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MULTI-ELECTRON ATOMS ORBITAL APPROXIMATION ELECTRON SPIN PAULI EXCLUSION PRINCIPLE AUFBAU BUILDING BLOCK PRINCIPLE HUND’S RULE PENETRATION AND SHIELDING, ZEFF ENERGY LEVEL SPLITTING ORBITAL FILLING AND ELECTRON CONFIGURATION MULTI-ELECTRON ATOMS • Schrödinger equation was for only one e-. • Electron-electron repulsion in multielectron atoms. • Hydrogen-like orbitals (by approximation). ELECTRON SPIN MULTI-ELECTRON ATOMS • The existence of more than one electron requires us to consider three features not relevant in the case of hydrogen: – need for a 4th quantum number; – a limit on the number of electrons allowed in a given orbital; and – a more complex set of orbital energy levels 1 ROLE OF MAGNETISM PAULI EXCLUSION PRINCIPLE • “No two electrons in an atom may have all four quantum numbers alike”. Paramagnetic Diamagnetic unpaired electrons all electrons paired 2p • An atomic orbital can hold a maximum of two electrons. These must have opposite spins. 2p ENERGY OF ORBITALS IN A SINGLE ELECTRON ATOM Energy only depends on principal quantum number n ENERGY OF ORBITALS IN A MULTI-ELECTRON ATOM Energy depends on n and l n=3 n=3 l = 2 n=2 En = -RH ( 1 n2 n=3 l = 1 ) n=2 l = 0 n=2 l = 1 n=1 n=1 l = 0 2 FACTORS AFFECTING ATOMIC ORBITAL ENERGIES THE EFFECT OF NUCLEAR CHARGE ON ORBITAL ENERGY • The Effect of Nuclear Charge (Zeffective): – Higher nuclear charge lowers orbital energy (stabilizes the system) by increasing nucleus-electron attractions. • The Effect of Electron Repulsions (Shielding): – Additional electron in the same orbital: • An additional electron raises the orbital energy through electron-electron repulsions. – Additional electrons in inner orbitals: • Inner electrons shield outer electrons more effectively than do electrons in the same sublevel. EFFECTIVE NUCLEAR CHARGE SHIELDING 3 THE EFFECT OF ORBITAL SHAPE Radial probability plots for the 1s, 2s and 2p orbitals. The 1s electrons effectively shield both the 2s and 2p electrons from the nucleus. The 2s orbital is more penetrating than the 2p orbital. PENETRATION AND SHIELDING Penetration of 2s DARTBOARD ANALOGY Zeff is the effective nuclear charge. ELECTRON CONFIGURATIONS Rules for assigning electrons to orbitals: • Aufbau process: – Build up and minimize energy. The lowest energy (most stable) orbitals are occupied first. • Pauli exclusion principle: – No two electrons can have all four quantum numbers alike • Hund’s rule: – When degenerate orbitals are available, electrons initially occupy these orbitals singly, and with parallel spins. 4 ORBITAL ENERGIES ORDER OF ORBITALS (FILLING) IN MULTI-ELECTRON ATOMS 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s Hund’s rule: The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins. AUFBAU PROCESS AND HUND’S RULE Ne97 C N O F 6 810 electrons electrons electrons 2 2 2 22p 5 246 3 C N 2s222p Ne O F 1s 1s2s 5 FILLING THE p ORBITALS FILLING THE d ORBITALS N O F Ne 1s 2s 2p ELECTRON CONFIGURATION ELECTRON CONFIGURATIONS AND THE PERIODIC TABLE 6 Problem Number 83: Wolfgang Pauli Wolfgang Paul Problem No. 84: 7