Chapter 10Atomic Structure and Atomic Spectra

Structures of many-electron atoms Because of electron correlation, no simple analyticalexpression for orbitals is possible

Therefore (r1, r2, .) can be expressed as (r1)(r2)

Called the orbital approximation

Individual hydrogenic orbitals modified by presence ofother electrons

Structures of many-electron atomsPauli exclusion principle no more than two electronsmay occupy an atomic orbital, and if so, must be of oppositespin

Structures 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

where shielding constant

Fig 10.20 Penetration of 3s and 3p electrons Shielding constant different for s and p electrons s-electron has greaterpenetration and is bound moretightly bound

Result: s < p < d < f

Structure 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 atom1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s

Fill up electrons in lowest energy orbitals (Aufbau principle)H 1 electronH 1s1He 2 electronsHe 1s2Li 3 electronsLi 1s22s1Be 4 electronsBe 1s22s2B 5 electronsB 1s22s22p1C 6 electrons

Structure of many-electron atoms In many-electron atoms, subshells are notdegenerate. Why?

Shielding and penetration

The building-up principle (Aufbau)

Mnemonic:

Hunds rule of maximum multiplicity

Results from spin correlation

C 6 electronsC 1s22s22p2N 7 electronsN 1s22s22p3O 8 electronsO 1s22s22p4F 9 electronsF 1s22s22p5Ne 10 electronsNe 1s22s22p6The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hunds rule).

Fig 10.21 Electron-electron repulsions in Sc atomIf configuration was[Ar] 3d2 4s1Reduced repulsionswith configuration[Ar] 3d1 4s2

Ionization energy (I) - minimum energy (kJ/mol) required to remove an electron from a gaseous atom in its ground stateI1 first ionization energyI2 second ionization energyI3 third ionization energyI1 < I2 < I3

Mg Mg+ + e I1 = 738 kJ/molMg+ Mg2+ + e I2 = 1451 kJ/molMg2+ Mg3+ + e I3 = 7733 kJ/molFor Mg2+ 1s22s22p6

Fig 10.22 First ionization energiesN [He] 2s2 2p3 I1 = 1400 kJ/molO [He] 2s2 2p4 I1 = 1314 kJ/mol

Spectra 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 electronsMultiplicity = (2S + 1) = (20 + 1) = 1Singlet state

Spins are perfectlyantiparallel

Fig 10.24 Vector model for parallel-spin electronsMultiplicity = (2S + 1) = (21 + 1) = 3Triplet state

Spins are partiallyparallelThree ways to obtain nonzero spin

Fig 10.25 Grotrian diagram for heliumSinglet triplet transitionsare forbidden

Fig 10.26 Orbital and spin angular momentaSpin-orbitcouplingMagnetogyric ratio

Fig 10.27(a) Parallel magnetic momentaTotal angular momentum (j) = orbital (l) + spin (s)e.g., for l = 0 j =

Fig 10.27(b) Opposed magnetic momentae.g., for l = 0 j = for l = 1 j = 3/2, Total angular momentum (j) = orbital (l) + spin (s)

Fig 10.27 Parallel and opposed magnetic momentaResult: For l > 0, spin-orbitcoupling splits a configurationinto levels

Fig 13.30 Spin-orbit coupling of a d-electron (l = 1)j = l + 1/2j = l - 1/2

Energy levels due to spin-orbit coupling Strength of spin-orbit coupling depends onrelative orientations of spin and orbitalangular momenta (= total angular momentum)

Total angular momentum described in terms ofquantum numbers: j and mj

Energy of level with QNs: s, l, and j

where A is the spin-orbit coupling constantEl,s,j = 1/2hcA{ j(j+1) l(l+1) s(s+1) }

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