Modern Atomic Theory Electron Atomic Orbitals Part I: Quantum Mechanical Model • The Bohr model’s prediction of electron energies and locations was limited in accuracy to the Hydrogen atom. • Scientists DeBroglie and Schrödinger proposed that the electrons is acting as a wave as well as a particle. • Schrödinger developed an equation which predicts the location of an electron based upon probabilities. • Electrons in this model are located in Orbitals not orbits, despite sounding similar, they are vastly different. • The location of the electron is given by four numbers called Quantum Numbers • These quantum numbers act like your street address that give you homes location. – Zip code – State – City – Street – Number – Suite Quantum Numbers [n, l, ml, ms] • n is the principle energy level. Limited to integers starting at 1. [n = 1, 2, 3….] • l is the orbital quantum number. Its values are limited to all integer values up to n-1. • ml is the magnetic quantum number. Its values are limited to integers from -l to +l. • ms is the electron spin designation. It is either +½ for spin up or -½ for spin down. Shapes of Orbitals • The shape of the orbital is given by the second and third quantum numbers. • Instead of using a number for the second quantum number, l, a letter designation is used. – – – – – – 0 is s (sharp) 1 is p (principle) 2 is d (diffuse) 3 is f (fundamental) 4 is g and so on down the alphabet • The third quantum number ml, determines the number of possible orientations of the orbital based on the second quantum number. • If l = 0 then ml can only be 0 and there is only one orientation of the orbital. • If l = 1 then ml can be [-1, 0, +1] and there are three orientations of a “p” orbital. • If l = 2 then ml can be [-2, -1, 0, +1, +2] so there are five orientations for a “d” orbital. • If l = 3 then ml can be [-3, -2, -1, 0, +1, +2, +3] so there are seven orientations for a “f” orbital. s Orbitals [l = 0] • The s orbital is spherically shaped. • There is only one possible orientation for the s orbital. • Each energy level has an s orbital and they get concentrically larger. • Two electrons fill each s orbital p Orbital [l = 1] • The p orbital is “dumbbell” shaped. • There are three possible orientations for the p orbital. • Each energy level n=2 and beyond has a p orbital and they get concentrically larger. • Two electrons fill each orientation of the p orbital for a total of 6 electrons per energy level. p Orbitals – three orientations d Orbital [l = 2] • The d orbitals are uniquely shaped. • There are five possible orientations for the d orbital. • Each energy level n=3 and beyond has a d orbital and they get concentrically larger. • Two electrons fill each orientation of the d orbital for a total of 10 electrons per energy level. d Orbitals f Orbital [l = 3] • The f orbitals are uniquely shaped. • There are seven possible orientations for the f orbital. • Each energy level n=4 and beyond has an f orbital and they get concentrically larger. • Two electrons fill each orientation of the f orbital for a total of 14 electrons per energy level. f Orbitals The location of electrons is a superposition of all of the individual orbitals.