Lect19 - Lecture 19: Building Atoms, Molecules and solids...

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Lecture 19: Building Atoms, Molecules and solids un g m , M u n U(r) r a + e r n = 3 n = 2 ψ 5 ψ 6 n = 1 ψ 4 + e r + e ψ 3 ψ 2 ψ even Lecture 19, p 1 ψ 1
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Today Atomic Configurations tates in atoms with many electrons States in atoms with many electrons – filled according to the Pauli exclusion principle Molecular Wave Functions: origins of covalent bonds Example: H + H H 2 Electron energy bands in Solids tates in atoms with many electrons States in atoms with many electrons filled according to the Pauli exclusion principle Lecture 19, p 2
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Pauli Exclusion Principle Let’s start building more complicated atoms to study th e Periodic Table. For atoms with many electrons (e.g., carbon: 6, iron: 26, etc.) … What energies do the electrons have? “Pauli Exclusion Principle” (1925) No two electrons can be in the same quantum state. For example, in a given atom they cannot have the same set of quantum numbers n, l , m l , m s . his means that each atomic orbital (n, can hold 2 electrons: = . This means that each atomic orbital (n, l ,m l ) can hold 2 electrons: m s ±½. Important consequence: lectrons do not pile up in the lowest energy state Electrons do not pile up in the lowest energy state. It’s more like filling a bucket with water. They are distributed among the energy levels ccording to the Exclusion Principle Lecture 19, p 3 according to the Exclusion Principle. Particles that obey this principle are called “ fermions ”. Protons and neutrons are also fermions, but photons are not.
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Filling Atomic Orbitals According to the Exclusion Principle 2 2 n Z n eV 6 . 13 E = Energy n l = 0 1 2 3 4 s p d f g Lecture 15 In a multi-electron atom, the H-atom energy level diagram is distorted by Coulomb repulsion between electrons. Nevertheless, the H-atom diagram is 4 3 useful (with some caveats) for figuring out the order in which orbitals are filled. 2 Example: Na (Z = 11) 1s 2 2s 2 2p 6 3s 1 l label #orbitals (2 l +1) 0 s 1 p 1 3 2d 5 3 f 7 Lecture 19, p 4 1 Z = atomic number = # protons
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Act 1 hich of the following states (n is/are OT llowed? 1. Which of the following states (n, l ,m l ,m s ) is/are NOT allowed? a. (2, 1, 1, -1/2) b. (4, 0, 0, 1/2) c. (3, 2, 3, -1/2) d. (5, 2, 2, 1/2) 2. Which of the following atomic electron configurations violates the Pauli e. (4, 4, 2, -1/2) Exclusion Principle? 0 a. 1s 2 , 2s 2 , 2p 6 , 3d 10 b. 1s 2 , 2s 2 , 2p 6 , 3d 4 c. 1s 2 , 2s 2 , 2p 8 , 3d 8 s 2s 2p 3d Lecture 19, p 5 d. 1s 1 , 2s 2 , 2p 6 , 3d 5 e. 1s 2 , 2s 2 , 2p 3 , 3d 11
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Solution hich of the following states (n is/are OT llowed? 1. Which of the following states (n, l ,m l ,m s ) is/are NOT allowed? a. (2, 1, 1, -1/2) b. (4, 0, 0, 1/2) c. (3, 2, 3, -1/2) m l > l d. (5, 2, 2, 1/2) 2. Which of the following atomic electron configurations violates the Pauli e. (4, 4, 2, -1/2) l = n Exclusion Principle? 0
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This note was uploaded on 04/04/2011 for the course PHYSICS 214 taught by Professor Mestre during the Spring '11 term at University of Illinois at Urbana–Champaign.

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Lect19 - Lecture 19: Building Atoms, Molecules and solids...

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