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
|Gamma rays||X rays||VacUV||UV||VIS||NIR||IR||FAR IR||: WAVE||RADIO|
|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
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.
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
b) Higher orders
c) slit diffraction
Equilibria - acid base pH control
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.
1. Eye - Colorimetry
No numerical Readout Most sensitive to Green
2. Photovoltaic Cells
No power supply needed
Response like eye
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
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
Glass 30-50 nm band width
5-20% T at max.
2. Prisms - Dk2A
3. Gratings - parallel lines on glass
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
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
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 Beers 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. Jobs 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