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The Discovery of the Hydrogen Spectrum Hydrogen's First 144 Photons

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The Discovery of the Hydrogen Spectrum Hydrogen's First 144 Photons The Discovery of the Hydrogen Spectrum by James Carter In 1996, I found a list of the first few photons in the Lyman, Balmer and Paschen series of Hydro- gen’s spectrum. After a few false starts, I was able to put together a simple mathematical system that could calculate the wavelength of each photon in the Hydrogen spectrum. The thermal radiation of Hydrogen’s spectra exists in many different series of precise photon wavelengths. The first 16 photons of the first nine series are illustrated in the chart Hydrogen’s First 144 Photons. The first of these groups is the Lyman series with photons in the ultraviolet part of the spectrum. The next group is the Balmer series with most of its photons in the visible portion of the spectrum. These groups of photons from Hydrogen and the other elements allows spectra of distant stars to be analyzed in order to determine their chemical composition. One example of this is that Helium was actually identified as an unknown element on the sun before it was discovered here on Earth. Each group is an endless series of photons with smaller and smaller wavelengths beginning at l1 and culminating at l∞. The most energetic photon possible for the Lyman series is the intrinsic photon Lyl∞ of Hydrogen. The energy of the intrinsic photon represents the total ion- ization energy between a proton and an electron. The formula invented to calculate Hydrogen’s -8 intrinsic wavelength is Lyl∞ = 4πao/a = 9.1176 x 10 m. (Wavelength is equal to 4 pi times the Bohr radius divided by the fine structure constant). The rest of Hydrogen’s other series of ther- mal photons form endless groups of photons with longer and longer wavelengths that can all be calculated with variations on this formula. The Hydrogen atom feeds on angular momentum. When an electron couples to a proton the pair shares the angular momentum contained in their relative velocity before they unite. The centripetal force between the electron and proton pulls the atom down toward the Bohr radius ao. The ionization energy generated by this force is released in a series of photons that each removes a unit of angular momentum Iω = MEaoαC from the atom. The atom reaches a ground state at the Bohr radius when it no longer has a unit of angular momentum Iω = mλC/2π to produce a photon when the tertiary coils of the proton and electron reach their equilibrium ratio of 1/√a. A ground- state atom remains dormant and cannot produce more photons until it can acquire more energy and units of angular momentum from contact with other atoms or the absorption of a photon. Hydrogen’s First 144 Photons The first four values at the top of this chart are in the octal system of counting. The octal system has far more beautiful equations than the decimal system when it comes to calculating the circlon model photons of the hydrogen atom. As this chart is carried farther out in octal, the values and equations become more and more symmetrical and repetitive. © 2017 by James Carter 1 Octal Numbers Hydrogen’s First 144 Photon Fractions with Base Eight Numbers Lyman Balmer Paschen Brackett Pfund #6 Orbit #7 Orbit #10 Orbit #11 Orbit 1 2 3 4 5 6 7 10 11 (1+1)2 (2+2)2 33 (4+4)2 (5+5)2 (6+6)2 (7+7)2 (10+10)2 (11+11)2 4 20 33 100 144 214 304 400 504 4πaο 16πaο 27πaο 64πaο 100πaο 144πaο 196πaο 256πaο 324πaο 1λ∞ = α 2λ∞ = α 3λ∞ = α 4λ∞ = α 5λ∞ = α 6λ∞ = α 7λ∞ = α 8λ∞ = α 9λ∞ = α 911.267052Å 3,645.06821Å 8,201.40347Å 14,580.2728Å 22,781.6763Å 32,805.6139Å 44,652.0856Å 58,321.0914Å 73,812.6312Å Μe Μe Μe Μe Μe = Μe Μe Μe Μe Lyλ = λ +1 λ = λ +1 Paλ = 3λ +1 λ = λ +1 Pfλ∞= 5λ∞ +1 #6λ∞ 6λ∞ +1 #7λ∞= 7λ∞ +1 #8λ = λ +1 λ = +1 ∞ 1 ∞ ( M p ) Ba ∞ 2 ∞(2M p ) ∞ ∞ (2M p ) Br ∞ 4 ∞ (2M p ) (2M p ) (2M p ) (2M p ) ∞ 8 ∞ (2M p ) #9 ∞ 9λ∞ (2M p ) Lyλ∞= 911.76334Å Baλ∞= 3,646.061Å Paλ∞= 8,203.637Å Brλ∞=14,584.243Å Pfλ∞=22,787.880Å #6λ∞= 32,814.547Å #7λ∞= 44,664.245Å #8λ∞= 58,336.972Å #9λ∞= 73,832.731Å obs (911.75348Å) obs (3,645.982Å) obs (8,203.569Å) obs (14,584.173Å) obs (22,787.803Å) obs (32,814.463Å) obs (44,664.153Å) obs (58,336.874Å) obs (73,832.627Å) 1.0000108143 1.0000216677 1.0000082891 1.0000047997 1.000003379 1.00000255985 1.0000020598 1.0000016799 1.0000014086 1/1=13.5983175 eV 1/4=3.3995794 eV 1/9=1.5109242 eV 1/16=.84989484 eV 1/25=.5439327 eV 1/36=.37773141 eV 1/49=.277516683 eV 1/64=.212473711 eV 1/81=.16788046 eV 2 2 2 2 2 2 2 2 2 2 4 Baλ = 3 9 Paλ = 4 16 5 25 6 36 7 49 #7λ = 8 64 9 81 10 100 Lyλ1= = 1 = 1 = Brλ1= = Pfλ1= = #6λ1= = 1 2 = #8λ1= = #9λ1= = 22-1 3 32-4 5 42-9 7 52-16 9 62-25 11 72-36 13 8 -49 15 92-64 17 102-81 19 32 9 42 4 52 25 62 9 72 49 82 16 92 81 102 25 112 121 Lyλ2= = Baλ2= = Paλ2= = Brλ2= = Pfλ2= = #6λ2= = #7λ2= = #8λ2= = #9λ2= 2 = 32-1 8 42-4 3 52-9 16 62-16 5 72-25 24 82-36 7 92-49 32 102-64 9 11 -81 40 42 16 52 25 62 4 72 49 82 64 92 9 102 100 112 121 122 16 Lyλ3= = Baλ3= = Paλ3= = Brλ3= = Pfλ3= = #6λ3= = #7λ3= = #8λ3= = #9λ3= = 42-1 15 52-4 21 62-9 3 72-16 33 82-25 39 92-36 5 102-49 51 112-64 57 122-81 7 52 25 62 9 72 49 82 4 92 81 102 25 112 121 122 9 132 169 Lyλ4= = Baλ4= = Paλ4= = Brλ4= = Pfλ4= = #6λ4= = #7λ4= = #8λ4= = #9λ4= = 52-1 24 62-4 8 72-9 40 82-16 3 92-25 56 102-36 16 112-49 72 122-64 5 132-81 88 2 2 2 2 2 4 2 2 2 2 6 36 7 49 8 64 9 81 Pfλ = 10 11 121 12 144 13 169 14 96 Lyλ5= = Baλ5= = Paλ5= 2 = Brλ5= = 5 2 = #6λ5= = #7λ5= = #8λ5= = #9λ5= = 62-1 35 72-4 45 8 -9 55 92-16 65 10 -25 3 112-36 85 122-49 95 132-64 105 142-81 115 72 49 82 16 92 9 102 25 112 121 122 4 132 169 142 49 152 25 Lyλ6= = Baλ6= = Paλ6= = Brλ6= = Pfλ6= = #6λ6= = #7λ6= = #8λ6= = #9λ6= = 72-1 48 82-4 15 92-9 8 102-16 21 112-25 96 122-36 3 132-49 120 142-64 33 152-81 16 82 64 92 81 102 100 112 121 122 144 132 169 142 4 152 225 162 256 Lyλ7= = Baλ7= = Paλ7= = Brλ7= = Pfλ7= = #6λ7= = #7λ7= = #8λ7= = #9λ = = 82-1 63 92-4 77 102-9 91 112-16 105 122-25 119 132-36 133 142-49 3 152-64 161 7 162-81 175 92 81 102 25 112 121 122 9 132 169 142 49 152 225 162 4 172 289 Lyλ8= = Baλ8= = Paλ8= = Brλ8= = Pfλ8= = #6λ8= = #7λ8= = #8λ8= = #9λ8= = 92-1 80 102-4 24 112-9 112 122-16 8 132-25 144 142-36 40 152-49 176 162-64 3 172-81 208 102 100 112 121 122 16 132 169 142 196 152 25 162 256 172 289 182 4 Lyλ9= = Baλ9= = Paλ9= = Brλ9= = Pfλ9= = #6λ9= = #7λ9= = #8λ9= = #9λ9= = 102-1 99 112-4 117 122-9 15 132-16 153 142-25 171 152-36 21 162-49 207 172-64 225 182-81 3 112 121 122 36 132 169 142 49 152 9 162 64 172 289 182 81 192 361 Lyλ10= = Baλ10= = Paλ10= = Brλ10= = Pfλ10= = #6λ10= = #7λ10= = #8λ10= = #9λ10= = 112-1 120 122-4 35 132-9 160 142-16 45 152-25 8 162-36 55 172-49 240 182-64 65 192-81 280 122 144 132 169 142 196 152 225 162 256 172 289 182 324 192 361 202 400 Lyλ11= = Baλ11= = Paλ11= = Brλ11= = Pfλ11= = #6λ11= = #7λ11= = #8λ11= = #9λ11= = 122-1 143 132-4 165 142-9 187 152-16 209 162-25 231 172-36 253 182-49 275 192-64 297 202-81 319 132 169 142 49 152 25 162 16 172 289 182 9 192 361 202 25 212 49 Lyλ12= = Baλ12= = Paλ12= = Brλ12= = Pfλ12= = #6λ12= = #7λ12= = #8λ12= = #9λ12= = 132-1 168 142-4 48 152-9 24 162-16 15 172-25 264 182-36 8 192-49 312 202-64 21 212-81 40 142 196 152 225 162 256 172 289 182 324 192 361 202 400 212 441 222 484 Lyλ13= = Baλ13= = Paλ13= = Brλ13= = Pfλ13= = #6λ13= = #7λ13= = #8λ13= = #9λ13= = 142-1 195 152-4 221 162-9 247 172-16 273 182-25 299 192-36 325 202-49 351 212-64 377 222-81 403 152 225 162 64 172 289 182 192 361 202 100 212 9 222 121 232 529 Lyλ14= = Baλ14= = Paλ14= = Brλ14= = 81 Pfλ14= = #6λ14= = #7λ14= = #8λ14= = #9λ14= = 152-1 224 162-4 63 172-9 280 182-16 77 192-25 336 202-36 91 212-49 8 222-64 105 232-81 448 2 2 2 2 2 2 2 2 2 16 256 17 289 18 36 19 361 20 16 21 49 #7λ = 22 484 23 529 24 Lyλ15= = Baλ15= = Paλ15= = Brλ15= = Pfλ15= = #6λ15= = 15 2 = #8λ15= = #9λ15= = 64 162-1 255 172-4 285 182-9 35 192-16 345 202-25 15 212-36 45 22 -49 435 232-64 465 242-81 55 2 2 2 2 2 2 2 2 2 Lyλ = 17 289 Baλ = 18 81 Paλ = 19 361 Brλ = 20 25 Pfλ = 21 441 22 121 23 529 24 9 25 625 16 2 = 16 2 = 16 2 = 16 2 = 16 2 = #6λ16= = #7λ16= 2 = #8λ16= = #9λ16= = 17 -1 288 18 -4 80 19 -9 352 20 -16 24 21 -25 416 222-36 112 23 -49 480 242-64 8 252-81 544 λ∞ = photon mass = 13.5983175 eV 4πaο -8 Μe Μe λ∞ λ∞ Me = electron mass = 510,999.06 eV λ∞ = = 9.11267052 x10 m = .000544617 + 1 =1.0002723085 = .00002661124 = .000000014492933 α Mp (2M p ) Me Mp Mp = proton mass = 938,272,310 eV The radiation of the circlon model atom is represented in these 144 circlon model equa- tions.
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