atomic structure and atomic spectra
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Atomic Structure and Atomic Spectra. Chapter 10. Structures of many-electron atoms. Because of electron correlation, no simple analytical expression for orbitals is possible Therefore ψ (r 1 , r 2 , ….) can be expressed as ψ (r 1 ) ψ (r 2 )… Called the orbital approximation - PowerPoint PPT PresentationTRANSCRIPT
Chapter 10
Atomic Structure and Atomic Atomic Structure and Atomic SpectraSpectra
Structures of many-electron atoms
• Because of electron correlation, no simple analyticalexpression for orbitals is possible
• Therefore ψ(r1, r2, ….) can be expressed as ψ(r1)ψ(r2)…
• Called the orbital approximation
• Individual hydrogenic orbitals modified by presence ofother electrons
Structures of many-electron atoms
Pauli exclusion principle – no more than two electronsmay occupy an atomic orbital, and if so, must be of oppositespin
Structures of many-electron atomsStructures of many-electron atoms
• In many-electron atoms, subshells are notdegenerate. Why?
• Shielding and penetration
Fig 10.19 Shielding and effective nuclear charge, Zeff
• Shielding from core electronsreduces Z to Zeff
Zeff = Z – σ
where σ ≡ shielding constant
Fig 10.20 Penetration of 3s and 3p electrons
• Shielding constant different for s and p electrons
• s-electron has greater
penetration and is bound more
tightly bound
• Result: s < p < d < f
Structure of many-electron atomsStructure of many-electron atoms
• In many-electron atoms, subshells are notdegenerate. Why?
• Shielding and penetration
• The building-up principle (Aufbau)
• Mnemonic:
Order of orbitals (filling) in a many-electron atom
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s
“Fill up” electrons in lowest energy orbitals (Aufbau principle)
H 1 electron
H 1s1
He 2 electrons
He 1s2
Li 3 electrons
Li 1s22s1
Be 4 electrons
Be 1s22s2
B 5 electrons
B 1s22s22p1
C 6 electrons
? ?
Structure of many-electron atomsStructure of many-electron atoms
• In many-electron atoms, subshells are notdegenerate. Why?
• Shielding and penetration
• The building-up principle (Aufbau)
• Mnemonic:
• Hund’s rule of maximum multiplicity
• Results from spin correlation
C 6 electrons
C 1s22s22p2
N 7 electrons
N 1s22s22p3
O 8 electrons
O 1s22s22p4
F 9 electrons
F 1s22s22p5
Ne 10 electrons
Ne 1s22s22p6
The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule).
Fig 10.21 Electron-electron repulsions in Sc atom
If configuration was
[Ar] 3d2 4s1
Reduced repulsions
with configuration
[Ar] 3d1 4s2
Ionization energy (I) - minimum energy (kJ/mol) required to remove an electron from a gaseous atom in its ground state
I1 + X(g) X+
(g) + e-
I2 + X+(g) X2+
(g) + e-
I3 + X2+(g) X3+
(g) + e-
I1 first ionization energy
I2 second ionization energy
I3 third ionization energy
I1 < I2 < I3
Mg → Mg+ + e− I1 = 738 kJ/mol
Mg+ → Mg2+ + e− I2 = 1451 kJ/mol
Mg2+ → Mg3+ + e− I3 = 7733 kJ/mol
For Mg2+
1s22s22p6
Fig 10.22 First ionization energies
N [He] 2s2 2p3 I1 = 1400 kJ/mol
O [He] 2s2 2p4 I1 = 1314 kJ/mol
Spectra of complex atomsSpectra of complex atoms
• Energy levels not solely given by energiesof orbitals
• Electrons interact and make contributions to E
Fig 10.18 Vector model for paired-spin electrons
Multiplicity = (2S + 1)
= (2·0 + 1)
= 1
Singlet state
Spins are perfectly
antiparallel
Fig 10.24 Vector model for parallel-spin electrons
Multiplicity = (2S + 1)
= (2·1 + 1)
= 3
Triplet state
Spins are partiallyparallel
Three ways to obtain nonzero spin
Fig 10.25 Grotrian diagram for helium
Singlet – triplet transitions
are forbidden
Fig 10.26 Orbital and spin angular momenta
Spin-orbit
coupling
Magnetogyric ratio
Fig 10.27(a) Parallel magnetic momenta
Total angular momentum (j) = orbital (l) + spin (s)
e.g., for l = 0 → j = ½
Fig 10.27(b) Opposed magnetic momenta
e.g., for l = 0 → j = ½
for l = 1 → j = 3/2, ½
Total angular momentum (j) = orbital (l) + spin (s)
Fig 10.27 Parallel and opposed magnetic momenta
Result: For l > 0, spin-orbit
coupling splits a configuration
into levels
Fig 13.30 Spin-orbit coupling of a d-electron (l = 1)
j = l + 1/2
j = l - 1/2
Energy levels due to spin-orbit couplingEnergy levels due to spin-orbit coupling
• Strength of spin-orbit coupling depends on
relative orientations of spin and orbital
angular momenta (= total angular momentum)
• Total angular momentum described in terms of
quantum numbers: j and mj
• Energy of level with QNs: s, l, and j
where A is the spin-orbit coupling constant
El,s,j = 1/2hcA{ j(j+1) – l(l+1) – s(s+1) }