Analytical Spectroscopy Review λ = wavelength ν = frequency V = velocity = ν x λ = 2.998 x 10 8 m/sec = c (in a vacuum) ν is determined by source and does not change as wave propogates, but V can change as wave passes through matter, it becomes less than c. Therfore, λ also changes in matter. Electromagnetic Spectrum & Quantum transitions Nuclear Inner electron Valence electron Molecular vibrations Molecular rotations Nuclear spin
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Analytical SpectroscopyReviewλ = wavelength
ν = frequency
V = velocity = ν x λ
= 2.998 x 108 m/sec
= c (in a vacuum)
ν is determined by source and does not change as wavepropogates, but V can change as wave passes through matter, it becomes less than c. Therfore, λ also changes in matter.
Electromagnetic Spectrum & Quantum transitions
Nuclear Inner electron
Valence electron Molecular
vibrationsMolecular rotations
Nuclear spin
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Superposition of wavesPrinciple of superposition – when two or more wave disturbances occupy the same space at the same time, the resultant disturbance can be predicted by the sum of the individual disturbances.
Electric Field representation
y = A sin (2πνt + φ) = A sin (ωt + φ)
A = amplitude
ω = angular frequency
)sin(1
iin
iitotal tAY φω +∑=
=
Constructive interference
Destructive interference
Wavelength Selection
Separation of EM radiation into it’s constituent frequency components (or colours).
In analytical spectroscopy, we may have wavelength selection devices BEFORE sample or AFTER sample, depending on the type of spectroscopy.
Line sources - have radiation at discrete quantized energies.
Mercury lamps - many discrete lines in UV and visible
Hollow cathode - for atomic spectroscopy
Lasers - a special light source in a class of it’s own, many different types and wavelengths
Fig. 1 Typical spectral irradiance of 200 W Hg Lamp.
Stimulated and Spontaneous Emission
M* 6 M + hν
Emission of photon from excited state species is random in time and direction
hν + M* 6 M + 2 hν
Emission of photon from excited state species is induced by first photon. Both photons that leave have the same direction, phase and frequency…coherent radiation!
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BlackbodiesBlackbody radiator absorbs all EM radiation without reflection (ie-black) but is in thermal equilibrium with surroundings…it’s rate of absorption is equal to rate of emission.
Planck’s Law (flux distribution)
112
/5
2
−=Φ kThc
b
ehc
λλ λπ
Wien’s Displacement Law (max λ)
TKnm
khc 6
max10897.2
5×
==λ
λ in nm, T in kelvins
Total radiation of black body
Stefan-Boltzmann constant
Kirchoffs Law
Real bodies are not "black", they do not absorb radiation with 100% efficiency at all wavelengths. Kirchoff's law states that if an object absorbs radiation with efficiency, ελ, , then it emits radiation with a fractional efficiency ελ of the blackbody emission at temperature, T.
Φλ (T) = ελ(T) Φλb(T)
The emission spectrum is known if we know the absorption spectrum and T
428
4432
45
0
1067.5
152
−−−
∞
=
==Φ=Φ ∫KWmx
TThckdtotal
σ
σπλλ
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Solar Radiation Spectra
Solar radiation flux at sea level is less than at the top of the atmosphere due to reflection by clouds, aerosols and absorption features by O2, O3, H2O and other trace gases.
The earth as a blackbody radiator
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LasersLight Amplification by Stimulated Emission of Radiation
Power source~100% ~95-99%
Lasing medium
Properties of Lasers
Monochromatic - single wavelength
Coherent - all photons appear to originate from a single point, electrical fields are all in phase.
Bright – spectral irradiance (intensity per unit wavelength) is much higher than conventional sources
Focussing – can be focussed to extremely small spots (λ/2)
Pumping and Population Inversions
Pumping – an external source provides energy to the lasing medium in order to achieve a "population inversion". A population inversion is necessary for a laser to operate. Pumps may include electrical discharge, optical energy from a flashlamp, or another laser (pump laser).
Population inversion – there more molecules or atoms are in the upper state (S2,) than in the lower state (S1) of the quantum transition. N2 > N1
x x x x x x x x x x x x
x x x x x x x x
S2 - State 2, E2 - Energy 2 N2 - # of molecules
S1 - State 1, E1 - Energy 1 N1 - # of molecules
Lasing transition – S2 S1
∆E = E2 – E1 = hν = hc/λ
N2 > N1
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2-Level Systemx x x x x x x x x x x x
x x x x x x x x
S2 , E2 , N2
σ2 1 cross section of stimulated emission
S1 , E1 , N1
σ1 2 cross section of absorption
Each absorption event causes a decrease in the radiant flux of photons, Φ, inside the lasing cavity. Each stimulated emission event causes an increase in Φ. From spectroscopic theory, it is known that σ1 2 = σ2 1.
The change in radiant flux, dΦ, inside a laser cavity along the axis starting from an arbitrary point, and travelling a distance dz is given by...
For lasing action to occur, the radiant flux of photons inside the cavity must be amplified ..ie- must be > 0. Therefore, (N2 - N1) > 0 OR N2 > N1 for lasing action.
If N2 > N1, dΦ > 0, population inversion exists, SE dominates, lasing action occurs.
If N2 = N1, dΦ = 0, no change in Φ (but considering other losses, NO lasing)
If N2 < N1, dΦ < 0, Φ decreases with z, absorption dominates, ...ie- Beers Law.
Boltzmann Considerations
Boltzmann Equation
Nj = number of molecules or atoms in state j
N0 = number of molecules or atoms in state 0 (ground state for example)
Pj = multiplicity of state j (2 electrons per state X number of levels with energy j)
P0 = multiplicity of state 0.
DE = energy difference between state j and 0 (Ej > E0) .
k = Boltzmann constant (1.28 x 10-23 J K-1)
T = temperature (Kelvin).
For 2 states with equal multiplicity, Nj / N0 < 1.0 at all times since T > 0K , and ∆E > 0. The best we can do is to heat a system to high T or to minimize the difference in energy between two states, but even if we do this, Nj/N0 only approaches 1.0, but is always less than 1. Therefore we cannot achieve a population inversion by heating a laser system....we must achieve a population inversion in some other way.
∆−=kTE
PP
NN jj exp
00
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3-Level and 4-Level Laser Systems
S1, E1
S0 , E0
fast non radiative transition
S2, E2
laser transitionpumpE
S2, E2
S0 , E0
fast non-radiative transition
S3, E3
laser transitionpumpE
S1, E1
fast transition
3-Level System
If σ0->2 > σ0->1, and if the 2 1 non-radiative transition is fast, then we can achieve a population inversion between state 1 and 0 by optically pumping at the E2 – E0 wavelength.
4-Level System
Since the laser transition in a 4-level system does not end up in the ground state, the population in the lowest state of the laser transition, S1 is very low. Thus it is even easier to obtain a population inversion, N2 > N1 in this type of system.
4-level systems are common. The first demonstrated laser, a ruby laser, was based upon a 3-level system
Types of LasersGas Lasers
He/Ne – a mixture of neutral gases in the laser cavity. the laser active gas is Ne. He gas is used for collisional pumping....see energy diagram. Lines at 632.8, 612.0 , 594.1, 543.5 nm. The red laser at 632.8nm is most common and most intense.
He/Cd – economical continuous wave laser source with lines at 442 and 325 nm. Cadmium is the active medium. heat is applied to a reservoir of Cd metal in order to vaporize the metal.
Ar+ - used extensively in Raman and laser induced fluorescence spectroscopy. Many laser lines available, most intense are at 488 and 514 nm.
Solid State Lasers - active medium is a host atom embedded in a solid state material.
Ruby – Cr III in Al2O3. pumped with a flash lamp; 3-level system.
Nd:YAG – Nd+3 in Yttrium Aluminum Garnet. 1064 nm IR laser. Very high power. these can be frequency doubled (532 nm) or tripled (355 nm). Used for commercial applications.
Dye Lasers – active lasing medium is a dye or mixture of dyes dissolved ain a solvent that is pumped through the lasing cavity. these lasers can be "tuned" to lase over a broad range of λ's. They are often pumped with a primary laser.
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Wavelength selectorsfilters, prisms, gratings and monochromators
these devices are used in all types of optical spectroscopy in order to select a specific range of wavelengths (bandwidth) from a much broader band of light.\
Excitation, Fluorescence and Phosphorescence of Phenanthrene
excitation
fluorescence phosphorescence
Schematic of a generic fluorescence instrument
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Filter Fluorometer
Excitation filterEmission filter
Spectrofluorometer
ORPDA or CCD
multichanneldetector
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Excitation and Fluorescence Spectra of Anthracene
Excitation Spectra – similar to absorbance spectra. Obtained by measuring luminescence at a fixed wavelength while scanning the excitation monochromatorwavelength.
Fluorescence (emission) Spectra – obtained by holding excitation wavelength constant while scanning the emission monochromator
Factors affecting fluorescence
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FAF2
Fluoresc vs abs
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Phosphorescence
Phos instrument
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Chemiluminescence 1
Chemilum 2
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Quiz 5Quizzes – worth 6%, best 3 out of 5.....2% each.For those who need a final quiz, it will be held on Monday April 4. Two times, 2 versions...QUIZ 5A - 12:30 - 1:00 QUIZ 5B – 2:30 – 3:00
Please meet at my office (PS 301) 5 minutes before quiz time, the location to write will be announced at that time.
Topic – Luminescence & Atomic Spectroscopy.
For those who do well, the quiz could be worth 4%, 2% applied to quiz mark, 2% applied to your last test mark (if you do better on the quiz than your test.