All spectroscopic techniques rely on the interaction of electromagnetic radiation with matter. Key concepts:
1. Electromagnetic Spectrum
- Radio waves (wavelengths > 1 mm) → used in NMR.
- Microwaves (1 mm to 1 cm) → rotational transitions in small molecules (gas‐phase microwave spectroscopy).
- Infrared (IR) (0.7 µm to 100 µm) → vibrational transitions in molecules.
- Visible (VIS) (400 nm to 700 nm) → electronic transitions involving valence electrons.
- Ultraviolet (UV) (10 nm to 400 nm) → electronic transitions, often higher‐energy than visible.
- X-rays (0.01 nm to 10 nm) → core‐electron transitions, used in X-ray crystallography and X-ray fluorescence.
- Gamma rays (< 0.01 nm) → nuclear transitions, used in nuclear spectroscopy.

1. Quantized Transitions
   Atoms and molecules can only absorb or emit photons whose energy exactly matches the difference between two quantized energy levels. Photon energy (E) is related to frequency (ν) and wavelength (λ) by:
   E (joules) = Planck’s constant (6.626×10⁻³⁴ J·s) × frequency ν (s⁻¹)
   E (joules) = (6.626×10⁻³⁴ J·s) × (speed of light 3.00×10⁸ m/s) ÷ (wavelength λ in meters).
2. Absorption vs. Emission
3. Absorption spectroscopy: A beam of light of varying wavelength passes through a sample; record how much light is absorbed at each wavelength. The result is an absorption spectrum.
4. Emission spectroscopy: The sample is excited (thermally, electrically, or optically) and emits photons as it relaxes. The spectrum of emitted light (intensity versus wavelength) is recorded.
5. Beer’s Law (UV-Visible)
   For dilute solutions and monochromatic light, absorbance A is proportional to concentration c and path length ℓ:
   A = ε × ℓ × c
   where ε is the molar absorptivity (extinction coefficient) with units L mol⁻¹ cm⁻¹ (or M⁻¹ cm⁻¹), ℓ is the path length in cm (typically 1.00 cm), and c is concentration in mol/L. Absorbance A is defined as:
   A = – log₁₀ (I / I₀)
   where I₀ is the incident light intensity and I is the transmitted light intensity.

UV-Vis spectroscopy measures electronic transitions in molecules or atoms. It is widely used for quantitative analysis of colored compounds (for instance, determining concentration of a dye, a metal‐ligand complex, or reaction kinetics).

1. Instrumentation Components
2. Light Source
3. Typically a deuterium lamp for ultraviolet (UV) region (190–400 nm).
4. Tungsten‐halogen lamp for visible region (400–700 nm).
5. Some instruments combine both lamps in a single housing and switch automatically.
6. Monochromator
7. Dispenses the broad‐spectrum light from the lamp into individual wavelengths using a prism or diffraction grating.
8. A narrow slit selects a small wavelength band, usually 1 nm or 2 nm wide.
9. Sample Compartment and Cuvette
10. The monochromatic beam passes through a transparent cuvette (typically quartz for UV measurements, or glass/plastic for visible only).
11. Path length ℓ is usually 1.00 cm, but shorter or longer cells may be used for very high or very low absorbance samples.
12. Detector
13. Measures transmitted light intensity I at each wavelength. Photodiodes, photomultiplier tubes, or silicon photodiodes are common.
14. Converts light intensity into an electrical signal measured by the instrument’s electronics.
15. Data Processor
16. Records absorbance versus wavelength (absorption spectrum).
17. For quantitative analysis, often used in single‐wavelength mode: set wavelength to the compound’s absorption maximum (λ_max) and measure absorbance of unknown sample to determine concentration via Beer’s law.

Infrared spectroscopy measures molecular vibrations. Each functional group has characteristic vibrational frequencies that absorb IR radiation. Modern FTIR (Fourier‐Transform IR) instruments are standard in analytical labs.

1. Fundamental Principles
2. Molecular Vibrations
3. Atoms in a molecule vibrate around equilibrium positions—stretching, bending, rocking, wagging, etc.
4. Only vibrations that change the dipole moment of the molecule absorb IR radiation (infrared active).
5. Wavelength and Frequency Units
6. Infrared spectra are commonly plotted as wavenumbers (ν̅, pronounced “nu bar”) in inverse centimeters (cm⁻¹).
7. Wavenumber ν̅ = 1 ÷ λ (with λ in cm). For example, a 5 µm wavelength corresponds to 1 ÷ (5×10⁻⁴ cm) = 2000 cm⁻¹.
8. Typical mid‐IR region is 4000–400 cm⁻¹.
9. Characteristic Absorption Bands
10. O–H stretch (alcohols, phenols): broad band around 3200–3600 cm⁻¹.
11. N–H stretch (amines, amides): 3300–3500 cm⁻¹ (often sharper than O–H).
12. C–H stretches: alkane C–H around 2850–2960 cm⁻¹; aromatic C–H around 3000–3100 cm⁻¹.
13. C=O stretch (carbonyls): strong band around 1650–1750 cm⁻¹ (depends on specific functional group: aldehyde ~1720, ketone ~1715, ester ~1735, acid ~1705, amide ~1650).
14. C≡C or C≡N (triple bonds): 2100–2260 cm⁻¹ (weak to medium intensity).
15. C–O stretches (alcohols, ethers, esters): 1000–1300 cm⁻¹ (fingerprint region).
16. Fingerprint Region
    The region below ~1500 cm⁻¹ contains many complex, molecule‐specific absorptions (bending modes, ring stretches, etc.). It is unique to each compound, hence called the fingerprint region. Matching spectra in this region can confirm identity.

NMR exploits the magnetic properties of certain atomic nuclei (commonly hydrogen-1, carbon-13) placed in a strong static magnetic field and exposed to radiofrequency pulses. Chemical shifts and coupling patterns provide detailed structural and quantitative information.

1. Basic Principles
2. Nuclear Spin and Magnetic Moment
3. Nuclei with an odd number of protons or neutrons (for example, ¹H, ¹³C, ³¹P) possess intrinsic angular momentum (spin) and associated magnetic moment.
4. In an external magnetic field B₀, these nuclear spins align either with (lower energy) or against (higher energy) the field, creating discrete energy levels.
5. Resonance Condition
6. The energy difference ΔE between spin states is proportional to B₀:
   ΔE = γ ℏ B₀,
   where γ is the gyromagnetic ratio for the nucleus (for ¹H, γ/2π ≈ 42.58 MHz/Tesla), ℏ is reduced Planck’s constant.
7. When the nucleus absorbs a photon of radiofrequency ν such that h ν = ΔE, it transitions between spin states (resonance).
8. Chemical Shift (δ)
9. The local electron density around a nucleus shields it from the external field, shifting its resonance frequency slightly.
10. Chemical shift δ is measured in parts per million (ppm) relative to a reference compound (for ¹H and ¹³C, typically tetramethylsilane, TMS, δ = 0 ppm).
11. Spin–Spin Coupling (J-Coupling)
12. Nuclei interact via bonds, causing splitting of resonance lines into multiplets (doublets, triplets, quartets, etc.) with spacing J in Hz.
13. The number of peaks and their relative intensities follow the “n + 1” rule for simple systems (for example, a ¹H coupled to n equivalent neighboring protons appears as an (n + 1)-peak multiplet).

Fluorescence spectroscopy measures emission of light by a substance that has absorbed light or electromagnetic radiation. It is highly sensitive and selective, often used for trace analysis.

1. Principles
2. Electronic Excitation and Emission
3. A fluorophore absorbs a photon and is promoted from the ground electronic state S₀ to an excited singlet state S₁ (or higher).
4. Vibrational relaxation occurs in S₁; the molecule then emits a photon returning to S₀, often from the lowest vibrational level of S₁. Emitted photon energy is lower (longer wavelength) than absorbed photon (Stokes shift).
5. Quantum Yield (Φ)
6. Ratio of number of photons emitted to number of photons absorbed. A fluorophore with high quantum yield (close to 1) emits most absorbed energy as fluorescence; one with low yield dissipates energy by nonradiative processes.
7. Fluorescence Intensity (Iᶠˡ)
8. Proportional to the product of incident light intensity I₀, absorption (1 – 10^(–εℓc)), and quantum yield Φ. In dilute solutions (εℓc << 1), absorbance A ≈ εℓc × ln(10) is small, so Iᶠˡ ∝ I₀ × ε × ℓ × c × Φ.
9. Therefore, fluorescence intensity is roughly proportional to concentration at low c, but deviates at higher concentration due to inner filter effects (reabsorption of emitted light and self‐quenching).

Atomic spectroscopy measures atoms in ground or excited states, typically in flame, graphite furnace, or plasma. It is used for trace metal analysis.

1. Atomic Absorption Spectroscopy (AAS)
2. Principle
3. A beam of light specific to the electronic transition of the metal of interest is passed through a flame or graphite furnace containing atomized sample. Ground‐state atoms absorb light at a characteristic wavelength.
4. Measure decrease in light intensity (absorbance). Using Beer’s law (in a modified form for atoms), absorbance is proportional to the concentration of free atoms in the optical path.
5. Light Source
6. Hollow cathode lamp (HCL) specific for the element. For example, a copper‐HCL emits narrow‐band light at copper’s resonance line (~324.8 nm).
7. Atomization
8. Flame Atomization: Sample solution is aspirated into a nebulizer, producing fine droplets; droplets mix with fuel (acetylene) and oxidant (air or nitrous oxide) to produce a flame (~2300–2800 °C). Metal salts lose molecular bonds, forming free atoms in the gaseous state.
9. Graphite Furnace Atomization: Sample is pipetted onto a graphite tube. The tube is resistively heated in steps (drying, ashing, atomization, cleaning). Atomization temperatures (2000–3000 °C) produce a dense atomic vapor in a small optical path, increasing sensitivity (detection limits in ppb).
10. Monochromator and Detector
11. A monochromator (diffraction grating) isolates the specific resonance wavelength. A PMT detector measures transmitted light intensity.
12. Calibration and Quantification
13. Prepare standards of known metal concentration (for example, 0, 1.0, 5.0, 10.0 ppm).
14. Measure absorbance for each standard; plot absorbance versus concentration to obtain calibration curve.
15. Run unknown samples under the same conditions; use curve to determine metal concentration.
16. Include blanks (solvent only) to correct background.