Instrumental Methods (General)

Classical tests — e.g. adding NaOH to detect metal ions by precipitate colour — have detection limits typically in the range 10–100 mg dm⁻³. Instrumental methods routinely achieve µg dm⁻³ (ppb) or lower. Precision is also better: an instrumental reading might carry ±0.5% uncertainty versus a subjective colour judgement. Speed matters in industry and medicine; automated instruments can process a blood sample in seconds. Selectivity is improved too — mass spectrometry can distinguish two compounds of nearly identical mass that no colour test could separate.

A sample solution is nebulised into a fine aerosol and drawn into a hot flame (typically 2000–3000 K). Solvent evaporates, leaving metal salt particles that atomise. Thermal energy from the flame promotes outer electrons of metal atoms to excited states. When these electrons fall back to lower energy levels, they emit photons at wavelengths that are unique to each element: sodium emits at 589 nm (yellow-orange), potassium at 766 nm (violet), calcium at 622 nm (red). A diffraction grating or interference filter isolates the wavelength of interest, and a photodetector measures the intensity of emitted light. Intensity is proportional to the concentration of the metal in the sample, so a calibration curve (intensity vs known concentration standards) allows quantitative analysis. FES is widely used for Na⁺ and K⁺ in clinical samples such as blood serum.

The energy of emitted photons is governed by the Bohr relationship: ΔE = hf = hc/λ, where h is Planck's constant (6.626 × 10⁻³⁴ J s), c is the speed of light, f is frequency, and λ is wavelength. Each transition between specific energy levels in a metal atom produces a photon of exactly that energy — hence a specific colour. Because no two elements have identical sets of energy levels, the emission spectrum acts as a 'fingerprint'. The Beer-Lambert type relationship for FES is: Emission Intensity (I) ∝ concentration (c), valid over a linear working range. Above this range, self-absorption occurs and the calibration curve flattens.

Mass spectrometry separates ions by their mass-to-charge ratio (m/z). The process has five stages: (1) Vaporisation — the sample is converted to the gas phase. (2) Ionisation — electrons are removed (or added) to form ions; in electron ionisation (EI), a beam of high-energy electrons knocks an electron from the molecule: M + e⁻ → M⁺• + 2e⁻. The resulting molecular ion M⁺• may further fragment. (3) Acceleration — ions are accelerated through a known electric potential difference V, gaining kinetic energy: KE = ½mv² = zqV (where z is the charge number and q is the elementary charge). (4) Deflection — a magnetic field B curves the ion paths; heavier ions curve less. The radius of curvature r is given by r = (1/B)√(2mV/zq), so ions of different m/z follow different paths. (5) Detection — ions strike a detector at a specific position or time, producing a signal recorded as a mass spectrum: a plot of relative abundance vs m/z. The molecular ion peak M⁺ gives the relative molecular mass; fragmentation patterns aid identification.

The base peak is the tallest peak, set to 100% relative abundance. The molecular ion peak (M⁺) is usually the highest m/z peak (excluding isotope peaks) and gives the molecular mass. Fragmentation peaks arise from bonds breaking within the molecule. For example, ethanol (CH₃CH₂OH, Mr = 46) shows M⁺ at m/z = 46, and a major fragment at m/z = 31 corresponding to loss of CH₃ (loss of 15 mass units) to give [CH₂OH]⁺. Isotope peaks: chlorine has two stable isotopes, ³⁵Cl and ³⁷Cl in a roughly 3:1 ratio, so any chlorine-containing compound shows characteristic M and M+2 peaks in a 3:1 ratio — a diagnostic tool for identifying halogens.

• \Delta E — Energy of emitted photon (J): Difference in energy between the excited state and the lower state the electron falls to
• h — Planck's constant (J s): Fundamental constant equal to 6.626 × 10⁻³⁴ J s
• f — Frequency of emitted light (Hz (s⁻¹)): Number of wave cycles per second; higher frequency = more energetic photon
• c — Speed of light (m s⁻¹): Approximately 3.00 × 10⁸ m s⁻¹ in a vacuum
• \lambda — Wavelength of emitted light (m): Distance between successive wave crests; shorter wavelength = higher energy

Problem. A student uses flame emission spectroscopy to determine the sodium concentration in a river water sample. She prepares five standard solutions of NaCl with known Na⁺ concentrations and records the emission intensity at 589 nm. The data are: 0 ppm → intensity 0; 2 ppm → 18; 4 ppm → 36; 6 ppm → 55; 8 ppm → 72. The river water sample gives an intensity reading of 45. (a) Plot a calibration curve and determine the concentration of Na⁺ in the sample. (b) Calculate the energy of a photon emitted at 589 nm.

Answer. The Na⁺ concentration in the river water is 5.0 ppm. Each photon emitted at 589 nm carries an energy of 3.37 × 10⁻¹⁹ J.

• Flame Tests for Metal Ions — Flame emission spectroscopy is the quantitative, instrumental development of the qualitative flame test; understanding both shows how an observation becomes a measurement.
• Isotopes and Relative Atomic Mass — Mass spectrometry separates isotopes by m/z; the mass spectrum of an element directly gives the masses and abundances needed to calculate relative atomic mass.
• Beer–Lambert Law and Colorimetry — FES uses a calibration curve based on the proportionality of signal to concentration, the same principle as Beer–Lambert absorbance measurements in colorimetry.
• Atomic Emission Spectra and Energy Levels — The emission lines observed in FES arise directly from electron transitions between quantised energy levels — the physical basis of all atomic spectra.
• Mass Spectrometry of Organic Molecules — The same MS principles applied to isotopes extend to organic molecules; fragmentation patterns and the M⁺ peak allow identification of unknown compounds.