2. Modern Atomic Theory and the Periodic Table Preparation for College Chemistry Luis Avila Columbia University Department of Chemistry

3. Total Energy of a Particle in Motion Trajectory : Statement of both p(t) and x(t) of a particle E = 1212 m v 2 + V Nature is Continuous m grafite = 9.8266kg e.m.f =.992 V Knowing the forces among particles it is possible to predict the future trajectory of a group of particles As a function of momentum p e.m.f = 1.0 V m grafite = 9.83kg Classical Mechanics Central Ideas End of 19th Century

4. 19101895 Einstein’s Photons 1905 Thomson discovers the electron Rutherford Experiment 1900 Planck’s Quantum Theory (Max Planck) 1913 Bohr’s atomic Model (Niels Bohr) 1924 De Broglie Waves (Louis De Broglie)

5. 19281925 Indeterminacy Principle (W. Heisemberg) 1927 Quantum Mechanics (Heisenberg, Max Born) Copenhagen Interpretation (Bohr, Heisemberg, Schrödinger) 1926 The Wave equation (Erwin Schrödinger) Complementarity Principle: Knowledge of atomic and molecular-scale phenomena is essentially incomplete until both particle and wave aspects of it are known. Paul Dirac Robert Oppenheimer

6. Failures of Classical Mechanics 2000 K M 12-C = 1.99265 x 10 -26 kg Atoms are discrete e = 1.6021773 x 10 -19 C 1750 K 1250 K 6000 2000 4000 (dU/d )Jm -1 / nm Visible region Black-body Radiation

7. Ultraviolet Catastrophe Raileigh-Jean 6000 2000 4000 Energy / nm Observed, Planck

8. Photoelectric Effect e- ≥ 0 < 0

9.  E The Work Function

10. Characteristics of a Wave Wavelength Amplitude Low frequency wave High frequency wave t(s)

11. Characteristics of a Wave 0° 90° 180° 270° 360° Progress of a cycle: Phase

12. Characteristics of a Wave Electric Field Orientation: Polarization Magnetic Field

13. Wave Interference = = Out of Phase In Phase Constructive Interference Destructive Interference

17. Atomic (line) Spectra Ground state 1st excited state 2nd excited state

18. h= Planck Constant = 6.621 x 10 -34 Js c= Speed of light in vacuum = 2.99 10 8 ms -1 Ex. The energy for the yellow line in the sodium spectrum with a = 589 nm Planck Equation. Max Plank 1900 EM radiation is emitted in QUANTA with energy E Planck-Einstein Equation

19. Atomic models Rutherford- Circular ORBITS Bohr -Circular Quantized ORBITS Bohr- Sommerfeld Circular and elliptical Quantized ORBITS

20. The Bohr-Sommerfeld Atom Circular Quantized ORBITS

21. The Quantum Mechanical Atom Probabilistic Region = ORBITAL Werner Heisenberg 1927 Uncertainty (Indeterminacy) Principle ∆x ~ ; ∆p ~ h/ Erwin Schrödinger 1925- Wave equation http://www.aip.org/history/heisenberg/

23. Four Quantum Numbers n: Principal Quantum number (orbital size, energy, # shells) l: Secondary Quantum number (orbital shape) m l : Magnetic Quantum number (orbital orientation in space) m s (s): Spin Quantum number (orbital energy)

24. Sublevels Quantum number l takes on values 0, 1, 2,...(n-1) according to values of n n l 1 2 3 4 0 0, 10, 1, 20, 1, 2, 3 Orbitals s s, p s, p, d s, p, d, f l = 0 (s); l =1 (p); l = 2 (d); l = 3(f)

25. Sublevels Magnetic Quantum number m l takes on values -l,...,0,...+l It divides the sublevels into individual orbitals. l mlml 0 1 2 0 -1, 0, 1 -2, -1, 0, 1, 2 Orbitals s p x, p y, p z d xz, d xy,, d yz, d z 2, d x 2 - z 2

30. Pauli Exclusion Principle “No two electrons in an orbital may have the same set of quantum numbers, or two electrons with the same spin may not occupy the same point in space at the same time” Maximum capacity of principal level = 2n 2

31. Energy Levels of Electrons n = 1 n = 2 n = 3 n = 4 Maximum capacity of principal level = 2n 2 2 8 18 32

32. Arrangement of electrons in orbitals [Aufbau (building up) principle] 3d63d6 r Electronic Configuration nl # electrons r Orbital diagram

33. Orbital Filling Z Element Electronic config. 1 2 3 4 5 6 7 8 9 10 H He Li Be B C N O F Ne 1s 1 1s 2 [He]2s 1 [He]2s 2 [He]2s 2 2p 1 [He]2s 2 2p 2 [He]2s 2 2p 3 [He]2s 2 2p 4 [He]2s 2 2p 5 [He]2s 2 2p 6 1s 2s 2p

34. Orbital Filling Z Element Electronic config. 11 12 13 14 15 16 17 18 Na Mg Al Si P S Cl Ar [Ne]3s 1 [Ne]3s 2 [Ne]3s 2 3p 1 3s 3p [Ne]3s 2 3p 2 [Ne]3s 2 3p 3 [Ne]3s 2 3p 4 [Ne]3s 2 3p 5 [Ne]3s 2 3p 6 When e- are added to equal energy orbitals. They will half fill every orbital before pairing Hund’s Rule

35. Sublevels of Increasing Energy 4f 4d 4p 4s 3d 3p 3s 2p 2s 1s 1 2 3 4 Energy

36. n + l rule 1. The electron will occupy the orbital with the smaller n + l value 1s 2s 3s 4s 5s 6s 7s 2p 3p 3d 4p4d 4f 5p 5d 5f 6p 6d 6f 7p 7d 7f 0 1 2 3 1 2 3 4 5 6 7 2. When two orbitals have the same n + l value, the electron will occupy the orbital with smaller n.

37. 47 11 3 87 55 37 19 4 20 12 88 56 38 21 57 39 89 22 72 40 23 73 41 24 74 42 25 75 43 26 76 44 27 77 45 104105106107108109 28 78 46 29 79 30 80 48 31 13 8l 49 82 50 8384 5 32 14 33 5152 85 1 67 15 8 34 16 9 35 17 53 10 36 18 86 54 2 90919293949596979899100101102 5859606162636465666768697071 103 Periodic Chart Ag Na Li Fr Cs Rb K Be Ca Mg Ra Ba Sr Sc La Y Ac Ti Hf Zr Rf V Ta Nb Ha Cr W Mo Sg Mn Re Tc Bh Fe Os Ru Hs Co Ir Rh Mt Ni Pt Pd Cu Au Zn Hg Cd Ga Al Tl In Pb Sn BiPo B Ge Si As SbTe At H CN P O Se S F Br Cl I Ne Kr Ar Rn Xe He Ce Th Pr Pa Nd U Pm Np Sm Pu Eu Am Gd Cm Tb Bk Dy Cf Ho Es Er Fm Tmi Md Yb No Lu Lr

38. Group 2: Alkali-Earth Metals (ns 2 ) Be Ca Mg Ra Ba Sr Na Li Fr Cs Rb K H Group 1: Alkali Metals (ns 1 ) Ag Na Li Fr Cs Rb K Be Ca Mg Ra Ba Sr Sc La Y Ac Ti Hf Zr Rf V Ta Nb Ha Cr W Mo Sg Mn Re Tc Bh Fe Os Ru Hs Co Ir Rh Mt Ni Pt Pd Cu Au Zn Hg Cd Ga Al Tl In Pb Sn BiPo B Ge Si As SbTe At H CN P O Se S F Br Cl I Ne Kr Ar Rn Xe He Ce Th Pr Pa Nd U Pm Np Sm Pu Eu Am Gd Cm Tb Bk Dy Cf Ho Es Er Fm Tmi Md Yb No Lu Lr He s-block

39. Ag Na Li Fr Cs Rb K Be Ca Mg Ra Ba Sr Sc La Y Ac Ti Hf Zr Rf V Ta Nb Ha Cr W Mo Sg Mn Re Tc Bh Fe Os Ru Hs Co Ir Rh Mt Ni Pt Pd Cu Au Zn Hg Cd Ga Al Tl In Pb Sn BiPo B Ge Si As SbTe At H CN P O Se S F Br Cl I Ne Kr Ar Rn Xe He Ce Th Pr Pa Nd U Pm Np Sm Pu Eu Am Gd Cm Tb Bk Dy Cf Ho Es Er Fm Tmi Md Yb No Lu Lr VIIIA Noble Gases, ns 2 p 6 Ga Al Tl In B Pb Sn Ge Si CN Bi As Sb P Po Te O Se S Br I At F ClNe Kr Ar Rn Xe He VIIA Halogens, ns 2 p 5 VIA Chalcogens, ns 2 p 4 VA ns 2 p 3 IVA ns 2 p 2 IIIA ns 2 p 1 p-block

40. Ag Na Li Fr Cs Rb K Be Ca Mg Ra Ba Sr Sc La Y Ac Ti Hf Zr Rf V Ta Nb Ha Cr W Mo Sg Mn Re Tc Bh Fe Os Ru Hs Co Ir Rh Mt Ni Pt Pd Cu Au Zn Hg Cd Ga Al Tl In Pb Sn BiPo B Ge Si As SbTe At H CN P O Se S F Br Cl I Ne Kr Ar Rn Xe He Ce Th Pr Pa Nd U Pm Np Sm Pu Eu Am Gd Cm Tb Bk Dy Cf Ho Es Er Fm Tmi Md Yb No Lu Lr AcRfHaSgBhHsMtScTiVCrMnFeCoNiCuZnLaHfTaWReOsIrPtAuHgAgYZrNbMoTcRuRhPdCd d-block Transition Metals 3d 4d 5d 6d

41. Ag Na Li Fr Cs Rb K Be Ca Mg Ra Ba Sr Sc La Y Ac Ti Hf Zr Rf V Ta Nb Ha Cr W Mo Sg Mn Re Tc Bh Fe Os Ru Hs Co Ir Rh Mt Ni Pt Pd Cu Au Zn Hg Cd Ga Al Tl In Pb Sn BiPo B Ge Si As SbTe At H CN P O Se S F Br Cl I Ne Kr Ar Rn Xe He Ce Th Pr Pa Nd U Pm Np Sm Pu Eu Am Gd Cm Tb Bk Dy Cf Ho Es Er Fm Tmi Md Yb No Lu Lr f-block. Inner Transition Metals 4f CePrNdPmSmEuGdTbDy HoEr Tmi Yb LuThPaUNpPuAmCmBkCf EsFm Md No Lr 5f

42. Li + Na + K+K+ Rb + Cs +

43. Outermost electron configuration 1s 1 1s 2 2s 1 3s 1 2s 2 3s 2 3s 2 3p 1 3s 2 3p 2 3s 2 3p 3 3s 2 3p 4 3s 2 3p 5 3s 2 3p 6 2s 2 2p 6 2s 2 2p 5 2s 2 2p 4 2s 2 2p 3 2s 2 2p 2 2s 2 2p 1 H He LiBe B C N OF N Na Al Mg Si PSClAr