spectroscopy V and VI

Spectroscopy High-Yield Notes (Units V and VI)

Built from the Spectroscopy Theory and Spectroscopy Applications decks. Items the slides flag as "know this" are marked [KNOW].

PART V. SPECTROSCOPY THEORY

V.A Electromagnetic radiation

Order of the spectrum [KNOW]

• Lowest to highest energy: radio, microwave, IR, visible, UV, X-ray, gamma.

• Visible runs from about 800 nm (red, low energy) to about 400 nm (blue/violet, high energy).

Light-matter interactions

Absorption energy

• The photon energy must equal the gap: ΔE = hν = hc/λ.

• Worked example, Hg lamp at 253.7 nm:

  • Step 1: E = (6.626e-34 J·s)(3e8 m/s) / (2.537e-7 m)

  • Step 2: top = 1.988e-25 J·m, so E = 7.84e-19 J per photon

  • Step 3: multiply by Avogadro's number to get 472 kJ per mole of photons

Quantum primer

• Atoms have only electronic states. Molecules also vibrate and rotate, so they have many more transitions.

• Light can move molecules between states, but not every transition is allowed.

Selection rules [KNOW]

1. Photon energy must equal the transition gap: E = hν = ΔE.

2. Spin multiplicity must not change: ΔS = 0.

   • S is the total spin quantum number (add up the spins, each ±½).

   • Multiplicity = 2S + 1.

   • S = 0 gives 2(0) + 1 = 1, a singlet.

   • S = 1 gives 2(1) + 1 = 3, a triplet.

3. Symmetry rules.

   • UV-vis: σ to σ* and π to π* type transitions.

   • IR: there must be a change in dipole moment.

Absorption lines

• Atoms give sharp line spectra in the gas phase. Example: Na 3s to 3p at 589.3 nm (about 203 kJ/mol).

• Molecular gas-phase electronic spectra show resolved vibronic fine structure.

• In solution the fine structure is lost and bands broaden, because of collisions and solvent perturbation of the quantum states.

Emission

• Excited states have a finite lifetime (τ). The uncertainty principle means there is always an uncertainty in the excited-state energy, so every transition has a width (natural or uncertainty broadening).

• Radiative relaxation emits a photon matching the energy gap.

• Non-radiative relaxation emits no photon (collisional deactivation, heat released to the solvent).

• Emission can be spontaneous or stimulated. Stimulated emission is the basis of lasers.

• Atomic emission line sources: Hg lamp, Nd:YAG laser, hollow cathode lamps. Excitation is by electrical means.

Jablonski diagram vocabulary [KNOW]

• IC (internal conversion): non-radiative, same multiplicity.

• ISC (intersystem crossing): non-radiative, different multiplicity.

• EC (external conversion): excitation lost to the solvent as heat.

• Fluorescence: radiative, same multiplicity (fast).

• Phosphorescence: radiative, different multiplicity (slow).

• The Jablonski diagram has no x-axis.

V.B Generalized instrument design

Five components

1. Radiation source (tunable or single wavelength, correct region of the spectrum).

2. Wavelength selection (scanning or broadband; some techniques need more than one).

3. Sample containment (static or dynamic).

4. Detector (sensitive, responds in the wavelength range of interest).

5. Signal processing and readout (Fourier transform, signal averaging).

Ideal source: high intensity, flat intensity versus wavelength, low variability.

Continuous sources (slides: "know examples, not details")

• Many are black-body emitters. Intensity and wavelength depend on temperature, and λmax is proportional to 1/T.

Line sources

• Low-pressure metal vapor lamps: Na (589.3 nm), Hg (254 nm).

• Hollow cathode lamp (HCL): element specific.

• Lasers: based on stimulated emission.

  • Problem: emission and absorption rates scale with the number of molecules in the excited and ground states.

  • Need a population inversion (more molecules in the excited state), which is impossible in a two-level system.

  • So lasers need three or four levels with suitable lifetimes.

  • Output is high intensity, monochromatic and coherent.

Monochromators (wavelength selectors)

• Bandwidth is the span of wavelengths leaving the monochromator.

• Gratings beat prisms on: linear dispersion, larger useful range, compact size.

• Gratings lose on: cost, more stray light, higher-order harmonics (overtones).

Detectors [KNOW the comparison]

• Geometry trap [KNOW]: with a single PMT the sample must go after the grating. With a photodiode array the sample goes between the source and the grating.

V.C Quantitation with absorption

Beer-Lambert law

• Transmittance: T = I/I0 (range 0 to 1). Percent transmittance: %T = 100 × T.

• Absorbance: A = -log(T) = -log(I/I0).

• A = ε b c, where ε is molar absorptivity (L mol^-1 cm^-1), b is path length (cm), and c is concentration (mol/L).

Worked example: riboflavin

• Given: ε = 3.24e4 L mol^-1 cm^-1, b = 1 cm, 30% decrease in radiant power.

• Step 1: 30% decrease means P/P0 = 0.70.

• Step 2: A = -log(0.70) = 0.155.

• Step 3: c = A / (ε b)

• Step 4: c = 0.155 / (3.24e4 × 1)

• Step 5: c = 4.8e-6 M.

Quantitation methods

• Calibration curve: interpolate between standards. Use internal standards. Only valid where Beer's law is linear.

• Standard addition: add increasing amounts of standard to fixed volumes of sample.

  • Plot A versus the amount of standard added.

  • The x-intercept equals the negative of the initial concentration.

  • Used when the matrix could change the response.

Worked example: Cu in an alloy

• Sample 0: 100 mg alloy in 100 mL, A0 = 0.30.

• Sample 1: 100 mg alloy in 95 mL, plus 5 mL of 0.1 M Cu(NO3)2, so the volume is again 100 mL. A1 = 0.45.

• Step 1: Added Cu = (5 mL × 0.1 M) / 100 mL = 0.005 M.

• Step 2: A0 = k·c0 and A1 = k·(c0 + 0.005).

• Step 3: A1 / A0 = 0.45 / 0.30 = 1.5.

• Step 4: So c0 + 0.005 = 1.5 c0, which gives 0.005 = 0.5 c0, so c0 = 0.010 M.

• Step 5: Moles Cu = 0.010 mol/L × 0.100 L = 1.0e-3 mol.

• Step 6: Mass Cu = 1.0e-3 mol × 63.55 g/mol = 0.0636 g = 63.6 mg.

• Step 7: %Cu = 63.6 mg / 100 mg = about 64% Cu.

Deviations from Beer's law

• Expect a linear response. Negative deviations are usual, positive ones are possible. Best fix: dilute.

Why %T error matters. A is logarithmic but we measure %T, and the error in %T is constant. Same 1% T error, ε = 1000, b = 1 cm:

• Best results (error under 3.5%) come from staying between about 15% and 65% T, which is roughly A = 0.82 down to 0.18.

Chemical deviations

• Beer's law holds only for dilute solutions. Molecules must not interact, because interactions alter electron clouds and energy levels.

• This gives an upper practical limit near A = 0.82.

• Too dilute, or ε too small, and the drop in intensity can't be measured well (A below 0.15). Then choose another detector.

Instrumental deviations

• Bandwidth: ε changes with λ, so always measure at the maximum of the ε versus λ curve. Use a monochromator with small bandwidth.

• Stray radiation also causes deviations.

PART VI. SPECTROSCOPY APPLICATIONS

VI.A Atomic absorption spectroscopy (AAS)

Atomic lines are very sharp (no vibrations or rotations)

• Natural linewidth is about 1e-5 nm (uncertainty principle on the excited-state lifetime).

• Doppler broadening: atoms move randomly, so their kinetic energy couples to ΔE. Blue shift is to shorter λ, red shift is to longer λ, and the peak broadens.

• Pressure broadening: collisions perturb the energy levels.

• Observed widths are still tiny: about 2 to 5 e-3 nm.

The catch: samples are rarely free gas-phase atoms. You must nebulize (turn liquid or solid into an aerosol) and atomize (free the atom from its partners). This needs a nebulizer and a heat source (flame or furnace).

Flame processes (example: Cr in an alloy)

1. Dissolve in HNO3 to get Cr3+ and NO3-.

2. Nebulize to get an aqueous aerosol of Cr(NO3)3.

3. Desolvation gives solid Cr(NO3)3.

4. Vaporization gives gas Cr(NO3)3.

5. Atomization gives Cr (g). This is what you want.

6. Unwanted side paths: excitation (Cr*), ionization (Cr+), oxidation (CrOx).

Flame goals: high atomization; low excitation, low ionization, low oxide formation. Flame temperature depends on the oxidant and fuel, the part of the flame, and the burner design.

Degeneracy (g) [KNOW]

• Rotational states: g = 2J + 1.

• Vibrational states: g = 1 always.

• Electronic states: for isolated atoms the slide gives 2l + 1 (this is likely 2J + 1; check against your lecture notes). For molecules, σ and n have g = 1 and π has g = 2.

• The instructor says g-values will be given on exams when they aren't 1.

• Why it matters: excited-state population depends on temperature and on g, so higher T means more excitation (unwanted in AAS).

Flame choice (trends to know, not every number)

• Air-acetylene is about 2300 °C. Nitrous oxide-acetylene is about 2800 to 2950 °C. Oxygen-acetylene is about 3100 °C. Air-methane is the coolest listed (about 1840 °C).

• Atomization efficiency depends on both flame and element. Examples from the table: Al is under 0.00005 in air-C2H2 but 0.2 in N2O-C2H2; Cr is 0.065 versus 0.6; Sn is 0.04 versus 0.8. Hotter flames atomize refractory, oxide-forming elements better.

• Ionization is worst for easily ionized elements (low IP): Cs (2.89 eV), Rb, K, Na, and Ba in air-C2H2. A hotter flame ionizes more.

Flame summary

Instrument path (in order): hollow cathode lamp, chopper, nebulizer and flame, grating monochromator, PMT.

• HCL: cathode made of the element under study. Inert gas (Ne or Ar) is ionized, ions strike the cathode and ablate metal atoms, some come off excited (M*) and emit lines unique to M. Bandwidth is 0.002 to 0.005 nm. Gives individual lines.

• Chopper: the flame also emits light (a DC signal). Modulating the HCL lets the detector separate lamp light from flame light. With lamp light, P = P(HCL) + P(flame); with the lamp blocked, P = P(flame). The difference isolates the lamp signal.

• Nebulizer: aspirates sample using the oxidant flow, giving droplets of 10 to 40 µm. Uniform droplets give a more stable signal; baffles (spoilers) remove large droplets.

• Monochromator: small-bandwidth grating. Biggest problems are flame light noise and absorption by impurities.

Atomizers: flame versus graphite furnace

Interferences and fixes [KNOW]

• Commercial pre-mixed modifiers contain element-specific releasing and protecting agents.

AAS summary

• More than 60 elements (limited by available HCLs).

• Excellent for quantitation, poor for qualitative work (change the lamp for every element).

• LOD: low ppm to ppb (FAAS), low ppb to ppt (GFAAS).

• Beer's law linear over about 2 to 3 orders of magnitude.

• Precision 1 to 2% relative (about 5% for GFAAS). Highly selective.

• Cost: instrument $50 to 75K by one slide (the comparison table says about $30 to 50K); about $300 to 500 per lamp.

VI.B Atomic emission spectroscopy (AES)

• The oldest spectroscopy (colored flames). Atoms are excited, then emit light, for example Na* to Na at 589.0 nm.

• Sources: flame (rarely used now), stars (astronomy), plasma torch (inductively coupled or DC).

• ICP: ionized argon (Ar+ and e-) at 4000 to 8000 °C. A spark starts it and radio-frequency radiation sustains it. Sample is nebulized into the torch, atomized and excited. The many electrons make the plasma reducing, so oxidation and ionization are suppressed.

• Monochromator: very high-quality grating (0.01 nm resolution).

• Big advantage: multi-element analysis in one run.

  • Scanning: exit slit, one wavelength at a time, computer-controlled, inefficient because most of the time is spent between lines. Uses a single PMT.

  • Simultaneous: no exit slit. Detect with a photodiode array, multiple PMTs on a Rowland circle, or a CCD camera with an Echelle grating.

AAS versus ICP-AES [KNOW]

VI.C Molecular absorption (UV-vis)

Regions: visible 400 to 800 nm; common UV 180 to 400 nm; vacuum UV 10 to 180 nm. O2 and N2 absorb near 180 nm, so work below that must be done in vacuum.

Fates of the excited state (M):* photochemistry (A + B), radiationless decay to heat, or fluorescence/phosphorescence. Lifetime ranges from about 1e-9 s to hours.

Orbitals

• π and π* require multiple bonds. n requires lone pairs.

• CH4: σ only. H2C=CH2: σ and π. NH3: σ and n. H2C=O: σ, π and n.

Allowed transitions [KNOW]

Color and complementary color: a compound absorbs one color and appears as its complement.

Inorganic color

• Transition metals have unfilled d (or f) shells. In an octahedral field, dx2-y2 and dz2 (the eg set) point at the ligands and are destabilized; dxy, dyz and dxz (the t2g set) point between ligands and are stabilized. The t2g to eg transition falls in the visible.

• The gap Δ depends on the ligand, the metal's row, and its oxidation state.

• Weak-field ligand: CrCl6 3-, λmax = 736 nm. Strong-field ligand: Cr(CN)6 3-, λmax = 380 nm. Bigger Δ means higher energy and shorter wavelength.

• Charge-transfer bands: an electron moves between ligand and metal, for example [Fe(III)(H2O)5SCN]2+ going to [Fe(II)(H2O)5SCN•]2+ (ligand to metal).

Applications

• Qualitative: not very useful (broad bands).

• Quantitative: very useful. ε is 10 to 1e5, giving a usable range of 1e-4 to 1e-7 M. Precision 1 to 3% relative. Selectivity is not great. Fast enough for kinetics, titrations and chromatography detection.

• Considerations: solvent cutoff, Beer's law linearity, work at λmax.

• Multicomponent analysis: absorbances are independent and additive, so

  • A at λ1 = ε(x,λ1) b c(x) + ε(y,λ1) b c(y)

  • A at λ2 = ε(x,λ2) b c(x) + ε(y,λ2) b c(y)

  • Measure at as many wavelengths as there are species and solve the simultaneous equations.

• Isosbestic point: for two interconverting species, the wavelength where both have the same absorbance. Its presence suggests a clean two-species conversion.

• Photometric titration: monitor A at a chosen wavelength. R, T or P (reactant, titrant, product) may absorb, which gives different curve shapes.

Instruments

• Photometer: no wavelength dispersion (filters), very cheap.

• Spectrophotometer: has wavelength selection.

  • Single beam: P0 measured once before the sample and reused. Simplest, but does not account for P0 drift.

  • Double beam: source split in two, P0 and P measured continuously (two detectors or a chopper). Compensates for source flicker and the source's power distribution. More expensive, and weaker signal from the extra optics.

  • Both are usually run in scan mode. A photodiode array measures all wavelengths at once; note the sample position relative to the monochromator.

VI.D Molecular emission (fluorescence and phosphorescence)

Jablonski sequence [KNOW]

1. Absorption (about 1e-15 s, fastest), often into excited vibrational levels of an excited electronic state. If light exits at the same energy: Rayleigh scattering. If it exits to a different vibrational level of the ground state: Raman scattering.

2. Intramolecular vibrational relaxation (about 1e-12 s) drops the molecule to v = 0 of the excited electronic state. All later processes start from v = 0.

3. Internal conversion (same molecule) and external conversion (to another molecule or solvent): radiationless, same multiplicity, need vibrational overlap.

4. Fluorescence: radiative, same multiplicity, short lived (ns to ms by the slide), broad band because many final vibrational levels are reachable. Fluorescence from S1 is preferred analytically because it is at a different wavelength than the excitation light.

5. Intersystem crossing: radiationless, different multiplicity. Spin forbidden but spin-orbit allowed. Needs strong spin-orbit coupling, from a heavy atom (Z above about 30) on or near the molecule, including in the solvent.

6. Phosphorescence: radiative, different multiplicity, also spin forbidden, so it is slow (ms to hours).

7. Competing losses: photodissociation (bond breaks after promotion into an antibonding orbital) and photochemistry (reactive center formed).

• Each pathway has a rate constant: kIC, kEC, kISC, kF, kP, kd (dissociation), kr (reaction). The fraction that fluoresces depends on kF compared with the sum of all the competing rate constants.

Why fluorescence is more sensitive than absorbance [KNOW]

• Absorbance: A = -log(P/P0) = ε b c. If you raise P0, P rises with it, so A does not change.

• Fluorescence: F = k'(P0 - P). F depends on the number of excited states created, so more P0 gives more excited states and more F.

• Detection is at a different wavelength from excitation, so background is near zero.

• Result: sub-ppb LOD and linearity over 4 to 6 orders of magnitude.

Deviations from linearity at high concentration or high ε

• Higher-order terms (Taylor series) curve the plot. Fix: dilute.

• Self-quenching: collisional deactivation (external conversion) of excited molecules.

• Self-absorption: emitted photons match an energy gap in other analyte molecules and get absorbed. Because emission is isotropic, the re-emission goes in random directions, so detected F power falls.

Instruments

• Fluorimeter: filters, no scanning. Source, filter, sample, filter, detector (detector at right angles to the source beam).

• Spectrofluorimeter: gratings; an excitation monochromator and an emission monochromator. Double-beam versions add a reference PMT and a sample PMT with a difference amplifier.

Fluorescence summary

• Good selectivity: most things don't fluoresce (tag those that don't). Aromatics often fluoresce, π to π* is favored, and polycyclic aromatic hydrocarbons fluoresce readily.

• Fluorescence is more common than phosphorescence; typically you see only one.

• Moderately expensive: pulsed lamps or lasers, two good gratings, very sensitive PMTs.

VI.E Master comparison [KNOW]

RAPID-FIRE REVIEW

Equations

• E = hν = hc/λ

• A = -log(T) = ε b c

• Spin multiplicity = 2S + 1

• F = k'(P0 - P)

• Atomic degeneracy: 2J + 1 (slide shows 2l + 1); σ and n: 1; π: 2; vibration: 1; rotation: 2J + 1

Likely exam traps

• Single PMT: sample after the grating. Diode array: sample before.

• Prisms: non-linear dispersion. Gratings: linear dispersion but more stray light and overtones.

• Fluorescence keeps the same multiplicity; phosphorescence changes it, so it is slower.

• In AAS you want atomization, not excitation, ionization or oxide formation.

• Releasing agent binds the interfering anion; protecting agent binds the analyte.

• Ionization fix: add an easily ionized alkali metal. Oxide fix: add V or Ti.

• Plasma is reducing, which is why ICP suppresses oxides and ionization.

• Quantify at λmax, and aim for A of about 0.18 to 0.82 (15 to 65% T).

• Double beam fixes source drift and flicker; single beam does not.

• Fluorescence beats absorbance in sensitivity because P0 helps F but cancels in A.

• Standard addition: x-intercept is the negative of the starting concentration.

Slide inconsistencies to confirm with your instructor

• AAS cost: $50 to 75K on the AAS summary slide versus about $30 to 50K in the AAS/ICP-AES table.

• Deuterium lamp range: 180 to 370 nm (source slide) versus 160 to 375 (summary table).

• Atomic electronic degeneracy printed as 2l + 1, likely meant 2J + 1.

• Na D line quoted as 589.3 nm in one place and 589.0 nm in another.