3.012 Fund of Mat Sci: Bonding Lecture 8. M. C. Escher, "Ascending and Descending," Image removed for copyright reasons.

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1 .0 Fund of Mat Sci: Bonding Lecture 8 THE PERIODIC TABLE M. C. Escher, "Ascending and Descending," 960. Image removed for copyright reasons..0 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 00

2 Homework for Fri Oct 7 Study:.,.,.,. Exam check all points mentioned in PS. Study all paragraphs assigned from textbook. Old problem sets, quizzes, available on Stellar, together with solutions Office hours.0 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 00

3 Last time:. Absorption/emission processes, XPS. Orbitals in a central potential. Accidental degeneracies removed by centripetal potential, and screening. Coupled ( Hartree equations for a many electron atom. Spin.0 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 00

4 Many-electron case.0 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 00

5 Helium atom.0 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 00

6 Hartree equations.0 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 00

7 Right experiment wrong theory (Stern-Gerlach ˆ ˆ µ r B ˆ ˆ µ B H H + L B= H + Lˆ zb h h z Image courtesy of Theresa Knott. ˆ ˆ µ r B ˆ ˆ ˆ B H H + ( L+ S B= H + µ ( Lˆ + Sˆ B h h.0 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 00 z z z Goudsmit and Uhlenbeck

8 Spin Eigenvalues/Eigenfunctions Norm (s integer bosons, half-integer fermions ˆ spin h s s S ( Z-axis projection (electron is a fermion with s=/ Sˆ Ψ = + Ψ h Ψ =± Ψ z spin spin spin Spin-orbital: product of the space wavefunction and the spin wavefunction.0 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 00

9 Pauli Exclusion Principle We can t have two electrons in the same quantum state Any two electrons in an atom cannot have the same quantum numbers n,l,m,m s.0 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 00

10 ENERGY LEVELS OF THE ELECTRONS ABOUT THEIR NUCLEI 6s 6p d f Auf-bau LOW ENERGY HIGH ENERGY s s s p p p d d p s s Figure by MIT OCW..0 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 00

11 The periodic table Source: Wikipedia.0 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 00

12 Periodic Table Electronic Configuration Z ELEMENT ELECTRONIC* CONFIGURATION TERM* IONIZATION POTENTIAL (ev Z ELEMENT ELECTRONIC* CONFIGURATION TERM* I ONIZATION POTENTIAL (ev H Hydrogen He Helium Li Lithium Be B C N O F Ne Na Mg Al Si P S Cl Ar K Beryllium Boron Carbon Nitrogen Oxygen Fluorine Neon Sodium Magnesium Aluminium Silicon Phosphorus Sulphur Chlorine Argon Potassium Ca Calcium Sc Scandium Ti Titanium V Vanadium Cr Chromium Mn Manganese Fe Iron Co Cobalt Ni Nickel Cu Zn Ga Ge As Se Br Kr Rb Sr Copper Zinc Gallium Germanium Arsenic Selenium Bromine Krypton Rubidium Strontium Y Yttrium Zr Zirconium Nb Niobium Mo Molybdenum Tc Technetium Ru Ruthenium Rh Rhodium Pd Ag Cd In Sn Sb Palladium Silver Cadmium Indium Tin Antimony s s [He]s [He]s [He]s p [He]s p [He]s p [He]s p [He]s p [He]s p 6 [Ne]s [Ne]s [Ne]s p [Ne]s p [Ne]s p [Ne]s p [Ne]s p [Ne]s p 6 [Ar]s [Ar]s [Ar]s d [Ar]s d [Ar]s d [Ar]sd [Ar]s d [Ar]s d 6 [Ar]s d 7 [Ar]s d 8 [Ar]sd 0 [Ar]s d 0 [Ar]s d 0 p [Ar]s d 0 p [Ar]s d 0 p [Ar]s d 0 p [Ar]s d 0 p [Ar]s d 0 p 6 [Kr]s [Kr]s [Kr]s d [Kr]s d [Kr]sd [Kr]sd [Kr]s d [Kr]s d 7 [Kr]s d 8 [Kr]d 0 [Kr]sd 0 [Kr]s d 0 [Kr]s d 0 p [Kr]s d 0 p [Kr]s d 0 p *Configurations and terms in parentheses are estimated. Figure by MIT OCW. S / S / P / P 0 S / P P / S / P / P 0 S / P P / S / D / F F / 7 S 6 S / D F 9/ F S / P / P 0 S / P P / S / D / F 6 D / 7 S 6 S / F F 9/ S / P / P 0 S / Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall Te I Xe Cs Ba La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po Ar Rn Fr Ra Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Tellurium Iodine Xenon Cesium Barium Lanthanum Cerium Praseodymium Neodymium Promethium Samarium Europium Gadolinium Terbium Dysprosium Holmium Erbium Thulium Ytterbium Lutetium Hafnium Tantalum Tungsten Rhenium Osmium Iridium Platinum Gold Mercury Thallium Lead Bismuth Polonium Astatine Radon Francium Radium Actinium Thorium Protactinium Uranium Neptunium Plutonium Americium Curium Berkelium Californium Einsteinium Fermium Mendelevium Nobelium 0 Lw Lawrencium [Kr]s d 0 p [Kr]s d 0 p [Kr]s d 0 p 6 [Xe]6s [Xe]6s [Xe]6s d [Xe](6s fd [Xe](6s f [Xe]6s f [Xe](6s f [Xe]6s f 6 [Xe]6s f 7 [Xe]6s 7 f d [Xe](6s f 9 [Xe](6s f 0 [Xe](6s f [Xe](6s f [Xe]6s f [Xe]6s f [Xe]6s f d [Xe]6s f d [Xe]6s f d [Xe]6s f d [Xe]6s f d [Xe]6s f d 6 [Xe]6s f d 7 [Xe]6sf d 9 [Xe]6sf d 0 [Xe]6s f d 0 [Xe]6s f d 0 6p [Xe]6s f d 0 6p [Xe]6s f d 0 6p [Xe]6s f d 0 6p [Xe](6s f d 0 6p [Xe]6s f d 0 6p 6 [Rn]7s [Rn]7s [Rn]7s 6d [Rn]7s 6d [Rn](7s f 6d [Rn]7s f 6d [Rn]7s f 6d [Rn]7s 6 f [Rn]7s 7 f [Rn]7s 7 f 6d [Rn]7s 8 f 6d [Rn]7s f 0 [Rn]7s f [Rn](7s f [Rn](7s f [Rn](7s f [Rn]7s f 6d P P / S / D / ( G ( I 9/ I ( 6 H / 7 F 0 8 S 7/ 9 D 6 H / ( I 8 ( I / ( H 6 F 7/ D / F F / D 0 6 S / D ( F 9/ D S / P / P 0 S / P P / S / D / F ( K / L 6 L / 7 F 0 8 S 7/ 9 D 8 H 7/ I 8 I / ( H 6 ( F 7/ ( ( D / Electronic configuration, term value, and ionization potential of the atoms in their ground state

13 Atomic radii Graph of atomic radius plotted against atomic number removed for copyright reasons. See Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 00

14 Graphs of ionization enthalpy plotted against atomic number removed for copyright reasons..0 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 00

15 Graphs of electron affinity plotted against atomic number removed for copyright reasons. See and Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 00

16 Good Quantum Numbers d A d Ψ Aˆ Ψ = = Aˆ, Hˆ dt dt ih If A commutes with the Hamiltonian, its expectation value does not change with time (it s a constant of motion if we are in an eigenstate, that quantum number will remain constant.0 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 00

17 Variational Principle E [ ] Φ = Φ Ĥ Φ ΦΦ E [ Φ] E0 [ Φ ] = E0 If, then Φ is the ground E state wavefunction, and viceversa.0 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 00

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