Spectroscopic analytical instruments

Why it matters

Spectroscopic instruments tell a plant what is in a sample and how much. UV-visible photometers track colour, concentration and water quality; infrared and FTIR analysers monitor gases and polymers; atomic absorption and flame photometers measure metals such as Na, K, Ca and heavy metals in water, food and pharmaceuticals; on-line near-infrared analysers control blending and moisture. All of them share the same building blocks — source, wavelength selector, sample cell, detector — and the same Beer–Lambert law.

Key ideas

Radiation and matter. Photon energy E = h·ν = h·c/λ. Different spectral regions excite different transitions:

• X-ray: inner-shell electrons (XRF for elemental analysis).
• Ultraviolet and visible (about 190–780 nm): valence electronic transitions; used for concentration of coloured or UV-absorbing species.
• Infrared (about 2.5–25 µm, i.e. 4000–400 cm⁻¹ in the mid-IR): molecular vibrations; identifies functional groups and measures gases such as CO and CO₂. Near-IR (780–2500 nm) gives overtone bands used for moisture, fat and protein on-line.
• Microwave: rotations. Radio-frequency in a magnetic field: nuclear spin (NMR), where the resonance frequency is f = γ·B/(2π).

Beer–Lambert law. For monochromatic light through a dilute, non-scattering sample, absorbance A = log₁₀(I₀/I) = −log₁₀T = ε·c·l. It is linear in concentration only within limits: deviations come from high concentration (above about 0.01 mol/L for many species), chemical association, stray light, polychromatic light and scattering. Best accuracy is at absorbances of roughly 0.2–0.8; very high absorbances (above about 2–3) transmit too little light to measure reliably.

Instrument building blocks.

• Sources: deuterium lamp (UV), tungsten-halogen lamp (visible, near-IR), Nernst glower or globar (mid-IR), hollow-cathode lamps (AAS, one per element), lasers (Raman), ICP or flame (emission).
• Wavelength selection: absorption or interference filters (photometers), or a monochromator with a prism or diffraction grating plus entrance and exit slits. The grating equation n·λ = d·(sin i + sin θ) fixes the diffracted angle; resolving power λ/Δλ = n·N grows with the number of grooves illuminated.
• Sample cells: quartz or fused silica for UV, glass or plastic for visible, NaCl, KBr or CaF₂ windows for IR (glass absorbs IR).
• Detectors: photomultiplier tube (very sensitive, UV-visible), silicon photodiodes and photodiode arrays or CCDs (fast, whole spectrum at once), and for IR thermal detectors (thermopile, bolometer, pyroelectric) or cooled photon detectors (MCT, InGaAs).
• Single-beam instruments measure blank and sample in turn; double-beam instruments split the beam through sample and reference continuously, cancelling source drift.

Important instrument types.

• UV-visible spectrophotometer and colorimeter: quantitative analysis by Beer–Lambert at a chosen wavelength.
• FTIR: a Michelson interferometer replaces the monochromator; all wavelengths are measured simultaneously and the spectrum is obtained by Fourier transform. Advantages: multiplex (Fellgett) and throughput (Jacquinot) gains and precise wavenumber calibration from a reference laser.
• Atomic absorption spectrometer (AAS): the sample is atomised in a flame or graphite furnace; a hollow-cathode lamp of the same element emits narrow lines that only that element's atoms absorb, giving high selectivity for metals.
• Flame photometer and ICP emission: excited atoms emit characteristic lines; intensity ∝ concentration (Na, K, Li, Ca in flame; many elements by ICP).
• Mass spectrometry: strictly not spectroscopy; ions are separated by mass-to-charge ratio (magnetic sector, quadrupole, time-of-flight).

Formulas

E = h·ν = h·c/λ, ν̃ = 1/λ (wavenumber)

A = log₁₀(I₀/I) = −log₁₀T = ε·c·l

A_total = Σ εᵢ·cᵢ·l (additivity for mixtures at one wavelength)

n·λ = d·(sin i + sin θ) (grating; i and θ on the same side of the normal taken positive)

λ/Δλ = n·N (grating resolving power)

f = γ·B/(2π) (NMR resonance)

Symbols: E = photon energy (J; 1 eV = 1.602 × 10⁻¹⁹ J); h = 6.626 × 10⁻³⁴ J·s; ν = frequency (Hz); c = 2.998 × 10⁸ m/s (in E = hc/λ); λ = wavelength (m); ν̃ = wavenumber (cm⁻¹); I₀, I = incident and transmitted intensity; T = transmittance; ε = molar absorptivity (L/(mol·cm)); c = concentration (mol/L, in A = εcl); l = path length (cm); n = diffraction order; d = groove spacing (m); i, θ = incidence and diffraction angles; N = number of illuminated grooves; γ = gyromagnetic ratio (rad/(s·T)); B = magnetic flux density (T).

Worked examples

Example 1 (standard): concentration from transmittance. Given: T = 40.0 % at 280 nm; ε = 1.20 × 10⁴ L/(mol·cm); l = 1.00 cm.

1. A = −log₁₀(0.400) = 0.398.
2. c = A/(ε·l) = 0.398/(1.20 × 10⁴ × 1.00) = 3.32 × 10⁻⁵ mol/L.
3. Answer: c ≈ 3.3 × 10⁻⁵ mol/L (33 µmol/L). The absorbance lies in the 0.2–0.8 band where photometric error is smallest.

Example 2 (GATE level): grating monochromator. Given: a grating with 1200 grooves/mm used at normal incidence (i = 0) for λ = 500 nm in first order; 50 mm of the grating is illuminated.

1. d = 1 mm/1200 = 8.333 × 10⁻⁷ m.
2. sin θ = n·λ/d = 1 × 500 × 10⁻⁹/8.333 × 10⁻⁷ = 0.600, so θ = 36.9°.
3. Second order would need sin θ = 1.2, which is impossible, so 500 nm appears only in first order here.
4. N = 1200 × 50 = 60 000 grooves; resolving power = 1 × 60 000.
5. Δλ = 500/60 000 = 0.0083 nm.
6. Answer: θ ≈ 36.9°; theoretical resolution ≈ 0.008 nm (real instruments are limited by slit width long before this).

Example 3 (photon energy and wavenumber). At 254 nm (mercury line used in UV detectors), E = h·c/λ = 6.626 × 10⁻³⁴ × 2.998 × 10⁸ / 254 × 10⁻⁹ = 7.82 × 10⁻¹⁹ J = 4.88 eV. A carbonyl IR band at 1700 cm⁻¹ lies at λ = 10⁴/1700 = 5.88 µm.

Common mistakes

• Using natural logarithms in the absorbance definition (A uses log₁₀).
• Mixing T in per cent with T as a fraction (A = 2 − log₁₀(%T)).
• Applying Beer–Lambert outside its linear range (high absorbance, scattering, stray light).
• Using glass cells in the UV or IR.
• Forgetting the units of ε (L/(mol·cm)) and path length in cm.
• Assuming one technique does everything: UV-visible quantifies, IR identifies functional groups, AAS measures metals, NMR and MS determine structure.

For GATE IN

Numericals: Beer–Lambert (absorbance, transmittance, concentration, mixtures), photon energy and wavelength or wavenumber conversions, grating equation and resolving power. Conceptual questions: sources, detectors and cell materials for each region, single versus double beam, FTIR advantages, AAS hollow-cathode lamps. Practise logarithms and the conversion between %T and absorbance.

Quick check

1. T = 10 %. What is A?
2. A = 0.30, ε = 200 L/(mol·cm), l = 1 cm. What is c?
3. Which cell material suits UV measurements?
4. What does a hollow-cathode lamp provide in AAS?
5. Convert 2000 cm⁻¹ to wavelength.

Answers: 1. 1.0. 2. 1.5 × 10⁻³ mol/L. 3. Quartz (fused silica). 4. Narrow emission lines of the element being measured, which only that element absorbs. 5. 5.0 µm.