The Polyelectronic Atom

Multi-electron Atoms 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  r 1, r 2, …) =  r 1 )  (r 2 )…. 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  Make multi electron atom look like a one electron atom  Assumes every electron to be on its own experiencing an effective nuclear charge, Z eff  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 Analogi atom 1 elektron Z eff Atom 2 elektronOrbital Approximation

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

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 m s 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

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 m l ) such that the spin projection quantum number, m s = +½, (spin up  or  ) and m s = - ½, (spin down  or  ) This is the final theoretical plank behind the structure of the periodic table.

Pauli Exclusion Principle Important no two electrons in the same atom can have the same 4 quantum numbers: n, l, m l, m s (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 m s : ±½

n 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. The Aufbau Principle

n l n = 2 2p n = 3 3s 3p 3d l = 1 (p) l = 0 (s) l = 1 (p) l = 2 (d) # of orbitals 2l+1 n = 1 l = 0 (s) 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. 2p 3s 3p 3d 1s 2s 4s

Principles of how to build up electron configurations (1)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, m l, m s ) 1 H = 1S 1 (1, 0, 0, ±½) 2 He = 1S 2 (1, 0, 0, +½) dan (1, 0, 0, -½) 3 Li = 1S 2 2S 1 4 Be = 1S 2 2S 1 5 B = 1S 2 2S 1 (2)states that electrons are added to orbitals in increasing order of energy

These “orbitals” are nonexistent These “orbitals” are 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: 26 Fe = [Ar] 4s 2 3d 6 24 Fe 2+ = [Ar] 3d 6 4s 0 Experimen 24 Fe 2+ = [Ar] 4s 2 3d 4 Salah 24 Elektron 26 proton Saat Ionisasi Lebih Stabil Proses ionisasi: elektron pertama yang hilang dari sub-kulit  n tertinggi, jika n sama  l tertinggi Dipengaruhi Oleh:  Gaya tarik inti dan elektron  Halangan satu elektron dengan lainnya  Tolakan interelektronik  Exchange force Dipengaruhi Oleh:  Gaya tarik inti dan elektron  Halangan satu elektron dengan lainnya  Tolakan interelektronik  Exchange force

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: 24 Cu = [Ar] 4s 2 3d 4 Prediksi Aufbau 24 Cu = [Ar] 4s 1 3d 5 Experimen

Anomali Prinsip Aufbau Periode 6, sub-kulit 4f dan 5d mempunyai energy yang sangat dekat example: 57 La = [Xe] 6s 2 5d 1 Most stable Shifted 4f Sedangkan, 58 Ce = [Xe] 6s 2 4f 2 5d 0 Prediksi Aufbau Pada Kasus Yang lainnya: 40 Zr = [Kr] 5s 2 4d 2 41 Nb = [Kr] 5s 2 4d 3 42 Mo = [Kr] 5s 1 4d 5 Seharusnya 42 Mo = [Kr] 5s 2 4d 4 43 Tc = [Kr] 5s 1 4d 6 Seharusnya 43 Tc = [Kr] 5s 2 4d 5 Pada Kasus Paladium: 46 Pd = [Kr] 5s 2 4d 8 Prediksi Aufbau 46 Pd = [Kr] 5s 0 4d 10 Eksperimen

Atomic State, Term Symbols, and Hund’s Rule n l n = 2 2p n = 3 3s 3p 3d l = 1 (p) l = 0 (s) l = 1 (p) l = 2 (d) n = 1 l = 0 (s) 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: 6 C = 1s 2 2s 2 2p 2 S = 1  multiplisitas tiga (Triplet) L = 1  pada orbital P Ground State  3 P (“triplet-P”) (term symbol) 1s 2 2p 2 2s 2