Periodic Table

Quantum Numbers  The Bohr model of hydrogen provided a single quantum number n. Principal quantum numberPrincipal quantum number One-dimensional solutionOne-dimensional solution  Schrödinger’s equation for a real atom is 3-D. Two other quantum numbersTwo other quantum numbers Orbital angular momentumOrbital angular momentum Orbital magnetic numberOrbital magnetic number Shells for the principal quantum number n

Orbital Shells  The orbital angular momentum l is quantized in steps of h. Values from 0 to n -1  The values are named based on early spectroscopy. n shells 1=K, 2=L, 3=M, 4=N, 5=O l shells 0=s, 1=p, 2=d, 3=f, 4=g A. Clark, Chemical Computing Group

 Spectral lines from atoms in a strong magnetic field are split. Zeeman effect Magnetic moment of orbiting electron  Orbital magnetic number ml lines up with applied field. Values from –l to l L z is with respect to field Zeeman Effect

Spin  Electrons possess intrinsic angular momentum. Spin angular momentum sSpin angular momentum s Spin magnetic number m sSpin magnetic number m s  Electron spin s can only have one value: 1/2. m s = +1/2 or -1/2m s = +1/2 or -1/2 Spin up or spin downSpin up or spin down  No two atomic electrons can occupy the same set of quantum numbers. Pauli exclusion principle Applies to fermions  Photons are spin 1

Electron Configurations  Electrons in atoms populate the lowest energies first. Two electrons per state for spinTwo electrons per state for spin  Atoms have unique ground states. Hydrogen has 1 1s electronHydrogen has 1 1s electron Helium adds another 1sHelium adds another 1s Lithium must start 2s shellLithium must start 2s shell Boron starts 2p shell which holds 6 electronsBoron starts 2p shell which holds 6 electrons H He Li Be B C N O

Germanium  Germanium (Ge) has an atomic number of 32. Find the shell configuration for the ground state.  Start counting shells from the lowest state. n = 1, l = 0: 1 s – 2 electrons n = 2, l = 0: 2 s – 2 electrons n = 2, l = 1: 2 p – 6 electrons n = 3, l = 0: 3 s – 2 electrons n = 3, l = 1: 3 p – 6 electrons n = 3, l = 2: 3 d – 10 electrons n = 4, l = 0: 4 s – 2 electrons n = 4, l = 1: 4 p – 2 electrons  Total =32

Organized Table  The periodic table was organized to explain chemical properties. Quantum physics explained structureQuantum physics explained structure

Energy Levels  Subshell: S G F D P  Period 1 1s1 1s 2 2s 2p2 2s 2p 3 3s 3p3 3s 3p 4 4s 3d 4p4 4s 3d 4p 5 5s 4d 5p5 5s 4d 5p 6 6s 4f 5d 6p6 6s 4f 5d 6p 7 7s 5f 6d 7p7 7s 5f 6d 7p 8 8s 5g 6f 7d 8p8 8s 5g 6f 7d 8p  The shells don’t fill up in exact order.  Energy levels are determined by quantum calculations. General patterns exist next