The Polyelectronic Atom

Multi-electron Atoms - 2+ Helium atom Schrödinger equation cannot be solved analytically anymore (apart from He) Need to develop an approximate picture for multi-electron atoms

The orbital approximation in quantum mechanics Y(r1, r2, …) = y(r1) y(r2)…. Total wavefunction of many electron atom Each electron is occupying its individual orbital with nuclear charge modified to take account of all other electrons’ presence (repulsion!)

The orbital approximation in words Analogi atom 1 elektron 2+ - Zeff Atom 2 elektron Orbital Approximation Make multi electron atom look like a one electron atom Assumes every electron to be on its own experiencing an effective nuclear charge, Zeff Then the orbitals for the electrons take the form of those in hydrogen but their energies and sizes are modified by simply using an effective nuclear charge

The Concept of Electron Spin The solution of the Schrödinger equation above accounts very well for the structure of the H-atom spectrum and, as we will see, for other atoms too. However under very high resolution “fine structure” is observed in the transitions which is not explained using this approach. Dirac extended wave mechanics to include Special relativity and an extra coordinate - time. Solution of the Dirac equation yields a new intrinsic angular momentum

Electron Spin need to consider another property of electrons to determine how electrons populate orbitals envisage electron as spinning on own axis quantized only 2 spin states distinguished by the spin -magnetic quantum number ms + 1 2 - 74

Electron Spin Stern-Gerlach experiment - when a beam of ground state H atoms (1s) is passed through a magnetic field, the beam splits into two beams 37 75

The Electron Spin Important Spin Electron An electron has The projection of this spin is also quantized (by analogy with orbital angular momentum; l and ml) such that the spin projection quantum number, ms= +½, (spin up  or a) and ms= - ½, (spin down  or b) This is the final theoretical plank behind the structure of the periodic table. Important

Pauli Exclusion Principle no two electrons in the same atom can have the same 4 quantum numbers: n, l, ml , ms Important (as all electrons necessarily have the same s = 1/2) Hence, no individual orbital may be occupied by more than 2 electrons Electrons occupying the same orbital must be “paired up”.

S = 0 Diamagnetik S ≠ 0 Paramagnetik Masing-masing orbital dapat berisi 2 elektron, bergantung pada dua nilai yang diikuti pada ms: ±½

The Aufbau Principle To obtain a ground state configuration for an atom we apply the Pauli exclusion and the Aufbau principle which states that electrons are added to orbitals in increasing order of energy.

n l 3d n = 3 3p 3s 2p n = 2 2s n = 1 1s l = 2 (d) l = 1 (p) l = 0 (s) # of orbitals 2l+1 n = 1 1s 2s # Konfigurasi Ground State

Principles of how to build up electron configurations The Aufbau Principle - “The building-up”principle When establishing the ground state configuration of an atom start at the energetic bottom and work your way up NB: The energy ordering of the orbitals changes with the number of electrons.

Principles of how to build up electron configurations The Pauli Exclusion Principle - No two electrons in one atom may have the same set of four quantum numbers (that is they must differ in one or more of (n, l, ml , ms) 1H = 1S1 (1, 0, 0, ±½) 2He = 1S2 (1, 0, 0, +½) dan (1, 0, 0, -½) 3Li = 1S22S1 4Be = 1S22S1 5B = 1S22S1 states that electrons are added to orbitals in increasing order of energy

These “orbitals” are not filled in known elements nonexistent These “orbitals” are not filled in known elements Energi orbital meningkat berdasarkan: S < p < d < f Energi yang lebih tinggi: 6s < 5d – 4f < 6p Energi orbital bergantung muatan inti dan mempunyai jenis orbital yang berbeda  Perbedaan tingkat 1s < 2s < 2p < 3s < 3p < 4s < 3d ......dst ~

Anomali Prinsip Aufbau Prinsip Aufbau tidak dapat memprediksikan konfigurasi elektron pada atom terionisasi. example: 26Fe = [Ar] 4s2 3d6 24Fe2+ = [Ar] 3d6 4s0 Experimen 24Fe2+ = [Ar] 4s2 3d4 Salah Saat Ionisasi Lebih Stabil Dipengaruhi Oleh: Gaya tarik inti dan elektron Halangan satu elektron dengan lainnya Tolakan interelektronik Exchange force 26 proton 24 Elektron Proses ionisasi: elektron pertama yang hilang dari sub-kulit  n tertinggi, jika n sama  l tertinggi

Anomali Prinsip Aufbau Meskipun sub-kulit (n-1)d dan sub-kulit ns berada pada posisi yang sangat dekat. Namun, sub-kulit (n-1)d memeliki bentuk energy yang sedikit lebih tinggi example: 24Cu = [Ar] 4s2 3d4 Prediksi Aufbau 24Cu = [Ar] 4s1 3d5 Experimen

Anomali Prinsip Aufbau Periode 6, sub-kulit 4f dan 5d mempunyai energy yang sangat dekat example: 57La = [Xe] 6s2 5d1 Most stable Shifted 4f Sedangkan, 58Ce = [Xe] 6s2 4f2 5d0 Prediksi Aufbau Pada Kasus Yang lainnya: 40Zr = [Kr] 5s2 4d2 41Nb = [Kr] 5s2 4d3 42Mo = [Kr] 5s1 4d5 Seharusnya 42Mo = [Kr] 5s2 4d4 43Tc = [Kr] 5s1 4d6 Seharusnya 43Tc = [Kr] 5s2 4d5 Pada Kasus Paladium: 46Pd = [Kr] 5s2 4d8 Prediksi Aufbau 46Pd = [Kr] 5s0 4d10 Eksperimen

Atomic State, Term Symbols, and Hund’s Rule 2p n = 3 3s 3p 3d l = 1 (p) l = 0 (s) l = 2 (d) n = 1 2s # Konfigurasi 1s P D S # Atomic State Bilangan Kuantum L = 0, 1, 2, 3, 4 dst

Chemist  Multiplicity (Jumlah elektron tak berpasangan) Jumlah elektron tak berpasangan  2S + 1 Jika, S = 0  multiplisitas satu, Aturan State  Singlet Jika, S = ½  multiplisitas dua, Aturan State  Doublet Jika, S = 1  multiplisitas Tiga, Aturan State  Triplet Dst.................... Contoh: 6C = 1s2 2s2 2p2 S = 1  multiplisitas tiga (Triplet) L = 1  pada orbital P Ground State  3P (“triplet-P”) (term symbol) 1s2 2p2 2s2

Effect of increased nuclear charge Repulsions between electrons Orbital Energies 1s n=1 n=3 n=2 2s 2p 3s 3p 3d Energy n=4 4s Many e- Atoms Energy 1s n=1 n=3 n=2 2s 2p 3s 3p 3d Hydrogen Need to consider Effect of increased nuclear charge Repulsions between electrons 66

Electrons and the Periodic Table Electron fit logically into the periodic table. The s block elements (see next slide) start filling at level 1, the p block at level 2, and the d block at level 3.

The Periodic Table Organisation of the elements electronic configurations related to position of element elements grouped according to type of orbital the outer shell electrons are in BLOCK: Named for last subshell occupied GROUP: the columns all elements have same outer orbital e- configuration similar chemical properties PERIODS: rows all elements same shell 81

The Periodic Table Subshell orbitals with same energy eg. 2p Shell orbitals with similar energy eg. 2s, 2p Valence Electrons occupy outermost shell Core Electrons occupy filled inner shells Cl 1s22s22p6 3s23p5 Ne core valence Closed Shell Atoms full outer shell - very stable - noble gases 85

Slater’s Rules - Zeff = Z - S Zeff Assume 5 Orbital Approximation e- of interest 3 e- found in sphere Eff. Nuclear charge = 5 – 3 = 2 Assume 5 Approximate method for estimating the effective nuclear charge: Zeff = Z - S Dimana: Z = Muatan inti sebenarnya S = Konstanta Shielding

Perhitungan S (Konstanta Shielding) Membagi orbital dalam kelompok-kelompoknya (1s) (2s2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) Catatan: s dan p pada n sama dikelompokkan menjadi satu Elektron grup lain di kanan (ns dan np) tidak mempengaruhi shielding constant Semua elektron lain dalam (ns dan np), masing-masing tolakan elektron valensi dikalikan 0,35 Semua elektron kulit n-1, masing-masing tolakannya dikalikan 0,85 Semua elektron dibawahnya (n-2),masing-masing tolakannya dikalikan 1,00 Jika elektron pada sub kulit nd dan nf, aturan 2 dan 3 sama tetapi aturan 4 dan 5 berubah menjadi: Semua elektron di kiri nd dan nf dikalikan 1,00

Example For 15P: (1s2) (2s2 2p6) (3s2 3p3) Zeff = Z - S Zeff = 15 – ((2 x 1.00)+ (8 x 0.85) + (4 x 0.35)) = 4.8 Trends right, actual values bad s and p orbitals treated the same – huge differences for the orbitals in terms of penetration!!!!!

Periodic Properties Predicted by considering e- configurations Sizes of atoms and ions Ionisation energies Electron affinities Electronegativities Polarising powers and polarisabilities 87

Sizes Of Atoms and Ions Atoms do not have sharply defined boundaries Hence, need to define atomic size Atomic size depends on chemical environment ie. Bonding. etc 88

This shielding means that each valence electron in effect only “feels” a +1 charge form the nucleus; this occurs for an highly excited valence electron. Otherwise the shielding makes the “seen” charge is higher than +1

Defining Atomic and Ionic Size estimating size atomic radius = half the distance between nearest atoms in element (in condensed phases) for ions, base ionic radii on interatomic distance in ionic crystals. (depends on charge...) Cu Cu Cu+ Cu+2 atom covalent bonding 1.28 1.17 0.96 0.69 Å 2r 89

Sizes of Atoms and Ions Decrease Increase Why? Consider: 1. Principle Quantum number (shell) 2. Effective nuclear charge 90

Across a Period……. Muatan ini semakin besar tidak ada inti elektron yang menempatai posisi sama Muatan infi efektif meningkat meskipun pada kulit yang sama Elektron semakin dekat dengan inti Ukuran atom menurun Example: Na 1s22s22p63s1 1.91 Å Mg 1s22s22p63s2 1.60 Å 91

Down A Group…. Semakin besar jarak elektron pada kulit yang dipakai, sedangkan efektifitas muatan inti sama Peningkatan ukuran atom Example: Li : 1s22s1 1.57 A0 Na : 1s22s22p63s1 1.91 Ao 92

Atomic radii

Radius of Ions Cation < Atom Contoh: Na+ < Na 0.96 Å 1.91 Å 1s22s22p6 1s22s22p63s1  Kehilangan satu e- Inti elektron terbuka Ikatan semakin rapat Menurun berdasarkan periode Contoh: Na+ > Mg2+

Radius of Ions Atom < Anion eg. Cl < Cl 0.99 Å 1.81 Å [Ne]3s23p5 [Ne]3s23p6  gained an e- electron cloud greater decreases nuclear pull by each electron Decreases across a period e.g. S2- > Cl-

Ionisation Energy X(g)  X+(g) + e- E = IE1 The energy required to remove an electron from a ground state atom X(g)  X+(g) + e- E = IE1 Measure of stability of outer shell electron configuration Depends on size of the atom effective nuclear charge screening effect of inner electrons type of electron 95

Ionisation Energy Increase Decrease Why? Consider 1. Effective nuclear charge 2. Distance of e- from nucleus 96

Across a Period…. Down a Group…... Muatan inti efektif meningkat Jarak semakin pendek Gaya tarik inti dengan elektron meningkat Energi Ionisasi (EI) meningkat Exceptions: “p” less stable than “s” (B < Be) orbitals “singly occupied” more stable than “doubly occupied” (O < N) Down a Group…... Jarak meningkat, sedangkan muatan inti efektif sama Gaya tarikan antara elekton dan inti menurun Energi Ionisasi (EI) menurun 97

Ionization energy

Electron Affinity The energy released when an e- added to atom to form anion Example: F(g) + e-  F-(g) EA = 328 kJ/mol a small EA means e- must be forced to stick measure of ability of atom to accept e-

Electron Affinities Low for Noble gases Increase Decrease Same as IE Why? Consider 1. Size 2. Effective Nuclear charge 100

Electron Affinities 1. F + e-  F- EA = 328.0 kJ mol-1 1s2 2s2 2p6 - stable closed shell = Ne 2. Ne + e-  Ne- EA = negative 1s2 2s2 2p6 3s1 - Kulit baru, jarak ke inti lebih jauh - almost totally screened from nuclear charge - so unstable 101

Electron Affinities Be 1s22s2 Low EA Filled s subshell Next e- higher energy level so need energy to add e- N 1s22s22p3 Low EA Half filled “p” Adding another e- will cause e- repulsion hence unfavourable 102

Electronegativity Kemapuan sebuah atom menggambarkan elektron pada dirinya sendiri dalam ikatan kimia useful for: predicting extent of charge transfer between atoms Contoh: “Covalent”  “Ionic” H—H C—H N—H Na—Cl 103

Electronegativity Related to EA and IE Cs and F IE1 EA Cs low small F high large (Cs gives up e- easily, while F accepts e- easily.) Electron acceptor Electronegative Electron donor Electropositive 104

Electronegativity ( size, nuclear charge ) Increase Decrease Size, same effective nuclear charge 105

Electronegativity and Bond Type Skala numerik pada elektronegatifitas berkembang Skala elektronegatifitas Pauling () caesium c=0.79 fluorine c=3.98 Pada dua atom yang berikatan: (), dihitung berdasarkan polaritas ikatan Semakin elektronegatif, atom mempunyai densitas elektron lebih besar 106

Electronegativity and Bond Type H+Cl- Examples Na Cl (0.93) (3.16) () = 2.23; ionic, Na+Cl- H Cl (2.20) (3.16) () = 0.96; polar covalent Cl Cl (3.16) (3.16) () = 0.00; covalent, Cl-Cl > 2.0 < 0.4 107