Lect19(2) - L ectur e 19: Bui l di ng Atoms, M ol ecul es...

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Lecture 19, p 1 Lecture 19: Building Atoms, Molecules and solids U(r) r a ψ 3 ψ 1 ψ 2 ψ 4 ψ ψ 6 + e r + e ψ even + e r n = 3 n = 2 n = 1
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Lecture 19, p 2 Today Atomic Configurations 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 States in atoms with many electrons – filled according to the Pauli exclusion principle
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Lecture 19, p 3 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 . This means that each atomic orbital (n, l ,m l ) can hold 2 electrons: m s = ±½. Important consequence: 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 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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Lecture 19, p 4
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Lecture 19, p 5 Filling Atomic Orbitals According to the Exclusion Principle 2 2 n Z n eV 6 . 13 E - = In a multi-electron atom, the H-atom energy level diagram is distorted by Coulomb repulsion between electrons. Nevertheless, the H-atom diagram is useful (with some caveats) for figuring out the order in which orbitals are filled. 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 Z = atomic number = # protons l label #orbitals (2 l +1) 0 s 1 1 p 3 2 d 5 3 f 7 Lecture 15
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Lecture 19, p 6 Act 1 1. Which of the following states (n, l ,m l ,m s ) is/are NOT allowed? 2. Which of the following atomic electron configurations violates the Pauli Exclusion Principle? a. (2, 1, 1, -1/2) b. (4, 0, 0, 1/2) c. (3, 2, 3, -1/2) d. (5, 2, 2, 1/2) e. (4, 4, 2, -1/2) 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 d. 1s 1 , 2s 2 , 2p 6 , 3d 5 e. 1s 2 , 2s 2 , 2p 3 , 3d 11
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Lecture 19, p 7 Filling Procedure for Atomic Orbitals Due to electron-electron interactions, the hydrogen levels fail to give us the correct filling order as we go higher in the periodic table.
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Lect19(2) - L ectur e 19: Bui l di ng Atoms, M ol ecul es...

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