Periodic Table Quantum Numbers The Bohr model of

Periodic Table

Quantum Numbers ] The Bohr model of hydrogen provided a single quantum number n. • Principal quantum number • One-dimensional solution ] Schrödinger’s equation for a real atom is 3 -D. • Two other quantum numbers • Orbital angular momentum • Orbital magnetic number 1 2 3 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

Zeeman Effect ] 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 • Lz is with respect to field

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

Electron Configurations ] Electrons in atoms populate the lowest energies first. • Two electrons per state for spin ] Atoms have unique ground states. • • Hydrogen has 1 1 s electron Helium adds another 1 s Lithium must start 2 s shell Boron starts 2 p 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 2+2+6+10+2+2=32

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

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