96 lines
3.3 KiB
Plaintext
96 lines
3.3 KiB
Plaintext
Mathematical verification: F = hbar^2/(gamma*m*r^3) vs k*e^2/r^2
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Repository: https://git.esus.name/esus/spin_paper/
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Bohr radius calculation:
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Force balance: hbar^2/(m*r^3) = k*e^2/r^2
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Solving for r: r = hbar^2/(m*k*e^2)
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a0 calculated = 5.29177210255e-11 m
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a0 defined = 5.29177210903e-11 m
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ratio = 0.999999998776072
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Hydrogen (Z = 1):
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Z_eff = 1.000000
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radius = 52.918 pm = 5.291772e-11 m
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gamma = 1.000027
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F_centripetal = 8.238504e-08 N
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F_coulomb = 8.238504e-08 N
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ratio = 0.999999998776072
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agreement = 99.9999998776072%
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deviation = 1.224 ppb
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Carbon (Z = 6):
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Z_eff = 5.689918
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radius = 9.300 pm = 9.300260e-12 m
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gamma = 1.000959
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F_centripetal = 1.516219e-05 N
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F_coulomb = 1.516219e-05 N
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ratio = 0.999999998776072
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agreement = 99.9999998776072%
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deviation = 1.224 ppb
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Gold (Z = 79):
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Z_eff = 78.688429
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radius = 0.672 pm = 6.724969e-13 m
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gamma = 1.223838
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F_centripetal = 3.279961e-02 N
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F_coulomb = 3.279961e-02 N
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ratio = 0.999999998776072
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agreement = 99.9999998776072%
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deviation = 1.224 ppb
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Verification across periodic table:
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Formula: F = hbar^2/(gamma*m*r^3) vs F = k*e^2/r^2
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Z Elem Z_eff gamma F_ratio Dev(ppb)
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------------------------------------------------------------
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1 H 1.000 1.0000 0.999999998776 1.224
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2 He 1.690 1.0001 0.999999998776 1.224
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3 Li 2.690 1.0002 0.999999998776 1.224
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4 Be 3.690 1.0004 0.999999998776 1.224
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5 B 4.690 1.0007 0.999999998776 1.224
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6 C 5.690 1.0010 0.999999998776 1.224
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7 N 6.690 1.0013 0.999999998776 1.224
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8 O 7.690 1.0017 0.999999998776 1.224
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9 F 8.690 1.0022 0.999999998776 1.224
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10 Ne 9.690 1.0027 0.999999998776 1.224
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11 Na 10.690 1.0032 0.999999998776 1.224
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12 Mg 11.690 1.0038 0.999999998776 1.224
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13 Al 12.690 1.0045 0.999999998776 1.224
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14 Si 13.690 1.0053 0.999999998776 1.224
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15 P 14.690 1.0060 0.999999998776 1.224
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16 S 15.690 1.0069 0.999999998776 1.224
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17 Cl 16.690 1.0078 0.999999998776 1.224
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18 Ar 17.690 1.0087 0.999999998776 1.224
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19 K 18.690 1.0098 0.999999998776 1.224
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20 Ca 19.690 1.0108 0.999999998776 1.224
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26 Fe 25.690 1.0185 0.999999998776 1.224
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47 Ag 46.689 1.0646 0.999999998776 1.224
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79 Au 78.688 1.2238 0.999999998776 1.224
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92 U 91.688 1.3493 0.999999998776 1.224
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------------------------------------------------------------
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Statistical results:
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Elements calculated: 100
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Mean ratio: 0.999999998776072
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Mean agreement: 99.99999987761%
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Mean deviation: 1.223928 ppb
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Std deviation: 0.000000 ppb
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Min deviation: 1.223928 ppb
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Max deviation: 1.223928 ppb
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Range of deviations: 0.000001 ppb
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Deviation range < 1 ppb: True
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All ratios > 0.999: True
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All ratios < 1.001: True
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Unit verification:
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F = hbar^2/(gamma*m*r^3)
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[F] = [J*s]^2 / ([kg][m^3]) = [kg*m*s^-2] = [N]
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F = k*e^2/r^2
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[F] = [N*m^2*C^-2][C^2] / [m^2] = [N]
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Key numbers:
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Mean force ratio across 100 elements: 0.999999998776072
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Deviation from unity: 1.224 ppb
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Expected if identical: 0.000 ppb
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CODATA electron mass uncertainty: ~300 ppb
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