110323 - Atomic orbitals and periodic table (Chapter 11...

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1 CHM3400 - Lecture 28 Mar 23 Atomic orbitals and periodic table (Chapter 11 426-439) Hydrogen atom: Schroedinger wave equation and orbitals Electron density Pauli exclusion and Hund’s rule Many-electron atoms and the periodic table Atomic radii and ionization energies
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2 Schroedinger equation for the hydrogen atom Three-dimensional problem: 0 ) ( 8 2 2 2 2 2 2 2 2 = + + + ψ π ψψ V E h m z y x e r e 0 2 4 πε Can be reduced to a spherical problem (spherical coordinates): ) ( ) ( ) ( ) , , ( φ θ Φ Θ = r R r Wavefunction is the product of the radial part R(r), and the angular part Θ ( θ ) Φ ( φ )
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3 Solutions to wavefunction equation Solution gives rise to the 3 quantum numbers: principal quantum number , n , determines the size of the wavefunction and the energy of the electron ( n = 1, 2, 3, 4, etc.) ( n = K, L, M, N, etc.) azimuthal quantum number , l , determines the shape of the wavefunction ( l =0, 1,2, …,(n-1))
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110323 - Atomic orbitals and periodic table (Chapter 11...

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