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2018 CODATA adjustment From: http://physics.nist.gov/constants Fundamental Physical Constants — Extensive Listing Relative std. Quantity Symbol Value Unit uncert. ur UNIVERSAL speed of light in vacuum c 299 792 458 m s−1 exact 2 −6 −2 −10 vacuum magnetic permeability 4pα¯h=e c µ0 1:256 637 062 12(19) × 10 NA 1:5 × 10 −7 −2 −10 µ0=(4p × 10 ) 1:000 000 000 55(15) NA 1:5 × 10 2 −12 −1 −10 vacuum electric permittivity 1/µ0c 0 8:854 187 8128(13) × 10 F m 1:5 × 10 −10 characteristic impedance of vacuum µ0c Z0 376:730 313 668(57) Ω 1:5 × 10 Newtonian constant of gravitation G 6:674 30(15) × 10−11 m3 kg−1 s−2 2:2 × 10−5 G=¯hc 6:708 83(15) × 10−39 (GeV=c2)−2 2:2 × 10−5 Planck constant∗ h 6:626 070 15 × 10−34 J Hz−1 exact 4:135 667 696 ::: × 10−15 eV Hz−1 exact ¯h 1:054 571 817 ::: × 10−34 J s exact 6:582 119 569 ::: × 10−16 eV s exact ¯hc 197:326 980 4 ::: MeV fm exact 1=2 −8 −5 Planck mass (¯hc=G) mP 2:176 434(24) × 10 kg 1:1 × 10 2 19 −5 energy equivalent mPc 1:220 890(14) × 10 GeV 1:1 × 10 5 1=2 32 −5 Planck temperature (¯hc =G) =k TP 1:416 784(16) × 10 K 1:1 × 10 3 1=2 −35 −5 Planck length ¯h=mPc = (¯hG=c ) lP 1:616 255(18) × 10 m 1:1 × 10 5 1=2 −44 −5 Planck time lP=c = (¯hG=c ) tP 5:391 247(60) × 10 s 1:1 × 10 ELECTROMAGNETIC elementary charge e 1:602 176 634 × 10−19 C exact e=¯h 1:519 267 447 ::: × 1015 AJ−1 exact −15 magnetic flux quantum 2p¯h=(2e) Φ0 2:067 833 848 ::: × 10 Wb exact 2 −5 conductance quantum 2e =2p¯h G0 7:748 091 729 ::: × 10 S exact −1 inverse of conductance quantum G0 12 906:403 72 ::: Ω exact 9 −1 Josephson constant 2e=h KJ 483 597:848 4 ::: × 10 Hz V exact 2 von Klitzing constant µ0c=2α = 2p¯h=e RK 25 812:807 45 ::: Ω exact −24 −1 −10 Bohr magneton e¯h=2me µB 9:274 010 0783(28) × 10 JT 3:0 × 10 5:788 381 8060(17) × 10−5 eV T−1 3:0 × 10−10 10 −1 −10 µB=h 1:399 624 493 61(42) × 10 Hz T 3:0 × 10 −1 −1 y −10 µB=hc 46:686 447 783(14) [m T ] 3:0 × 10 −1 −10 µB=k 0:671 713 815 63(20) KT 3:0 × 10 −27 −1 −10 nuclear magneton e¯h=2mp µN 5:050 783 7461(15) × 10 JT 3:1 × 10 3:152 451 258 44(96) × 10−8 eV T−1 3:1 × 10−10 −1 −10 µN=h 7:622 593 2291(23) MHz T 3:1 × 10 −2 −1 −1 y −10 µN=hc 2:542 623 413 53(78) × 10 [m T ] 3:1 × 10 −4 −1 −10 µN=k 3:658 267 7756(11) × 10 KT 3:1 × 10 ATOMIC AND NUCLEAR General 2 −3 −10 fine-structure constant e =4p0¯hc α 7:297 352 5693(11) × 10 1:5 × 10 inverse fine-structure constant α−1 137:035 999 084(21) 1:5 × 10−10 2 2 15 −12 Rydberg frequency α mec =2h = Eh=2h cR1 3:289 841 960 2508(64) × 10 Hz 1:9 × 10 −18 −12 energy equivalent hc R1 2:179 872 361 1035(42) × 10 J 1:9 × 10 13:605 693 122 994(26) eV 1:9 × 10−12 −1 y −12 Rydberg constant R1 10 973 731:568 160(21) [m ] 1:9 × 10 2 2 −11 −10 Bohr radius ¯h/αmec = 4p0¯h =mee a0 5:291 772 109 03(80) × 10 m 1:5 × 10 2 2 2 −18 −12 Hartree energy α mec = e =4p0a0 = 2hcR1 Eh 4:359 744 722 2071(85) × 10 J 1:9 × 10 27:211 386 245 988(53) eV 1:9 × 10−12 −4 2 −1 −10 quantum of circulation p¯h=me 3:636 947 5516(11) × 10 m s 3:0 × 10 Page 1 2018 CODATA adjustment From: http://physics.nist.gov/constants Fundamental Physical Constants — Extensive Listing Relative std. Quantity Symbol Value Unit uncert. ur −4 2 −1 −10 2p¯h=me 7:273 895 1032(22) × 10 m s 3:0 × 10 Electroweak z 3 −5 −2 −7 Fermi coupling constant GF=(¯hc) 1:166 3787(6) × 10 GeV 5:1 × 10 x weak mixing angle θW (on-shell scheme) 2 2 2 2 −3 sin θW = sW ≡ 1 − (mW=mZ) sin θW 0:222 90(30) 1:3 × 10 Electron, e− −31 −10 electron mass me 9:109 383 7015(28) × 10 kg 3:0 × 10 5:485 799 090 65(16) × 10−4 u 2:9 × 10−11 2 −14 −10 energy equivalent mec 8:187 105 7769(25) × 10 J 3:0 × 10 0:510 998 950 00(15) MeV 3:0 × 10−10 −3 −8 electron-muon mass ratio me=mm 4:836 331 69(11) × 10 2:2 × 10 −4 −5 electron-tau mass ratio me=mt 2:875 85(19) × 10 6:8 × 10 −4 −11 electron-proton mass ratio me=mp 5:446 170 214 87(33) × 10 6:0 × 10 −4 −10 electron-neutron mass ratio me=mn 5:438 673 4424(26) × 10 4:8 × 10 −4 −11 electron-deuteron mass ratio me=md 2:724 437 107 462(96) × 10 3:5 × 10 −4 −11 electron-triton mass ratio me=mt 1:819 200 062 251(90) × 10 5:0 × 10 −4 −11 electron-helion mass ratio me=mh 1:819 543 074 573(79) × 10 4:3 × 10 −4 −11 electron to alpha particle mass ratio me=ma 1:370 933 554 787(45) × 10 3:3 × 10 11 −1 −10 electron charge to mass quotient −e=me −1:758 820 010 76(53) × 10 C kg 3:0 × 10 −7 −1 −10 electron molar mass NAme M(e);Me 5:485 799 0888(17) × 10 kg mol 3:0 × 10 −13 −10 reduced Compton wavelength ¯h=mec = αa0 λC 3:861 592 6796(12) × 10 m 3:0 × 10 −12 y −10 Compton wavelength λC 2:426 310 238 67(73) × 10 [m] 3:0 × 10 2 −15 −10 classical electron radius α a0 re 2:817 940 3262(13) × 10 m 4:5 × 10 2 −29 2 −10 Thomson cross section (8p=3)re σe 6:652 458 7321(60) × 10 m 9:1 × 10 −24 −1 −10 electron magnetic moment µe −9:284 764 7043(28) × 10 JT 3:0 × 10 −13 to Bohr magneton ratio µe/µB −1:001 159 652 181 28(18) 1:7 × 10 −11 to nuclear magneton ratio µe/µN −1838:281 971 88(11) 6:0 × 10 electron magnetic moment −3 −10 anomaly jµej/µB − 1 ae 1:159 652 181 28(18) × 10 1:5 × 10 −13 electron g-factor −2(1 + ae) ge −2:002 319 304 362 56(35) 1:7 × 10 −8 electron-muon magnetic moment ratio µe/µm 206:766 9883(46) 2:2 × 10 −10 electron-proton magnetic moment ratio µe/µp −658:210 687 89(20) 3:0 × 10 electron to shielded proton magnetic ◦ 0 −8 moment ratio (H2O, sphere, 25 C) µe/µp −658:227 5971(72) 1:1 × 10 −7 electron-neutron magnetic moment ratio µe/µn 960:920 50(23) 2:4 × 10 −9 electron-deuteron magnetic moment ratio µe/µd −2143:923 4915(56) 2:6 × 10 electron to shielded helion magnetic ◦ 0 −8 moment ratio (gas, sphere, 25 C) µe/µh 864:058 257(10) 1:2 × 10 11 −1 −1 −10 electron gyromagnetic ratio 2jµej=¯h γe 1:760 859 630 23(53) × 10 s T 3:0 × 10 28 024:951 4242(85) MHz T−1 3:0 × 10−10 Muon, m− −28 −8 muon mass mm 1:883 531 627(42) × 10 kg 2:2 × 10 0:113 428 9259(25) u 2:2 × 10−8 2 −11 −8 energy equivalent mmc 1:692 833 804(38) × 10 J 2:2 × 10 105:658 3755(23) MeV 2:2 × 10−8 −8 muon-electron mass ratio mm=me 206:768 2830(46) 2:2 × 10 −2 −5 muon-tau mass ratio mm=mt 5:946 35(40) × 10 6:8 × 10 −8 muon-proton mass ratio mm=mp 0:112 609 5264(25) 2:2 × 10 Page 2 2018 CODATA adjustment From: http://physics.nist.gov/constants Fundamental Physical Constants — Extensive Listing Relative std. Quantity Symbol Value Unit uncert. ur −8 muon-neutron mass ratio mm=mn 0:112 454 5170(25) 2:2 × 10 −4 −1 −8 muon molar mass NAmm M(m);Mm 1:134 289 259(25) × 10 kg mol 2:2 × 10 −15 −8 reduced muon Compton wavelength ¯h=mmc λC;m 1:867 594 306(42) × 10 m 2:2 × 10 −14 y −8 muon Compton wavelength λC;m 1:173 444 110(26) × 10 [m] 2:2 × 10 −26 −1 −8 muon magnetic moment µm −4:490 448 30(10) × 10 JT 2:2 × 10 −3 −8 to Bohr magneton ratio µm/µB −4:841 970 47(11) × 10 2:2 × 10 −8 to nuclear magneton ratio µm/µN −8:890 597 03(20) 2:2 × 10 muon magnetic moment anomaly −3 −7 jµmj=(e¯h=2mm) − 1 am 1:165 920 89(63) × 10 5:4 × 10 −10 muon g-factor −2(1 + am) gm −2:002 331 8418(13) 6:3 × 10 −8 muon-proton magnetic moment ratio µm/µp −3:183 345 142(71) 2:2 × 10 Tau, t− { −27 −5 tau mass mt 3:167 54(21) × 10 kg 6:8 × 10 1:907 54(13) u 6:8 × 10−5 2 −10 −5 energy equivalent mtc 2:846 84(19) × 10 J 6:8 × 10 1776:86(12) MeV 6:8 × 10−5 −5 tau-electron mass ratio mt=me 3477:23(23) 6:8 × 10 −5 tau-muon mass ratio mt=mm 16:8170(11) 6:8 × 10 −5 tau-proton mass ratio mt=mp 1:893 76(13) 6:8 × 10 −5 tau-neutron mass ratio mt=mn 1:891 15(13) 6:8 × 10 −3 −1 −5 tau molar mass NAmt M(t);Mt 1:907 54(13) × 10 kg mol 6:8 × 10 −16 −5 reduced tau Compton wavelength ¯h=mtc λC;t 1:110 538(75) × 10 m 6:8 × 10 −16 y −5 tau Compton wavelength λC;t 6:977 71(47) × 10 [m] 6:8 × 10 Proton, p −27 −10 proton mass mp 1:672 621 923 69(51) × 10 kg 3:1 × 10 1:007 276 466 621(53) u 5:3 × 10−11 2 −10 −10 energy equivalent mpc 1:503 277 615 98(46) × 10 J 3:1 × 10 938:272 088 16(29) MeV 3:1 × 10−10 −11 proton-electron mass ratio mp=me 1836:152 673 43(11) 6:0 × 10 −8 proton-muon mass ratio mp=mm 8:880 243 37(20) 2:2 × 10 −5 proton-tau mass ratio mp=mt 0:528 051(36) 6:8 × 10 −10 proton-neutron mass ratio mp=mn 0:998 623 478 12(49) 4:9 × 10 7 −1 −10 proton charge to mass quotient e=mp 9:578 833 1560(29) × 10 C kg 3:1 × 10 −3 −1 −10 proton molar mass NAmp M(p), Mp 1:007 276 466 27(31) × 10 kg mol 3:1 × 10 −16 −10 reduced proton Compton wavelength ¯h=mpc λC;p 2:103 089 103 36(64) × 10 m 3:1 × 10 −15 y −10 proton Compton wavelength λC;p 1:321 409 855 39(40) × 10 [m] 3:1 × 10 −16 −3 proton rms charge radius rp 8:414(19) × 10 m 2:2 × 10 −26 −1 −10 proton magnetic moment µp 1:410 606 797 36(60) × 10 JT 4:2 × 10 −3 −10 to Bohr magneton ratio µp/µB 1:521 032 202 30(46) × 10 3:0 × 10 −10 to nuclear magneton ratio µp/µN 2:792 847 344 63(82) 2:9 × 10 −10 proton g-factor 2µp/µN gp 5:585 694 6893(16) 2:9 × 10 −7 proton-neutron magnetic moment ratio µp/µn −1:459 898 05(34) 2:4 × 10 0 −26 −1 −8 shielded proton magnetic moment µp 1:410 570 560(15) × 10 JT 1:1 × 10 ◦ (H2O, sphere, 25 C) 0 −3 −8 to Bohr magneton ratio µp/µB 1:520 993 128(17) × 10 1:1 × 10 0 −8 to nuclear magneton ratio µp/µN 2:792 775 599(30) 1:1 × 10 proton magnetic shielding correction 0 ◦ 0 −5 −4 1 − µp/µp (H2O, sphere, 25 C) σp 2:5689(11) × 10 4:2 × 10 Page 3 2018 CODATA adjustment From: http://physics.nist.gov/constants Fundamental Physical Constants — Extensive Listing Relative std.
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  • Status of the Redefinition of the Mole

    Status of the Redefinition of the Mole

    Status of the redefinition of the mole Dr. Bernd Güttler Physikalisch-Technische Bundesanstalt (PTB) Germany CCQM WG on the mole Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 1 of X Definition of the mole "Let us generally refer to the weight in Wilhelm Ostwald grams of a substance that is numerically identical to the molecular weight of that substance, as one mole...” relation to the international system of units (later called SI) is established unit of mass, no relation to particle number at this stage Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 2 of X Definition of the mole The mole, mol, is the unit of amount of substance of a specified elementary entity, which may be an atom, molecule, ion, electron, any other particle or a specified group of such particles; "Let us generally refer to the weight in its magnitude is set by fixing the grams of a substance that is numerically numerical value of the Avogadro identical to the molecular weight of that constant to be equal to exactly 6.022 substance, as one mole...” 141X·1023 when it is expressed in the unit mol-1. Ostwald 1893 ? proposed definition Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 3 of X Definition of the mole "Let us generally refer to the weight in grams of a substance that is numerically M(X) = Ar(X) x Mu identical to the molecular weight of that substance, as one mole...” nx = Mx/M(X) M(X) molar mass of X Ar(X) Σ rel.
  • Modernizing the SI – Implications of Recent Progress with the Fundamental Constants Nick Fletcher, Richard S

    Modernizing the SI – Implications of Recent Progress with the Fundamental Constants Nick Fletcher, Richard S

    Modernizing the SI – implications of recent progress with the fundamental constants Nick Fletcher, Richard S. Davis, Michael Stock and Martin J.T. Milton, Bureau International des Poids et Mesures (BIPM), Pavillon de Breteuil, 92312 Sèvres CEDEX, France. e-mail : [email protected] Abstract Recent proposals to re-define some of the base units of the SI make use of definitions that refer to fixed numerical values of certain constants. We review these proposals in the context of the latest results of the least-squares adjustment of the fundamental constants and against the background of the difficulty experienced with communicating the changes. We show that the benefit of a definition of the kilogram made with respect to the atomic mass constant (mu) may now be significantly stronger than when the choice was first considered 10 years ago. Introduction The proposal to re-define four of the base units of the SI with respect to fixed numerical values of four constants has been the subject of much discussion and many publications. Although the possibility had been foreseen in publications during the 1990’s [1] they were not articulated as a complete set of proposals until 2006 [2]. Subsequently, the General Conference on Weights and Measures, the forum for decision making between the Member States of the BIPM on all matters of measurement science and measurement units, addressed the matter at its 23rd meeting in 2007. It recognised the importance of considering such a re- definition, and invited the NMIs to “come to a view on whether it is possible”. More recently at its 24th meeting in 2011, it noted that progress had been made towards such a re-definition and invited a final proposal when the experimental data were sufficiently robust to support one.
  • Definition of the Mole

    Definition of the Mole

    IUPAC Definition of the mol e For Peer Review Only Journal: Pure and Applied Chemistry Manuscript ID PAC-REC-17-01-06 Manuscript Type: Recommendation Date Submitted by the Author: 11-Jan-2017 Complete List of Authors: Marquardt, Roberto; Université Louis Pasteur, Laboratoire de Chimie Quantique Theorique Meija, Juris; National Research Council Canada, Measurement Science and Standards Mester, Zoltan; National Research Council of Canada, Institute for National Measurement Standards Towns, Marcy; Purdue University System, Department of Chemistry Weir, Ron; Royal Military College of Canada, Dep. of Chemistry & Chemical Engineering Davis, Richard Stohner, Jürgen; ZHAW Zürich Univ. for Applied Sciences, ICBC Institute for Chemistry and Biological Chemistry; ETH-Zürich, Physical Chemistry Keywords: the mole, definition, Avogadro constant, Avogadro number Author-Supplied Keywords: P.O. 13757, Research Triangle Park, NC (919) 485-8700 Page 1 of 5 IUPAC Pure Appl. Chem. 201X; aop 1 2 3 Sponsoring bodies: IUPAC Physical and Biophysical Chemistry Division, IUPAC Inorganic Chemistry Division, IUPAC Analyt- 4 ical Chemistry Division, IUPAC Committee on Chemistry Education, and IUPAC Interdivisional Committee on Terminology, 5 Nomenclature and Symbols: see more details on page XXX. 6 IUPAC Provisional Recommendation 7 8 9 Roberto Marquardt, Juris Meija, Zoltán Mester, Marcy Towns, Ron Weir, Richard Davis, 10 and Jürgen Stohner* 11 12 Definition of the mole (IUPAC Provisional 13 14 For Peer Review Only 15 Recommendation 201X) 16 17 18 DOI: 10.1515/pac-201X-XXXX, Received ...; accepted ... 19 Abstract: In 2011 the General Conference on Weights and Measures (CGPM) noted the intention of the 20 21 International Committee of Weights and Measures (CIPM) to revise the entire International System of 22 Units (SI) by linking all seven base units to seven fundamental physical constants.
  • Chapter 1 Elementary Kinetic Theory of Gases

    Chapter 1 Elementary Kinetic Theory of Gases

    Chapter 1 Elementary kinetic theory of gases 1.1. Introduction. Molecular description of gases 1.2. Molecular quantities and macroscopic gas parameters 1.3. Gas laws 1.4. Collision frequency. Free molecular, transitional, and continuum flow regimes 1.5. Transfer of molecular quantities 1.6. Transfer equation 1.7. Diffusion, viscous drag, and heat conduction 1.8. Appendix: Probability and Bernoulli trial ME 591, Non‐equilibrium gas dynamics, Alexey Volkov 1 1.1. Introduction. Molecular description of gases Subject of kinetic theory. What are we going to study? Historical perspective Hypothesis of molecular structure of gases Sizes of atoms and molecules Masses of atoms and molecules Properties of major components of atmospheric air and other gases Length and time scale of inter‐molecular collisions Characteristic distance between molecules in gases Density parameter. Dilute and dense gases Purpose of the kinetic theory Chaotic motion of molecules. Major approach of the kinetic theory Specific goals of the kinetic theory Applications of the kinetic theory and RGD ME 591, Non‐equilibrium gas dynamics, Alexey Volkov 2 1.1. Introduction. Molecular description of gases Subject of kinetic theory. What are we going to study? Kinetic theory of gases is a part of statistical physics where flows of gases are considered on the molecular level, i.e. on the level of individual molecules, and described in terms of changes of probabilities of various states of gas molecules in space and time based on known laws of interaction between individual molecules. Word “Kinetic” came from a Greek verb meaning "to move“ or “to induce a motion.” Rarefiedgasdynamics(RGD)is often used as a synonymous of the kinetic theory of gases.