Atomic Spectroscopy: Atomic Emission Spectroscopy Atomic Absorption Spectroscopy Atomic Fluorescence Spectroscopy * Elemental Analysis * Sample is atomized * Absorption, emission or fluorescence of atoms or ions in the gas phase gas phase

Atomic Emission Spectroscopy Ingle and Crouch, Spectrochemical Analysis

Electronic Levels for Individual Electrons Ingle and Crouch, Spectrochemical Analysis

Electronic Configuration of Atoms Al: 1s 2 2s 2 2p 6 3s 2 3p 1

Electronic Configuration of Atoms l = 0 s-orbital m l = 0 l = 1 p-orbital m l = 0, ±1 l = 2 d-orbital m l = 0, ± 1, ±2 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f Aufbau Order

Electronic Configuration of Atoms Al: 1s 2 2s 2 2p 6 3s 2 3p 1

Electronic States of Atoms Quantum numbers for electronsQuantum numbers for many-electron atoms l: orbital angular momentum quantumL: orbital angular momentum quantum number number (0,1, … n-1 e.g., for 2 e-: L = l 1 +l 2, l 1 +l 2 -1, l 1 +l 2 -2, …,| l 1 -l 2 | number (0,1, … n-1 e.g., for 2 e-: L = l 1 +l 2, l 1 +l 2 -1, l 1 +l 2 -2, …,| l 1 -l 2 | where 0=s, 1=p, 2=d, 3=f) 0 = S, 1 = P, 2 = D, 3 = F where 0=s, 1=p, 2=d, 3=f) 0 = S, 1 = P, 2 = D, 3 = F m l : orbital magnetic quantum numberM L : orbital magnetic quantum number (  m l ) (l, l-1, …, 0, …, -l ) 2L+1 possible values (l, l-1, …, 0, …, -l ) 2L+1 possible values s: electron spin quantum number (1/2) S: total spin quantum number S = s 1 +s 2, s 1 +s 2 -1, …,| s 1 -s 2 | S = s 1 +s 2, s 1 +s 2 -1, …,| s 1 -s 2 | S = 0 singlet, S = 1 doublet, S = 2 triplet S = 0 singlet, S = 1 doublet, S = 2 triplet m s : spin magnetic quantum numberM S : spin magnetic quantum number (  m s ) (+1/2, -1/2) 2S+1 possible values (+1/2, -1/2) 2S+1 possible values J: total angular quantum number J = L+S, L+S-1, …, | L-S| J = L+S, L+S-1, …, | L-S|

Spectroscopic Description of Atomic Electronic States – Term Symbols Multiplicity (2S +1) describes the number of possible orientations of total spin angular momentum where S is the resultant spin quantum number (1/2 x # unpaired electrons) Resultant Angular Momentum (L) describes the coupling of the orbital angular momenta of each electron (add the m L values for each electron) Total Angular Momentum (J) combines orbital angular momentum and intrinsic angular momentum (i.e., spin). To Assign J Value: To Assign J Value: if less than half of the subshell is occupied, take the minimum value J = | L − S | ; if more than half-filled, take the maximum value J = L + S; if the subshell is half-filled, L = 0 and then J = S.

Spectroscopic Description of Ground Electronic States – Term Symbols Term Symbol Form: 2S+1 {L} J 2S+1 – multiplicity L – resultant angular momentum quantum number J – total angular momentum quantum number Ground state has maximal S and L values. Example: Ground State of Sodium – 1s 2 2s 2 2p 6 3s 1 Consider only the one valence electron (3s 1 ) L = l = 0, S = s = ½, J = L + S = ½ so, the term symbol is 2 S ½

Are you getting the concept? Write the ground state term symbol for fluorine.

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

To calculate the energy of a single electron atom with quantum numbers L, S, and J: E L,S,J = ½ hc [J(J+1) - L(L+1) – S(S+1)] where  is the spin-orbit coupling constant Calculating Energies for Transitions

Atomic emission spectra show a doublet in the Na spectrum due to spin-orbit coupling of the 2 P state. Given that = 11.4 cm -1, find the energy spacing (in cm -1 ) between the upper 2 P 3/2 and 2 P 1/2 states. Are you getting the concept? 2 P 3/2 2 P 1/2 2 S 1/2 1 eV = cm -1