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Orbitals Orbitals are NOT circular orbits for electrons Orbitals are “areas of probability” for locating electrons A function of the coordinates (x, y, and z) of the electron’s position in 3-D space Heisenberg Uncertainty Principle “ There is a fundamental limitation on how precisely we can know both the position and momentum of a particle at a given time.” The more accurately we know the position of any particle, the less accurately we can know its momentum and vice versa Physical Meaning of a Wave Function Square of the absolute value of the wave function gives a probability distribution Electron density map indicates the most probable distance from the nucleus Wave functions and probability maps do not describe How an electron arrived at its location Where an electron will go next When the electron will be in a particular location Quantum Numbers Principal Quantum Number (n) Integral values: 1,2,3, etc Indicates probable distance from the nucleus Higher number – greater distance Greater distance – less tightly bound Higher energy Angular Momentum Quantum (l) Integral values from 0 to n-1 for each principal quantum number n Indicates the shape of the atomic orbital Angular Momentum & Orbital Angular Momentum Quantum Numbers and Corresponding Atomic Orbital Number Value of l (angular) 0 1 2 3 Letter Used s p d f Quantum Numbers Magnetic Quantum Number (ml) Integral values from l to -l (including 0) Related to the orientation of the orbital in space relative to the other orbitals Electron Spin Quantum Number An orbital can hold only two electrons They must have opposite spins + ½ or - ½ Pauli Exclusion Principle No two electrons can have the same set of four quantum numbers Quantum Numbers for the First Four Levels of Orbitals in the H Atom n l Orbital ml # of orbitals 1 0 1s 0 1 2 0 2s 0 1 1 2p -1, 0, 1 3 0 3s 0 1 1 3p -1, 0, 1 3 2 3d -2, -1, 0, 1, 2 5 0 4s 0 1 1 4p -1, 0, 1 3 2 4d -2, -1, 0, 1, 2 5 3 4f -3, -2, -1, 0, 1, 2, 3 7 3 4 Orbital Shapes & Energies Size of Orbitals Defined as the surface that contains 90% of the total electron probability Orbitals of the same shape (eg: s) grow larger as n increases S Orbitals Spherical Nodes (s orbitals of n≥2) Internal regions of zero probability See p. 309 p Orbitals Two lobes each Occur in levels n≥2 Each orbital lies along an axis 2px 2py 2pz d Orbitals Occur in levels n≥3 Two fundamental shapes Four orbitals with four lobes each Centered on each indicated plane dxz, dyz, dxy, dx2y2 Fifth orbital is uniquely shaped Two lobes along the z axis and a belt centered in the xy plane – dz2 d Orbitals f Orbital Occur in levels n≥4 Highly complex shapes Not involved in bonding in most compounds Orbital Energies All orbitals with the same value of n have the same energy The lowest E state is the ground state When atoms absorb energy – electrons may move to higher energy levels Excited state