Chapter 28 Quantum Mechanics of Atoms

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28.6 Quantum Mechanics of the Hydrogen Atom; Quantum Numbers 4. The spin quantum number, m s , which for an electron can take on the values +½ and -½. The need for this quantum number was found by experiment; spin is an intrinsically quantum mechanical quantity, although it mathematically behaves as a form of angular momentum. 28.6 Quantum Mechanics of the Hydrogen Atom; Quantum Numbers This table summarizes the four quantum numbers. 28.6 Quantum Mechanics of the Hydrogen Atom; Quantum Numbers Lowest state has no angular momentum, that is no orbit in classical sense. Why does it not fall into the nucleus? Remember Heisenberg’s uncertainty principle! The electron cannot be localized so well. 2 2 2 e m 2 p h k = E = v = ≈ 2 2 r 2 2m 2π mr 2 2 2 2 4 1 2π ke 2π k e ≈ E ≈ = 13.6 eV 2 2 r h h 28.6 Quantum Mechanics of the Hydrogen Atom; Quantum Numbers The angular momentum quantum numbers do not affect the energy level much, but they do change the spatial distribution of the electron cloud. 28.6 Quantum Mechanics of the Hydrogen Atom; Quantum Numbers “Allowed” transitions between energy levels occur between states whose value of l differ by one: This is a quantum-mechanical variant of momentum conservation because the photon also has angular momentum. 28.7 Complex Atoms; the Exclusion Principle Complex atoms contain more than one electron, so the interaction between electrons must be accounted for in the energy levels. This means that the energy depends on both n and l. A neutral atom has Z electrons, as well as Z protons in its nucleus. Z is called the atomic number. 4
28.7 Complex Atoms; the Exclusion Principle In order to understand the electron distributions in atoms, another principle is needed. This is the Pauli exclusion principle: No two electrons in an atom can occupy the same quantum state. The quantum state is specified by the four quantum numbers; no two electrons can have the same set. 28.7 Complex Atoms; the Exclusion Principle This chart shows the occupied – and some unoccupied – states in He, Li, and Na. 28.8 The Periodic Table of the Elements 28.8 The Periodic Table of the Elements We can now understand the organization of the periodic table. Electrons with the same n are in the same shell. Electrons with the same n and l are in the same subshell. The exclusion principle limits the maximum number of electrons in each subshell to 2(2l + 1). Each value of l is given its own letter symbol. 28.8 The Periodic Table of the Elements Electron configurations are written by giving the value for n, the letter code for l, and the number of electrons in the subshell as a superscript. For example, here is the ground-state configuration of sodium: 28.8 The Periodic Table of the Elements This table shows the configuration of the outer electrons only. 5
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Chapter 28 Quantum Mechanics of Atoms

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