Welcome to 3.091 Lecture 6 September 1, 009 ParticleWave Duality
1 3.091 Periodic Table Quiz 3 5 6 7 8 9 10 11 1 13 1 15 16 17 18 19 0 1 3 5 6 7 8 9 30 31 3 33 3 35 36 37 38 39 0 1 3 5 6 7 8 9 50 51 5 53 5 55 56 57 7 73 7 75 76 77 78 79 80 81 8 83 8 85 86 87 88 89 Name Grade /10
n l Subshell Designation m l Number of Orbitals in Subshell Number of Orbitals in Shell 1 0 1s 0 1 1 0 s 0 1 1 p 1, 0, 1 3 3 0 3s 0 1 9 1 3p 1, 0, 1 3 3d, 1, 0, 1, 5 0 s 0 1 16 1 p 1, 0, 1 3 d, 1, 0, 1, 5 3 f 3,, 1, 0, 1,, 3 7 Values of n, l, and m, through n =
1.0079 59.3 5.87 0.0899.0 13.598 1s 1 Hydrogen 6.91 180.5 13 0.53 0.98 5.39 [He]s 1 Lithium 1 IA IA.989768 97.7 883 0.97 0.93 5.139 [Ne]3s 1 Sodium 39.0983 63.38 759 0.86 0.8.31 [Ar]s 1 Potassium 85.678 39.31 688 1.53 0.8.177 [Kr]5s 1 Rubidium 13.9053 8. 671 1.879 0.79 3.89 [Xe]6s 1 Cesium (3.0197) 7 677 0.7 [Rn]7s 1 Francium 1 H 1 3 Li 1 11 Na 1 19 K 1 37 Rb 1 55 Cs 1 87 Fr 1 9.0118 187 71 1.877 1.57 9.3 [He]s Beryllium.3050 650 1090 1.7 1 7.66 [Ne]3s Magnesium 0.078 8 18 1.5 1.00 6.113 [Ar]s Calcium 87.6 777 138.6 0.95 5.695 [Kr]5s Strontium 137.37 77 1897 3.59 0.89 5.1 [Xe]6s Barium (6.05) 700 <110 5.8 0.9 5.79 [Rn]7s Radium IIA IIA Be 1 Mg 0 Ca 38 Sr 56 Ba 88 Ra 3 IIIA IIIB.955910 151 830.989 6 6.5 [Ar]3d 1s Scandium 88.90585 156 3336.69 1. 6.38 [Kr]d 15s Yttrium 138.9055 90 355 * 6.16 1.10 5.577 [Xe]5d 16s Lanthanum (7.078) 1051 3198 10.07 1.1 6.9 [Rn]6d 17s Actinium 1 Sc 3 39 Y 3 57 La 3 89 ** Ac 3 7.88 16 8 387.5 1.5 6.8 [Ar]3d s Titanium 91. 1855 09 6.9 3 6.8 IVA IVB [Kr]d 5s Zirconium 178.9 33 7 603 13.31 Hf 7.0 [Xe]f 15d6s Hafnium (61) 10 Rf [Rn]5f 16d7s Rutherfordium** 5 6 7 8 VA VIA VIIA VIIIA VB VIB VIIB VIII 50.915 51.9961 5.93805 55.87 1910 3 1907 16 5 1538 6 3, 307,3,,5 671,3,6 061,3,,6,7 861 5.96 7.0 7.7 7.86 1.63 1.66 1.55 1.83 V Cr Mn 6.7 6.766 7.35 7.870 Fe,3 [Ar]3d 3s [Ar]3d 5s1 [Ar]3d 5s [Ar]3d 6s Vanadium Chromium Manganese Iron 9.90638 95.9 (97.907) 101.07 0 77 1 63 157 3 33 7 639 65 150 8.57 10. 11.5 1.3 1.6.16 1.9. Nb 3,5,3,,5,6 Mo Tc 7,3,,6,8 Ru 6.9 7.099 7.8 7.37 [Kr]d 5s1 [Kr]d 55s1 [Kr]d 55s [Kr]d 75s1 Niobium Molybdenum Technetium Ruthenium 180.979 183.8 186.07 190.3 3017 73 3 7 3186 75 3033 76 558 5555 5596 501 16.6 19.35 0.5.61 1.5.36 1.9. Ta 5,3,,5,6 1,,,6,7,3,,6,8 W Re Os 7.89 7.98 7.88 8.7 [Xe]f 15d36s Tantalum [Xe]f 15d6s Tungsten [Xe]f 15d56s Rhenium [Xe]f 15d66s Osmium (6) (63) (6) 107 (65) 105 106 108 Bh Db Sg Hs [Rn]5f 16d37s [Rn]5f 16d7s [Rn]5f 16d57s [Rn]5f 16d57s Dubnium** Seaborgium** Bohrium** Hassium** Ti Zr 58.9330 195 97 8.9 1.88 7.86 [Ar]3d 7s Cobalt 10.90550 196 3695 1..8 7.6 [Kr]d 85s1 Rhodium 19. 6 8.65.0 9.1 9 VIIIA VIII [Xe]f 15d76s Iridium 58.693 155 913 8.90 1.91 Co,3 Ni 7.635 [Ar]3d 8s Nickel 106. 5 155.9 6 963 1.0.0 Rh,3, Pd, 8.3 [Kr]d 10 Palladium 195.08 77 1768. 78,3,,6 385 1.5.8 Ir Pt 9.0 (66) [Rn]5f 16d77s Meitnerium** 7 109 Mt [Xe]f 15d96s1 Platinum (69) 10 VIIIA VIII 110 Uun [Rn]5f 16d97s1 Ununnilium 63.56 8 108.6 9,3 56 8.9 1.90 Cu 1, 7.76 [Ar]3d 10s1 Copper 107.858 961.78 16 10.5 1.93 7.576 [Kr]d 105s1 Silver 196.9665 106.18 79, 856 19.31.5 Au 1,3 9.5 [Xe]f 15d106s1 Gold (7) 11 IB IB 7 Ag 1 111 Uuu [Rn]5f 16d107s1 Unununium 65.39 19.53 907 7.1 5% 1.65 9.39 [Ar]3d 10s Zinc 11.11 31.07 767 8.6 1.69 8.993 [Kr]d 105s Cadmium 00.59 38.83 356.73 13.56.00 10.37 [Xe]f 15d106s Mercury (77) 1 IIB IIB 30 Zn 8 Cd 80 Hg 1, 11 Uub [Rn]5f 16d107s Ununbium 10.811 075 000.31.0 8.98 [He]s p1 Boron 6.981539 660.3 519.70 1.61 5.986 [Ne]3s p1 Aluminum 69.73 9.76 0 6.095 1.81 5.999 [Ar]3d 10sp1 Gallium 11.818 156.60 07 7.30 1.78 5.786 [Kr]d 105sp1 Indium 0.3833 30 173 11.85.0 6.108 [Xe]f 15d106sp1 Thallium 13 IIIB IIIA Ununtrium 5 B 3 13 Al 3 31 1.011 9 TP 385 SP.5.55 11.60 [He]s p Carbon 7.61 938.5 833 5.35.01 Ge 7.899 [Ar]3d 10sp Germanium 118.710 9 31.93 50 60 7.8 1.96 Sn, 7.3 [Kr]d 105sp Tin 07. 81 37.6 8 1,3 179 1.33 Pb, 7.16 [Xe]f 15d106sp Lead Ga 3 In 3 Tl 113 Uut (85) 1 IVB IVA 8.0855 11 365.33 1.90 8.151 [Ne]3s p Silicon 6, C 1 Si 3 11 Uuq [Rn]5f 16d107s7p Ununquadium 7.9159 817 TP 61 SP 5.77 5o C.18 9.81 [Ar]3d 10sp3 Arsenic 11.757 630.63 1587 6.68 5o C.05 8.61 [Kr]d 105sp3 Antimony 08.98037 71.0 156 9.78.0 7.89 78.96 79.90 83.80 33 1 3 7. 35 157.36 36 685 58.6 153..81 3.119 3.7.55.96 As 3,5 Se Br Kr 9.75 11.81 13.999 [Ar]3d 10sp [Ar]3d 10sp3 [Ar]3d 10sp5 Selenium Bromine Krypton 17.60 16.907 131.9 51 9.51 5 113.7 53 111.75 5 988 18. 108.0 6.5.93 5.89.1.66 Sb Te 1,5,7 I Xe 9.009 10.51 1.130 [Kr]d 105sp [Kr]d 105sp5 [Kr]d 105sp6 Tellurium Iodine Xenon (08.98) (09.9871) (.0176) 83 5 8 85 30 71 86 96 337 61.7 9.196 9.73.0. Bi Po, 1,3,5,7 At Rn 8. 10.78 [Xe]f 15d106sp Polonium [Xe]f 15d106sp5 Astatine [Xe]f 15d106sp6 Radon [Xe]f 15d106sp3 Bismuth 15 VB VA 1.0067 10.00 195.79 1.506 3.0 1.53 [He]s p3 Nitrogen 30.97376.15 77 1.8.19 10.86 [Ne]3s p3 Phosphorus 115 Uup Ununpentium 7, 3,,5 N 15 3,,5 P (89) 16 VIB VIA 15.999 18.79 18.95 1.9 3. 13.618 [He]s p Oxygen 3.066 115.1.60.07.58 10.360 [Ne]3s p Sulfur 8 O 16,,6 S 116 Uuh [Rn]5f 16d107s7p Ununhexium 17 VIIB VIIA 18.99803 19.6 188.1 1.69 3.96 17. [He]s p5 Fluorine 35.57 101.5 3.0 3.1 3.16 1.967 [Ne]3s p5 Chlorine 117 Uus Ununseptium 9 F 1 17 1,3,5,7 Cl 18 VIII 0,0060 7.6 atm 68.93 0.1785.587 1s Helium 0.1797 8.59 6.08 0.900 1.56 [He]s p6 Neon 39.98 189.35 185.85 1.78 15.759 [Ne]3s p6 Argon (93) He 10 Ne 18 Ar 118 Uuo [Rn]5f 16d107s7p6 Ununoctium * ** 10.115 799 3 6.770 1.1 5.66 [Xe]f 15d16s Cerium 3.0381 1750 788 11.7 6.08 [Rn]6d 7s Thorium 58 Ce 3, 90 Th 10.90765 931 3510 6.773 1.13 5. [Xe]f 36s Praseodymium 31.03588 157 15.37 1.5 5.89 [Rn]5f 6d17s Protactinium 1. (1.917) 59 1016 60 10 61 3066 3000 7.00 7.5 1.1 1.13 Pr 3, 5.89 Nd 3 5.55 Pm 3 [Xe]f 6s [Xe]f 56s Neodymium Promethium 38.089 (37.08) 91 1135 9 6 93 131 3,,5,6 3,,5,6 19.05+0.0 0.5 8 6 Pa,5 6.05 U 6.19 Np [Rn]5f 36d17s [Rn]5f 6d17s Uranium Neptunium 150.36 107 1790 7.536 1.17 5.631 [Xe]f 56s Samarium (.06) 60 38 19.816 1.8 5.8 [Rn]5f 67s Plutonium 6 Sm,3 9 3,,5,6 Pu 151.965 8 1596 5. 1. 5.666 [Xe]f 76s Europium (3.061) 1176 507 13.67 5.993 [Rn]5f 77s Americium 63 Eu,3 95 3,,5,6 Am 157.5 131 36 7.901 1.0 6.11 [Xe]f 75d16s Gadolinium (7.0703) 135 13.51 6.0 [Rn]5f 76d17s Curium 6 Gd 3 96 Cm 3 158.953 1359 31 8.30 1. 5.8 [Xe]f 96s Terbium (7.0703) 1050 1.78 6.3 [Rn]5f 97s Berkelium 65 Tb 3, 97 Bk 3, 16.50 111 561 8.551 1. 5.97 [Xe]f 106s Dysprosium (51.0796) 900 6.30 [Rn]5f 107s Californium 66 Dy 3 98 Cf 3 16.9303 17 69 8.80 1.3 6.018 [Xe]f 116s Holmium (5.083) 860 6. [Rn]5f 117s Einsteinium 67 Ho 3 99 Es 3 167.6 159 86 9.066 1. 6.101 [Xe]f 16s Erbium (57.0951) 157 6.50 [Rn]5f 17s Fermium 68 Er 3 100 Fm 3 69 70 71 168.931 155 173.0 8 17.967 1663 196 119 3393 9.31 6.966 9.8 1.5 1.1 1.7 6.1836Tm 6.539Yb 5.589 [Xe]f 136s Thulium [Xe]f 16s Ytterbium [Xe]f 15d16s Lutetium (58.10) (59.1009) (5.11) 87 101 87 10 167 Md,3 No,3 6.58 6.65 [Rn]5f 137s [Rn]5f 17s [Rn]5f 16d17s Mendelevium Nobelium Lawrencium Lu 3 103 Lr 3
electronic configuration 1.011 9 TP 385 SP.5.55 11.60 [He]s p Carbon 6, C
Principal shells 3d f d p 5d 5p 5s 6s All values negative 3p s Energy p 3s E < 0 s 1s n = 1 3 5 6
d 5p 3d p 5s s 3p 3s p s 1 IA IA 1.0079 59.3 5.87 0.0899.0 13.598 1s 1 Hydrogen 6.91 180.5 13 0.53 0.98 5.39 [He]s 1 Lithium.989768 97.7 883 0.97 0.93 5.139 [Ne]3s 1 Sodium 39.0983 63.38 759 0.86 0.8.31 [Ar]s 1 Potassium 85.678 39.31 688 1.53 0.8.177 [Kr]5s 1 Rubidium 13.9053 8. 671 1.879 0.79 3.89 [Xe]6s 1 Cesium (3.0197) 7 677 0.7 [Rn]7s 1 Francium 1 H 1 3 Li 1 11 Na 1 19 K 1 37 Rb 1 55 Cs 1 87 Fr 1 IIA IIA 9.0118 187 71 1.877 1.57 9.3 [He]s Beryllium.3050 650 1090 1.7 1 7.66 [Ne]3s Magnesium 0.078 8 18 1.5 1.00 6.113 [Ar]s Calcium 87.6 777 138.6 0.95 5.695 [Kr]5s Strontium 137.37 77 1897 3.59 0.89 5.1 [Xe]6s Barium (6.05) 700 <110 5.8 0.9 5.79 [Rn]7s Radium Be 1 Mg 0 Ca 38 Sr 56 Ba 88 Ra 3 5 IIIA IVA VA IIIB IVB VB.955910 7.88 50.915 151 1 16 8 1910 3 830 387 307.989.5 5.96 6 1.5 1.63 Sc 3 Ti 3,,3,,5 V 6.5 6.8 6.7 [Ar]3d 1s [Ar]3d s [Ar]3d 3s Scandium Titanium Vanadium 88.90585 91. 9.90638 156 39 1855 0 77 1 3336 09 7.69 6.9 8.57 1. 3 1.6 Y 3 Zr Nb 3,5 6.38 6.8 6.9 [Kr]d 15s [Kr]d 5s [Kr]d 5s1 Yttrium Zirconium Niobium 138.9055 178.9 180.979 90 57 33 7 3017 73 355 * 603 558 6.16 13.31 16.6 1.10 1.5 La 3 Hf Ta 5 5.577 7.0 7.89 [Xe]5d 16s [Xe]f 15d6s [Xe]f 15d36s Lanthanum Hafnium Tantalum (7.078) (61) (6) 1051 89 10 105 3198 ** 10.07 1.1 Ac 3 Rf Db 6.9 [Rn]6d 17s [Rn]5f 16d7s [Rn]5f 16d37s Actinium Rutherfordium** Dubnium**,0060 7.6 atm 68.93 0.1785 13 1 15 16 17.587 He IIIB IVB VB VIB VIIB 1s IIIA IVA VA VIA VIIA Helium 10.811 1.011 1.0067 15.999 18.99803 0.1797 075 5 9 6 TP 10.00 7 18.79 8 19.6 9 8.59 10 000 385 SP.31.5.0.55 8.98 B 3, 195.79 18.95 1.9 3. 11.60 13.618 O 188.1 1.69 3.96 17. F 1 6.08, 3,,5 1.506 0.900 3.0 C 1.53 N 1.56 Ne [He]s p1 [He]s p [He]s p3 [He]s p [He]s p5 [He]s p6 Boron Carbon Nitrogen Oxygen Fluorine Neon 6.981539 8.0855 30.97376 3.066 35.57 39.98 660.3 13 11 1.15 15 115.1 16 101.5 17 189.35 18 519.70 1.61 5.986 Al 3 365.33 1.90 8.151 Si 77 185.85 3,,5.60 1.8 1.78.19 10.86 P,,6 3.0.07.58 10.360 S 1,3,5,7 3.1 6 7 8 9 10 11 1 3.16 1.967 Cl 15.759 Ar VIA VIIA VIIIA VIIIA VIIIA IB IIB [Ne]3s p1 [Ne]3s p [Ne]3s p3 [Ne]3s p [Ne]3s p5 [Ne]3s p6 VIB VIIB VIII VIII VIII IB IIB Aluminum Silicon Phosphorus Sulfur Chlorine Argon 51.9961 5.93805 55.87 58.9330 58.693 63.56 65.39 69.73 7.61 7.9159 78.96 79.90 83.80 1907 16 5 1538 6 195 7 155 8 108.6 9 19.53 30 9.76 31 938.5 3 817 33 TP 1 3 7. 35 157.36 36 671,3,6 061,3,,6,7 861 97 913 56 907 0 833 61 SP 685 58.6 153. 7.0 7.7 7.86 8.9 8.90 8.9 7.1 5% 6.095 5.35 5.77 5o C.81 3.119 3.7 1.66 1.55 1.83 1.88 1.91 1.90 1.65 1.81.01.18.55.96 Cr Mn Fe,3 Co,3 Ni,3 Cu 1, Zn Ga 3 Ge As 3,5 Se,,6 Br 1,5 Kr 6.766 7.35 7.870 7.86 7.635 7.76 9.39 5.999 7.899 9.81 9.75 11.81 13.999 [Ar]3d 5s1 [Ar]3d 5s [Ar]3d 6s [Ar]3d 7s [Ar]3d 8s [Ar]3d 10s1 [Ar]3d 10s [Ar]3d 10sp1 [Ar]3d 10sp [Ar]3d 10sp3 [Ar]3d 10sp [Ar]3d 10sp3 [Ar]3d 10sp5 Chromium Manganese Iron Cobalt Nickel Copper Zinc Gallium Germanium Arsenic Selenium Bromine Krypton 95.9 (97.907) 101.07 10.90550 106. 107.858 11.11 11.818 118.710 11.757 17.60 16.907 131.9 63 157 3 33 196 5 155.9 6 961.78 7 31.07 8 156.60 9 31.93 50 630.63 51 9.51 5 113.7 53 111.75 5 639,3,,5,6 65 150 3695 963 16 767 07 60 1587 988 18. 108.0 10. 11.5 1.3 1. 1.0 10.5 8.6 7.30 7.8 6.68 5o C 6.5.93 5.89.16 1.9..8.0 1.93 1.69 1.78 1.96.05.1.66 Mo Tc 7,3,,6,8 Ru Rh,3, Pd, Ag 1 Cd In 3 Sn, Sb 3,5 Te,,6 1,5,7 I Xe 7.099 7.8 7.37 7.6 8.3 7.576 8.993 5.786 7.3 8.61 9.009 10.51 1.130 [Kr]d 55s1 [Kr]d 55s [Kr]d 75s1 [Kr]d 85s1 [Kr]d 10 [Kr]d 105s1 [Kr]d 105s [Kr]d 105sp1 [Kr]d 105sp [Kr]d 105sp3 [Kr]d 105sp [Kr]d 105sp5 [Kr]d 105sp6 Molybdenum Technetium Ruthenium Rhodium Palladium Silver Cadmium Indium Tin Antimony Tellurium Iodine Xenon 183.8 186.07 190.3 19. 195.08 196.9665 00.59 0.3833 07. 08.98037 (08.98) (09.9871) (.0176) 3 7 3186 75 3033 76 6 77 1768. 78 106.18 79 38.83 80 30 81 37.6 8 71.0 83 5 8 85 30 71 86 5555,3,,5,6 5596 1,,,6,7 501,3,,6,8 8,3,,6 385 856 356.73 173 179 156 96 337 61.7 19.35 0.5.61.65 1.5 19.31 13.56 11.85 1 9.78 9.196 9.73.36 1.9..0.8.5.00.0.33.0.0. W Re Os Ir Pt, Au 1,3 Hg 1, Tl 1,3 Pb, Bi 3,5 Po, 1,3,5,7 At Rn 7.98 7.88 8.7 9.1 9.0 9.5 10.37 6.108 7.16 7.89 8. 10.78 [Xe]f 15d6s [Xe]f 15d56s [Xe]f 15d66s [Xe]f 15d76s [Xe]f 15d96s1 [Xe]f 15d106s1 [Xe]f 15d106s [Xe]f 15d106sp1 [Xe]f 15d106sp [Xe]f 15d106sp3 [Xe]f 15d106sp [Xe]f 15d106sp5 [Xe]f 15d106sp6 Tungsten Rhenium Osmium Iridium Platinum Gold Mercury Thallium Lead Bismuth Polonium Astatine Radon (63) (6) 107 (65) 108 (66) 109 (69) (7) 111 (77) 11 113 (85) 11 115 (89) 116 117 (93) 106 110 Bh Hs Mt Uuu Uub Uut Uuq Uup Uuh Uus Sg Uun [Rn]5f 16d7s [Rn]5f 16d57s [Rn]5f 16d57s [Rn]5f 16d77s [Rn]5f 16d97s1 [Rn]5f 16d107s1 [Rn]5f 16d107s [Rn]5f 16d107s7p [Rn]5f 16d107s7p [Rn]5f 16d107s7p6 Seaborgium** Bohrium** Hassium** Meitnerium** Ununnilium Unununium Ununbium Ununtrium Ununquadium Ununpentium Ununhexium Ununseptium Ununoctium 18 VIII 0 118 Uuo * ** 10.115 799 3 6.770 1.1 5.66 Ce 3, [Xe]f 15d16s Cerium 3.0381 1750 788 11.7 6.08 [Rn]6d 7s Thorium 58 90 Th 10.90765 1. 931 59 1016 60 3510 3066 6.773 7.00 1.13 1.1 5. Pr 3, 5.89 Nd 3 [Xe]f 36s [Xe]f 6s Praseodymium Neodymium 91 31.03588 157 15.37 1.5 5.89 Pa,5 [Rn]5f 6d17s Protactinium 9 38.089 1135 131 3,,5,6 19.05+0.0 8 6.05 U [Rn]5f 36d17s Uranium (1.917) 10 3000 7.5 1.13 5.55 [Xe]f 56s Promethium 61 Pm 3 93 (37.08) 6 3,,5,6 0.5 6 6.19 Np [Rn]5f 6d17s Neptunium 6 150.36 107 1790 7.536 1.17 5.631 Sm,3 [Xe]f 56s Samarium 9 (.06) 60 38 3,,5,6 19.816 1.8 5.8 Pu [Rn]5f 67s Plutonium 63 151.965 8 1596 5. 1. 5.666 Eu,3 [Xe]f 76s Europium 95 (3.061) 1176 507 13.67 5.993Am 3,,5,6 [Rn]5f 77s Americium 157.5 131 36 7.901 1.0 6.11 [Xe]f 75d16s Gadolinium (7.0703) 135 13.51 6.0 [Rn]5f 76d17s Curium 6 Gd 3 96 Cm 3 65 158.953 1359 31 8.30 1. 5.8 Tb 3, [Xe]f 96s Terbium 97 (7.0703) 1050 1.78 6.3 Bk 3, [Rn]5f 97s Berkelium 16.50 111 561 8.551 1. 5.97 [Xe]f 106s Dysprosium (51.0796) 900 6.30 [Rn]5f 107s Californium 66 Dy 3 98 Cf 3 16.9303 17 69 8.80 1.3 6.018 [Xe]f 116s Holmium (5.083) 860 6. [Rn]5f 117s Einsteinium 67 Ho 3 99 Es 3 167.6 159 86 9.066 1. 6.101 [Xe]f 16s Erbium (57.0951) 157 6.50 [Rn]5f 17s Fermium 68 Er 3 100 Fm 3 69 168.931 155 196 9.31 1.5 6.1836Tm,3 [Xe]f 136s Thulium 101 (58.10) 87 Md,3 6.58 [Rn]5f 137s Mendelevium 70 173.0 8 119 6.966 1.1 6.539Yb,3 [Xe]f 16s Ytterbium 10 (59.1009) 87 No,3 6.65 [Rn]5f 17s Nobelium 17.967 1663 3393 9.8 1.7 5.589 [Xe]f 15d16s Lutetium (5.11) 167 [Rn]5f 16d17s Lawrencium 71 Lu 3 103 Lr 3
(A) Destructive Interference (B) Standing Wave
Fundamental Overtones Node n = 1 n = String length Overtones String length n = 3 Nodes String length
The Schrödinger Equation Wave Functions For OneElectron Atoms ψ (1s) ψ (s) = = ( 1 π)1/ 1( 1 π)1/ ( Z a 0)3/ ( Z a 0)3/ e Zr/a 0 ( Zr 0) e a Zr/a 0 ψ (p x ) = 1( 1 π)1/ ( Z a 0)3/ ( Zr 0) a e Zr/a 0 sin θ cos φ ψ (p y ) = 1( 1 π)1/ ( Z a 0)3/ ( Zr 0) a e Zr/a 0 sin θ sin φ ψ (p z ) = 1( 1 π)1/ ( Z a 0)3/ ( Zr 0) e a Zr/a 0 cos θ h a 0 = = 0.59 X 10 8 cm π me
ψ 1 10 8 6 ψ 1s Radial Probability Densities of Orbitals of Atomic Hydrogen " a o " a o ψ s 0 1s s p 6 8 0 6 8 0 6 8 r(a) r(a) r(a) 9a o ψ 3s 3s 3p 3d 0 6 8 10 1 1 0 6 8 10 1 1 0 6 8 10 1 1 r(a) r(a) r(a)
Radial Probability Electron probability (Ψ r ) 1s s 3s Distance from nucleus (r)
Electron Probability Nodes Node 3s s 1s
Z axis XY plane
Nodal plane Z Z Z X Y X Y X Y p x p y p z
Z Z Nodal planes X Y X Y Z 3d xy 3d xz Z Z X Y 3d z X Y X Y 3d yz 3dx _ y
Figures removed due to copyright restrictions. Rigden, John S. Hydrogen: The Essential Element. Cambridge, MA: Harvard University Press, 003. ISBN: 9780670153. Peat, David F. From Certainty to Uncertainty: The Story of Science and Ideas in the Twentieth Century. Washington, DC: Joseph Henry Press, 00. ISBN: 978030907618.
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