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Name___________________________________________________ QUANTUM MECHANICAL MODEL OF THE ATOM Contributors to the quantum mechanical model in mid-1920s: Louis deBroglie Erwin Schrödinger Werner Heisenberg Schrödinger – treat e– as a wave Schrödinger equation: Ĥ = E solve to get wave functions, which predict locations of electrons wave function = ORBITAL – region with 90% probability of holding an e– QUANTUM NUMBERS orbitals characterized by 4 no.’s: 1. principal quantum number (n) value of n corresponds to: o n= o 2. angular momentum quantum # (l) l = 0, 1, … n-1 (l ≠ n) If n = 1 then l = If n = 2 then l = If n = 3 then l = value tells you: assign a letter: l =0 1 2 3 shapes: pages 311 – 313 ___ ___ ___ ___ put first 2 quantum numbers together: n = 1, l = 0 _____ n = 4, l = 2 _____ n = 3, l = 1 _____ 3s _______________ 5f _______________ 3. magnetic quantum number (ml) ml = -l to +l including zero values of ml tell you: If l = 0 then ml = o If l = 1 then ml = o If l = 2 then ml = 4. spin quantum # (ms) ms = + ½ or – ½ value gives: A maximum of ____ e– fit in each orbital! PAULI EXCLUSION PRINCIPLE In a given atom, no two electrons can have four identical quantum numbers. Complete the chart below: n l orbitals # orbitals # e– List 4 possible quantum numbers for the following using the notation (n, l, ml, ms): an e– in a 2s orbital an e– in a 3p orbital an e– in a 4d orbital