where binding is weak and large excesses of reagent are required to force complete reaction.

xM + yL =====> MxLy

Add small amounts of metal to large excess of ligand - drives reaction to completion even if Kf is small. Measure slope of graph of Abs vs conc. Slope = eb/x

Add small amounts of ligand with large constant excess of metal - excess metal drives reaction to completion.

Slope = eb/y

(eb/x)/(eb/y) = y/x




Excited electron returns to ground state and emits a photon.

Excitation - GS to Excited Electronic State

Fluorescence - Excited Electronic State to Excited Vibrational state of electroninc GS.

Eexc > EFlu

Lambda exc < Lambda em

Very sensitive and selective since 2 wavelengths involved

Non-Linearity at solutions with A> 0.03