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QUANTUM NUMBERS & ELECTRON CONFIGURATION General Chemistry I 1 QUANTUM MODEL QUANTUM THEORY Describes mathematically the wave properties of electrons and other very small particles QUANTUM MECHANICAL MODEL Electrons are treated as waves and makes no attempt to describe electron’s path Calculated the probability of finding the electron within a volume of space around the nucleus PLOshikiri/04 2 QUANTUM MECHANICAL MODEL 90% Probability of finding electrons PLOshikiri/04 3 Probability Distribution PLOshikiri/04 4 Probability Distribution PLOshikiri/04 5 QUANTUM NUMBERS Numbers that describe the energies of electrons in atoms Specify the properties of atomic orbitals and the properties of electrons in orbitals Think of the quantum numbers as addresses for electrons PLOshikiri/04 6 FOUR QUANTUM NUMBERS Principal Quantum Number (n) Angular Momentum Quantum Number (l ) Magnetic Quantum Number (ml) Spin Quantum Number (s ) PLOshikiri/04 7 PRINCIPAL QUANTUM NUMBER Electron Cloud Size (n) Indicates the main energy level occupied by the electron Can take on integer values n = 1, 2, 3,…. Largely determine the energy of the orbital (bigger n value = higher energy) All electrons in an atom with the same value of n belong to the same shell PLOshikiri/04 8 PRINCIPAL QUANTUM NUMBER . . . Spectroscopists use the following names for shell Shell n Name n Shell Name 1 K 5 O 2 L 6 P 3 M 7 Q 4 N PLOshikiri/04 9 ANGULAR MOMENTUM QUANTUM NUMBER Shape of Electron Cloud (l) Also known as sublevel or subshell Indicates the shape of the orbital within a shell Only integer values between 0 and n-1 are allowed Affects orbital energies (bigger l = higher energy) All electrons in an atom with the same value of l are said to belong to the same subshell Sometimes called the orbital azimuthal quantum number PLOshikiri/04 10 ANGULAR MOMENTUM QUANTUM NUMBER . . . Spectroscopists use the following notation for subshells l PLOshikiri/04 Subshell Name 0 s (sharp) 1 p (principal) 2 d (diffuse) 3 f (fundamental) 11 MAGNETIC QUANTUM NUMBER Orientation in space of orbitals (ml) Determines the orientation of orbitals within a subshell Does not affect orbital energy (except in magnetic fields!) Only integer values between –l and +l are allowed The number of ml values within a subshell is the number of orbitals within a subshell PLOshikiri/04 12 MAGNETIC QUANTUM NUMBER . . . Number of ml values determines the number of orbitals in a subshell l 0 (s) 1 (p) 2 (d) 3 (f) PLOshikiri/04 Possible values of ml # orbitals in the subshell 0 1 -1 , 0 ,+1 3 -2, -1, 0, +1, +2 5 -3, -2, -1, 0, +1,+2,+3 7 13 SPIN QUANTUM NUMBER Direction of spin (s) Spin makes the electron behave like tiny magnets Spin can be clockwise or counterclockwise Spin quantum numbers can have values of +½ or -½ PLOshikiri/04 14 SPIN QUANTUM NUMBER PLOshikiri/04 15 Quantum Numbers & Atomic Structure PLOshikiri/04 16 ATOMIC ORBITALS Region in space where there is a high probability of finding an electron Shapes s – spherical p – dumbbell-shaped d & f – complex shapes Special People Don’t Forget 1, 3, 5, 7 PLOshikiri/04 17 ATOMIC ORBITALS (s-orbital) PLOshikiri/04 18 ATOMIC ORBITALS (p-orbital) PLOshikiri/04 19 ATOMIC ORBITALS PLOshikiri/04 20 ATOMIC ORBITALS PLOshikiri/04 21 ATOMIC ORBITALS f - orbitals PLOshikiri/04 22 ELECTRON CONFIGURATION An arrangement of electrons in an atom GROUND STATE – the lowest energy state of an atom EXCITED STATE – a state in which an atom has a higher potential energy DEGENERATE ORBITALS – two or more orbitals that have the same energy (p, d, f) ELECTRON ARRANGEMENT DETERMINES THE CHEMICAL BEHAVIOR OF ATOMS PLOshikiri/04 23 ELECTRON CONFIGURATION (RULES) AUFBAU PRINCIPLE Electrons enter atomic orbitals of lower energy first PLOshikiri/04 24 Aufbau Principle PLOshikiri/04 25 Diagonal Diagram 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s PLOshikiri/04 26 PAULI EXCLUSION PRINCIPLE No two electrons can have the same set of quantum numbers An atomic orbital contains a maximum of two electrons PLOshikiri/04 27 HUND’S RULE Orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron Electrons in singly occupied orbitals must have the same spins PLOshikiri/04 28 Representing Electron Configurations ORBITAL NOTATION –orbital is represented by a line, with the orbital’s name written under the line and the electrons are represented by arrows. PLOshikiri/04 29 Electron Configuration & Periodic Table PLOshikiri/04 30 OUTERMOST SUBLEVEL BEING FILLED PLOshikiri/04 31 Representing Electron Configurations ELECTRON CONFIGURATION NOTATION Carbon: 1s22s22p2 HIGHEST OCCUPIED LEVEL Electron-containing main energy level with the highest principal quantum number VALENCE ELECTRONS Electrons in the highest occupied main energy level INNER SHELL (CORE) ELECTRONS Electrons that are not in the highest occupied energy level PLOshikiri/04 32 Inner Core & Valence Electrons PLOshikiri/04 33 Representing Electron Configurations NOBLE GAS NOTATION Na: [Ne]3s1 P: [Ne]3s23p3 Noble Gas Configuration An outer main energy level fully occupied, in most cases, by eight electrons (octet) Ne: 1s22s22p6 Ar: [Ne] 3s23p6 PLOshikiri/04 34 Noble Gas Notation PLOshikiri/04 35 Outer Electron Config. PLOshikiri/04 36 Electron Dot Notation PLOshikiri/04 37 EXCEPTIONS TO RULES Half filled orbitals - Cr24 1s22s22p63s23p6 4s2 3d4 ] [[[[p Stable configuration is 1s22s22p63s23p6 4s1 3d5 [ [[[[[ PLOshikiri/04 38 EXCEPTIONS TO RULES Filled Orbitals - Cu29 1s22s22p63s23p6 4s2 3d9 ] ]]]][ Stable configuration is 1s22s22p63s23p6 4s1 3d10 [ ]]]]] PLOshikiri/04 39 Quantum Numbers & Atomic Orbitals PLOshikiri/04 40 Quantum Number Set PLOshikiri/04 41 EC & Quantum Numbers n =2 N: 1s22s22p3 fff l= 1 n =1 l= 0 ml=+1 s=+1/2 fg ml=0 s =-1/2 PLOshikiri/04 42