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| GarryDenke Quote | Reply | This message was updated on 7/12/2005 11:06:28 AM by GarryDenke | hbar=e^2*z0 ; hbar=e^2/e0*c ; hbar=e^2*u0*c posted on: 6/9/2005 8:26:08 AM hbar=e^2*z0 ; hbar=e^2/e0*c ; hbar=e^2*u0*c Garry W. Denke, Geologist/Geophysicist Copyright © 1st April 2002 All rights reserved Abstract: hbar = e^2*z0 hbar = [(1.6021765(31) x 10^-19 A-s)^2] * (3.767303134... x 10^2 kg-m^2/A^2-s^3) hbar = 9.6705527(59) x 10^-36 kg-m^2/s hbar = e^2/e0*c hbar = [(1.6021765(31) x 10^-19 A-s)^2] / (8.854187817... x 10^-12 A^2-s^4/kg-m^3) * (2.99792458 x 10^8 m/s) hbar = 9.6705527(59) x 10^-36 kg-m^2/s hbar = e^2*u0*c hbar = [(1.6021765(31) x 10^-19 A-s)^2] * (1.256637061... x 10^-6 kg-m/A^2-s^2) * (2.99792458 x 10^8 m/s) hbar = 9.6705527(59) x 10^-36 kg-m^2/s Introduction: reduced Planck constant: hbar = 9.6705527(59) x 10^-36 kg-m^2/s elementary charge: e = 1.6021765(31) x 10^-19 A-s impedance of vacuum: z0 = 3.767303134... x 10^2 kg-m^2/A^2-s^3 electric constant: e0 = 8.854187817... x 10^-12 A^2-s^4/kg-m^3 speed of light in vacuum: c = 2.99792458 x 10^8 m/s magnetic constant: u0 = 1.256637061... x 10^-6 kg-m/A^2-s^2 Newtonian constant: G = 6.6723635(22) x 10^-11 m^3/kg-s^2 Boltzmann constant: k = 1.3806504(11) x 10^-23 kg-m^2/s^2-K Planck constant: h = 6.6260693(11) x 10^-34 kg-m^2/s-rad molar mass: M = 3.9696032(93) x 10^15 kg/mol fine-structure constant: a = 7.2973525(68) x 10^-3 sr Derivation: 1) temperature: [(hbar*c^5/G)^1/2]/k = 4.2909537(19) x 10^31 K 2) electric current: e/[(hbar*G/c^5)^1/2] = 9.8151428(37) x 10^24 A 3) fine-structure angle: e^2/(e0*h*c) = 1.4594705(14) x 10^-2 rad 4) fine-structure constant: e^2/(2*e0*h*c) = 7.2973525(68) x 10-3 sr 5) mass: (hbar*c/G)^1/2 = 6.5916805(34) x 10^-9 kg 6) amount of substance: [(hbar*c/G)^1/2]/M = 1.6605388(62) x 10^-24 mol 7) length: (hbar*G/c^3)^1/2 = 4.8936673(50) x 10^-36 m 8) luminous intensity: [(hbar*G/c^5)^1/2]/a = 2.2369094(91) x 10^-42 cd 9) time: (hbar*G/c^5)^1/2 = 1.6323517(22) x 10^-44 s Conclusion: 001) radiance = 2.0767757(14) x 10^125 kg/s^3-sr 002) irradiance = 1.5154964(59) x 10^123 kg/s^3 003) radiant density = 5.0551520(52) x 10^114 kg/m-s^2 004) density = 8.5329002(01) x 10^105 /m^3 005) mass density = 5.6246152(16) x 10^97 kg/m^3 006) inverse luminous efficacy = 2.2233614(62) x 10^96 kg-m^2/cd-sr-s^3 007) electric current density = 4.0985263(82) x 10^95 A/m^2 008) thermal transfer = 3.5318406(08) x 10^91 kg/s^3-K 009) electric charge density = 1.3671212(44) x 10^87 A-s/m^3 010) angular acceleration = 5.4773165(63) x 10^85 rad/s^2 011) molar concentration = 1.4169212(39) x 10^82 mol/m^3 012) surface tension = 2.4738232(55) x 10^79 kg/s^2 013) dynamic viscosity = 8.2517861(57) x 10^70 kg/m-s 014) inverse area = 4.1757175(11) x 10^70 /m^2 015) electric field strength = 7.5560138(70) x 10^62 kg-m/A-s^3 016) surface density = 2.7524995(83) x 10^62 kg/m^2 017) absorbed dose rate = 5.5058916(94) x 10^60 m^2/s^3 018) magnetic field strength = 2.0056824(74) x 10^60 A/m 019) thermal conductivity = 1.7283653(07) x 10^56 kg-m/s^3-K 020) radiant intensity = 4.9734583(54) x 10^54 kg-m^2/s^3-sr 021) magnetic flux density = 2.5204149(30) x 10^54 kg/A-s^2 022) power = 3.6293079(10) x 10^52 kg-m^2/s^3 023) field acceleration = 1.8365677(81) x 10^52 m/s^2 024) electric flux density = 6.6902365(97) x 10^51 A-s/m^2 025) surface concentration = 6.9339412(05) x 10^46 mol/m^2 026) force = 1.2106068(09) x 10^44 kg-m/s^2 027) frequency = 6.1261307(02) x 10^43 /s 028) angular velocity = 8.9409071(24) x 10^41 rad/s 029) inverse luminous intensity = 4.4704535(62) x 10^41 /cd 030) mass flow rate = 4.0381496(49) x 10^35 kg/s 031) wave number = 2.0434572(45) x 10^35 /m 032) electric conductivity = 5.4241911(83) x 10^32 A^2-s^3/kg-m^3 033) molar energy = 3.5677015(17) x 10^32 kg-m^2/s^2-mol 034) temperature = 4.2909537(19) x 10^31 K 035) luminance = 9.3407021(33) x 10^28 cd/m^2 036) electric potential = 3.6976618(38) x 10^27 kg-m^2/A-s^3 037) mass field = 1.3469817(34) x 10^27 kg/m 038) luminous flux density = 6.8162396(71) x 10^26 cd-sr/m^2 039) electric current = 9.8151428(37) x 10^24 A 040) Avogadro constant = 6.0221415(04) x 10^23 /mol 041) thermal conductance = 8.4580448(72) x 10^20 kg-m^2/s^3-K 042) magnetic potential = 1.2334072(25) x 10^19 kg-m/A-s^2 043) displacement = 4.4930474(34) x 10^18 kg-s/m^2 044) luminous density = 2.2736528(18) x 10^18 cd-sr-s/m^3 045) absorbed dose = 8.987551787… x 10^16 m^2/s^2 046) electric displacement = 3.2739792(40) x 10^16 A-s/m 047) molar mass = 3.9696032(93) x 10^15 kg/mol 048) Josephson quantum = 4.8359787(99) x 10^14 A-s^2-rad^2/kg-m^2-sr 049) Josephson constant = 2.4179893(99) x 10^14 A-s^2-rad/kg-m^2 050) Coulomb constant = 8.987551787... x 10^9 kg-m^3/A^2-s^4-(4pi) 051) energy = 5.9243070(17) x 10^8 kg-m^2/s^2 052) speed of light in vacuum = 2.99792458 x 10^8 m/s 053) inverse mass = 1.5170638(12) x 10^8 /kg 054) Faraday constant = 9.6485337(83) x 10^4 A-s/mol 055) von Klitzing constant = 2.5812807(44) x 10^4 kg-m^2/A^2-s^3-rad 056) inverse conductance quantum = 1.2906403(72) x 10^4 kg-m^2-sr/A^2-s^3-rad^2 057) impedance of vacuum = 3.767303134… x 10^2 kg-m^2/A^2-s^3 058) inverse fine-structure constant = 1.3703599(91) x 10^2 /sr 059) inverse fine-structure angle = 6.8517999(54) x 10^1 /rad 060) molar gas constant = 8.3144721(43) x 10^0 kg-m^2/s^2-mol-K 061) spin two = 2.00000000 x 10^0 rad/sr 062) momentum = 1.9761361(10) x 10^0 kg-m/s 063) relative permeability = 1.00000000 x 10^0 rad/rad 064) dielectric constant = 1.00000000 x 10^0 sr/sr 065) spin one-half = 5.00000000 x 10^-1 sr/rad 066) fine-structure angle = 1.4594705(14) x 10^-2 rad 067) second radiation = 1.4387752(21) x 10^-2 m-K/rad 068) fine-structure constant = 7.2973525(68) x 10^-3 sr 069) conductance quantum = 7.7480917(34) x 10^-5 A^2-s^3-rad^2/kg-m^2-sr 070) electric conductance = 3.8740458(67) x 10^-5 A^2-s^3-rad/kg-m^2 071) magnetic constant = 1.256637061... x 10^-6 kg-m/A^2-s^2 072) magnetic permeability = 1.256637061... x 10^-6 kg-m/A^2-s^2 073) mass = 6.5916805(34) x 10^-9 kg 074) radiant distribution = 3.335640952... x 10^-9 s/m 075) density of states = 1.6879611(36) x 10^-9 s^2/kg-m^2 076) molar Planck constant = 3.9903127(01) x 10^-10 kg-m^2/s-mol-rad 077) Newtonian constant = 6.6723635(22) x 10^-11 m^3/kg-s^2 078) magnetic pole strength = 4.8032044(04) x 10^-11 A-m 079) magnetic exposure = 2.4306040(36) x 10^-11 A-s/kg 080) electric constant = 8.854187817... x 10^-12 A^2-s^4/kg-m^3 081) electric permittivity = 8.854187817... x 10^-12 A^2-s^4/kg-m^3 082) magnetic flux = 4.1356674(29) x 10^-15 kg-m^2/A-s^2-rad 083) specific heat = 2.0945347(76) x 10^-15 m^2/s^2-K 084) magnetic flux quantum = 2.0678337(14) x 10^-15 kg-m^2-sr/A-s^2-rad^2 085) molality = 2.5191434(16) x 10^-16 mol/kg 086) first radiation spectral radiance = 1.1910428(19) x 10^-16 kg-m^4/s^3-sr 087) first radiation = 5.9552140(93) x 10^-17 kg-m^4/s^3-rad 088) elementary charge = 1.6021765(31) x 10^-19 A-s 089) thermal resistance = 1.1823063(31) x 10^-21 s^3-K/kg-m^2 090) Boltzmann constant = 1.3806504(11) x 10^-23 kg-m^2/s^2-K 091) amount of substance = 1.6605388(62) x 10^-24 mol 092) inverse electric current = 1.0188338(74) x 10^-25 /A 093) kinematic viscosity = 1.4670845(63) x 10^-27 m^2/s 094) electric resistivity = 1.8435928(35) x 10^-33 kg-m^3/A^2-s^3 095) relative expansion = 2.3304842(36) x 10^-32 /K 096) Planck constant = 6.6260693(11) x 10^-34 kg-m^2/s-rad 097) reduced Planck constant = 9.6705527(59) x 10^-36 kg-m^2/s 098) length = 4.8936673(50) x 10^-36 m 099) absorption-emission = 2.4763817(26) x 10^-36 s/kg 100) inductance = 6.1495637(59) x 10^-42 kg-m^2/A^2-s^2 101) luminous intensity = 2.2369094(91) x 10^-42 cd 102) moment = 3.2257491(81) x 10^-44 kg-m 103) time = 1.6323517(22) x 10^-44 s 104) luminous flux = 1.6323517(22) x 10^-44 cd-sr 105) magnetic moment = 2.3505284(57) x 10^-46 A-m^2 106) capacitance = 4.3329449(84) x 10^-47 A^2-s^4/kg-m^2 107) electric moment = 7.8405189(79) x 10^-55 A-s-m 108) area = 2.3947980(13) x 10^-71 m^2 109) fluidity = 1.2118588(40) x 10^-71 m-s/kg 110) inertial moment = 1.5785743(45) x 10^-79 kg-m^2 111) molar volume = 7.0575553(01) x 10^-83 m^3/mol 112) electric charge volume = 7.3146401(91) x 10^-88 m^3/A-s 113) luminous energy = 2.6645721(44) x 10^-88 cd-sr-s 114) electric current volume = 2.4399013(37) x 10^-96 m^2/A 115) luminous efficacy = 4.4976942(22) x 10^-97 cd-sr-s^3/kg-m^2 116) mass volume = 1.7778993(97) x 10^-98 m^3/kg 117) volume = 1.1719344(85) x 10^-106 m^3 118) radiant volume = 1.9781798(64) x 10^-115 m-s^2/kg 119) inverse irradiance = 6.5984977(67) x 10^-124 s^3/kg 120) inverse radiance = 4.8151564(63) x 10^-126 s^3-sr/kg Bibliography: 1. Whilhelm Frederick Denke, Sr "H-BAR" (1888) GDG 2. William Herman Denke, Sr "H-Bar" (1947) GDG 3. http://physics.nist.gov/cuu/Constants |