C – 1s 2 2s 2 2p 2 Step 1:Consider two valence p electrons 1 st 2p electron has n = 2, l = 1, m l = 0, ±1, m s = ±½ → 6 possible sets of quantum numbers 2 nd 2p electron has 5 possible sets of quantum numbers (Pauli Exclusion Principle) For both electrons, (6x5)/2 = 15 possible assignments since the electrons are indistinguishable Spectroscopic Description of All Possible Electronic States – Term Symbols Step 2: Draw all possible microstates. Calculate M L and M S for each state.

C – 1s 2 2s 2 2p 2 Step 3: Count the number of microstates for each M L —M S possible combination Spectroscopic Description of All Possible Electronic States – Term Symbols Step 4: Extract smaller tables representing each possible term

C – 1s 2 2s 2 2p 2 Step 5: Use Hund’s Rules to determine the relative energies of all possible states. 1. The highest multiplicity term within a configuration is of lowest energy. 2. For terms of the same multiplicity, the highest L value has the lowest energy (D < P < S). 3. For subshells that are less than half-filled, the minimum J-value state is of lower energy than higher J-value states. 4. For subshells that are more than half-filled, the state of maximum J-value is the lowest energy. Based on these rules, the ground electronic configuration for carbon has the following energy order: 3 P 0 < 3 P 1 < 3 P 2 < 1 D 2 < 1 S 0 Spectroscopic Description of All Possible Electronic States – Term Symbols

Write term symbols in analogous manner except consider the orbital to which an electron is promoted. For example, excitation of Na promotes one valence electron into the 3p orbital. In this case, n = 3, S = ½, 2S+1 = 2, L = 1 (P term), J = 3/2, 1/2. There are two closely spaced levels in the excited term of sodium with term symbols 2 P 1/2 and 2 P 3/2 Spectroscopic Description of Excited States – Term Symbols This type of splitting (same L but different J) is called fine structure. Transition from 2 P 1/2 → 2 S 1/2

Allowed and Forbidden Transitions Only a fraction of all possible transitions are observed. Allowed transitions -high probability, high intensity, electric dipole interaction Forbidden transitions -low probability, weak intensity, non-electric dipole interaction Selection rules for allowed transitions: * The parity of the upper and lower level must be different. (The parity is even if  l i is even. The parity is odd if  l i is odd.) * l = ±1 *  l = ±1 *  J = 0 or ±1, but J = 0 to J = 0 is forbidden.

Additional Splitting Effects Hyperfine splitting due to magnetic coupling of spin and orbital motion of electrons with the nuclear spin.Hyperfine splitting due to magnetic coupling of spin and orbital motion of electrons with the nuclear spin. Isotope shift. Sufficient to determine isotope ratios.Isotope shift. Sufficient to determine isotope ratios. Splitting in an electric field (Stark effect): Relevant for arc and spark techniques.Splitting in an electric field (Stark effect): Relevant for arc and spark techniques. Splitting in a magnetic field (Zeeman effect):Splitting in a magnetic field (Zeeman effect): * In absence of a magnetic field, states that differ only by their M J values are degenerate, i.e., they have equivalent energies. * In presence of a magnetic field, this is not true anymore. * Can be used for background correction.

Pretsch/Buhlmann/Affolter/Badertscher, Structure Determination of Organic Compounds

Pretsch/Buhlmann/Affolter/Badertscher, Structure Determination of Organic Compounds

Stark Splitting For H: split  E For others: split  (E) 2

Zeeman Splitting Ingle and Crouch, Spectrochemical Analysis M J – Resultant total magnetic quantum number M J = J, J-1, …, -J 2J +1 possible values NormalAnomalous

Sample Introduction and Atomization Atomization: Atomization: Convert solution → vapor-phase free atoms Measurements usually made in hot gas or enclosed furnace: flamesflames plasmasplasmas electrical discharges (arcs, sparks)electrical discharges (arcs, sparks) heated furnacesheated furnaces Free Atoms IonsIons Mole- cules Nebulization Desolvation Volitalization Adapted from Ingle and Crouch

Atomic Emission Spectroscopy (AES) See also: Fundamental reviews in Analytical Chemistry e.g. Bings, N. H.; Bogaerts, A.; Broekaert, J. A. C. Anal. Chem. 2002, 74, (“Atomic Spectroscopy”) e.g. Bings, N. H.; Bogaerts, A.; Broekaert, J. A. C. Anal. Chem. 2002, 74, (“Atomic Spectroscopy”) Beginning 19th century: alcohol flame (Brewster, Herschel, Talbot, Foucault) Beginning 19th century: alcohol flame (Brewster, Herschel, Talbot, Foucault) mid 1800s: Discovery of Cs, Tl, In, Ga by atomic spectroscopy (Bunsen, Kirchhoff) mid 1800s: Discovery of Cs, Tl, In, Ga by atomic spectroscopy (Bunsen, Kirchhoff) 1877: Gouy designs pneumatic nebulizer 1877: Gouy designs pneumatic nebulizer 1920s: Arcs and sparks used for AES 1920s: Arcs and sparks used for AES 1930s: First commercial AES spectrometer (Siemens-Zeiss) 1930s: First commercial AES spectrometer (Siemens-Zeiss) 1960s: Plasma sources (commercial in 1970s) 1960s: Plasma sources (commercial in 1970s)

Atomic Emission Spectroscopy (AES) 2 S 1/2 2 D 3/2, 5/2 2 P 3/2 2 P 1/2 2 S 1/2 At RT, nearly all electrons in 3s orbital Excite with flame, electric arc, or spark Common electronic transitions

An Ideal AES Source 1. complete atomization of all elements 2. controllable excitation energy 3. sufficient excitation energy to excite all elements 4. inert chemical environment 5. no background 6. accepts solutions, gases, or solids 7. tolerant to various solution conditions and solvents 8. simultaneous multi-element analysis 9. reproducible atomization and excitation conditions 10. accurate and precise analytical results 11. inexpensive to maintain 12. ease of operation

Flame AES Background signals due to flame fuel and oxidants – line spectra:Background signals due to flame fuel and oxidants – line spectra: OH 281.1, 306.4, nmOH 281.1, 306.4, nm from O + H 2 H + OH from O + H 2  H + OH H + O 2 O + OH H + O 2  O + OH O 2 250, 400 nmO 2 250, 400 nm CH 431.5, 390.0, nmCH 431.5, 390.0, nm CO bands between 205 to 245 nmCO bands between 205 to 245 nm CN, C 2, CH, NH bands between 300 to 700 nmCN, C 2, CH, NH bands between 300 to 700 nm Unlike bands of atomic origin, these molecular bands are fairly broad. Unlike bands of atomic origin, these molecular bands are fairly broad. Continuum emission from recombination reactionsContinuum emission from recombination reactions e.g. H + OH H 2 O + h  CO + O CO 2 + h e.g. H + OH  H 2 O + h  CO + O  CO 2 + h Flames used in AES nowadays only for few elements. Cheap but limited. {Flame AES often replaced by flame AAS.}  Flames used in AES nowadays only for few elements. Cheap but limited. {Flame AES often replaced by flame AAS.}

Inductively Coupled Plasma AES Spectral interference more likely for plasma than for flame due to larger population of energetically higher states.Spectral interference more likely for plasma than for flame due to larger population of energetically higher states. Modern ICP power: 1–5 kW (4 to 50 MHz)Modern ICP power: 1–5 kW (4 to 50 MHz) 4000 to 10,000 K: Very few molecules4000 to 10,000 K: Very few molecules Long residence time (2–3 ms)Long residence time (2–3 ms) results in high desolvation results in high desolvation and volatilization rate and volatilization rate High electron density suppressesHigh electron density suppresses ionization interference effects ionization interference effects Background: Ar atomic lines and,Background: Ar atomic lines and, in hottest plasma region, in hottest plasma region, Bremsstrahlung (continuum radiation Bremsstrahlung (continuum radiation from slowing of charged particles) from slowing of charged particles) Price > $ 50 kPrice > $ 50 k Operating cost relatively high dueOperating cost relatively high due to Ar cost (10–15 mL/min) and to Ar cost (10–15 mL/min) and training. training. Ingle and Crouch

Microwave Plasma AES Power 25 to 1000 W (ICP 1000–2000 W)Power 25 to 1000 W (ICP 1000–2000 W) Frequency 2450 MHz (ICP 4 to 50 MHz)Frequency 2450 MHz (ICP 4 to 50 MHz) Argon, helium or nitrogenArgon, helium or nitrogen Thermodynamic equilibrium typically not reached (temperatureThermodynamic equilibrium typically not reached (temperature estimated to be around 2000 to 3000 K) estimated to be around 2000 to 3000 K) Low temperature causes problems with liquidsLow temperature causes problems with liquids Useful for gases: GC–microwave plasma AESUseful for gases: GC–microwave plasma AES

AES: Figures of Merit Linearity over 4 to 5Linearity over 4 to 5 concentration decades concentration decades Reasons for deviations Reasons for deviations from linearity: from linearity: - Self-absorption - Extent of ionization affected by sample affected by sample - Flow rate - Atomization efficiency Ingle and Crouch

AES: Figures of Merit Linearity over 4 to 5 concentration decadesLinearity over 4 to 5 concentration decades Precision: Typically a few % (lower in calibration solutions)Precision: Typically a few % (lower in calibration solutions) Limited by stability of source and random electrical noise Accuracy: An optimized spectrometer should be capable of precision-limited accuracyAccuracy: An optimized spectrometer should be capable of precision-limited accuracy Limited in ICP AES by spectral overlap Applicability: 3/4 of all elements (ICP)Applicability: 3/4 of all elements (ICP) Limitations in detection limits: * Major transitions in UVLimitations in detection limits: * Major transitions in UV * Temperature too high for alkali metals (ion emission in UV as they have fully occupied electron shells)

Detection Limits for Flame AES Ingle and Crouch, Spectrochemical Analysis

Detection Limits for ICP AES Ingle and Crouch, Spectrochemical Analysis

AES: Instrumental Aspects Ingle and Crouch, Spectrochemical Analysis