Lect13 - Last week of Course Last week of Course z Today --...

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Unformatted text preview: Last week of Course Last week of Course z Today -- Atoms, Molecules, Solids z States with many electrons filled according to the Pauli exclusion principle Final Exam Monday March 3 Review session Sunday March 2 Extra office hours (Wed.,Sun.,Mon) z Next time Consequences of quantum mechnanics z Metals, insulators, semiconductors, superconductors, lasers, . . Any students who cannot take the 214 final and the conflict should email Professor Tai C. Chiang [chiang@mrl.uiuc.edu] ASAP, and no later than noon, Wednesday. Do not email Professor Clegg (as it says on the web site). He will just forward your email Building Atoms, Molecules and solids U(r) r a 3 1 2 4 5 6 + e r + e even + e r n = 3 n = 2 n = 1 Overview Overview z Molecular Wavefunctions: origins of covalent bonds z Example: H + H H 2 z Atomic Configurations z States in atoms with many electrons filled according to the Pauli exclusion principle z Electron energy bands in Solids z States in atoms with many electrons filled according to the Pauli exclusion principle Review session Sunday Extra office hours (TBA) z Therefore, electrons do not pile up in the lowest energy state, i.e, the (1,0,0) orbital. z They are distributed among the higher energy levels according to the Pauli Principle. z Particles that obey the Pauli Principle are called fermions Pauli Exclusion Principle Pauli Exclusion Principle From spectra of complex atoms, Wolfgang Pauli (1925) deduced a new rule: No two electrons* can be in the same quantum state, i.e. in a given atom they cannot have the same set of quantum numbers n, l , m l , m s -- i.e., every atomic orbital with n, l ,m l can hold 2 electrons: ( ) Pauli Exclusion Principle Lets start building more complicated atoms to study the Periodic Table . For atoms with many electrons (e.g., carbon: 6, iron: 26, etc.) - what energies do they have? *Note: More generally, no two identical fermions (any particle with spin of /2, 3 /2, etc.) can be in the same quantum state. Repeat from Lect. 12 Filling the atomic Filling the atomic orbitals orbitals according to the according to the Pauli Principle Pauli Principle 2 2 n Z n eV 6 . 13 E = is valid only for one electron in the Coulomb potential of Z protons. The energy levels shift as more electrons are added, due to electron-electron interactions. Nevertheless, this hydrogenic diagram helps us keep track of where the added electrons go. Energy n 4 3 2 1 l = 0 1 2 3 4 s p d f g Example: Na Z = 11 1s 2 2s 2 2p 6 3s 1 l label #orbitals (2 l +1) Z = atomic number = number of protons 0 s 1 1 p 3 2 d 5 3 f 7 Act 1: Pauli Exclusion Principle Act 1: Pauli Exclusion Principle 1. Which of the following states (n, l ,m l ,ms) is/are NOT allowed?...
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Lect13 - Last week of Course Last week of Course z Today --...

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