DOCSLIB.ORG

CODATA Recommended Values of the Fundamental Physical Constants: 2014*

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

REVIEWS OF MODERN PHYSICS, VOLUME 88, JULY–SEPTEMBER 2016 CODATA recommended values of the fundamental physical constants: 2014* Peter J. Mohr,† David B. Newell,‡ and Barry N. Taylor§ National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8420, USA (published 26 September 2016) This paper gives the 2014 self-consistent set of values of the constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA). These values are based on a least-squares adjustment that takes into account all data available up to 31 December 2014. Details of the data selection and methodology of the adjustment are described. The recommended values may also be found at physics.nist.gov/ constants. DOI: 10.1103/RevModPhys.88.035009 CONTENTS A. Relative atomic masses of atoms 5 B. Relative atomic masses of ions and nuclei 6 I. Introduction 2 C. Relative atomic mass of the deuteron, triton, A. Background 2 and helion 7 B. Highlights of the CODATA 2014 adjustment 3 IV. Atomic Transition Frequencies 8 1. Planck constant h, elementary charge e, A. Hydrogen and deuterium transition frequencies, the Boltzmann constant k, Avogadro constant NA, Rydberg constant R∞, and the proton and deuteron and the redefinition of the SI 3 charge radii r , r 8 2. Relative atomic mass of the electron A e 4 p d r 1. Theory of hydrogen and deuterium energy 3. Proton magnetic moment in units of theð nuclearÞ levels 9 magneton μ =μ 4 p N a. Dirac eigenvalue 9 4. Fine-structure constant α 4 b. Relativistic recoil 9 5. Relative atomic masses 4 c. Nuclear polarizability 10 6. Newtonian constant of gravitation G 4 d. Self energy 10 7. Proton radius r and theory of the muon p e. Vacuum polarization 10 magnetic-moment anomaly a 4 μ f. Two-photon corrections 11 C. Outline of the paper 5 g. Three-photon corrections 12 II. Special Quantities and Units 5 h. Finite nuclear size 12 III. Relative Atomic Masses 5 i. Nuclear-size correction to self energy and vacuum polarization 13 * j. Radiative-recoil corrections 13 This review is being published simultaneously by the Journal of k. Nucleus self energy 13 Physical and Chemical Reference Data. l. Total energy and uncertainty 13 This report was prepared by the authors under the auspices of the m. Transition frequencies between levels with CODATA Task Group on Fundamental Constants. The members of n 2 and the fine-structure constant α 13 the task group are F. Cabiati, Istituto Nazionale di Ricerca Metro- 2. Experiments¼ on hydrogen and deuterium 14 logica, Italy; J. Fischer, Physikalisch-Technische Bundesanstalt, 3. Nuclear radii 14 Germany; J. Flowers (deceased), National Physical Laboratory, a. Electron scattering 15 United Kingdom; K. Fujii, National Metrology Institute of Japan, b. Isotope shift and the deuteron-proton radius Japan; S. G. Karshenboim, Pulkovo Observatory, Russian Federation difference 15 and Max-Planck-Institut für Quantenoptik, Germany; E. de Mirandés, c. Muonic hydrogen 15 Bureau international des poids et mesures; P. J. Mohr, National B. Hyperfine structure and fine structure 16 Institute of Standards and Technology, United States of America; V. Magnetic Moments and g-factors 16 D. B. Newell, National Institute of Standards and Technology, United A. Electron magnetic-moment anomaly a and the States of America; F. Nez, Laboratoire Kastler-Brossel, France; e fine-structure constant α 17 K. Pachucki, University of Warsaw, Poland; T. J. Quinn, Bureau 1. Theory of a 17 international des poids et mesures; C. Thomas, Bureau international e 2. Measurements of a 18 des poids et mesures; B. N. Taylor, National Institute of Standards and e B. Muon magnetic-moment anomaly a 18 Technology, United States of America; B. M. Wood, National μ 1. Theory of a 18 Research Council, Canada; and Z. Zhang, National Institute of μ Metrology, People’s Republic of China. 2. Measurement of aμ: Brookhaven 19 †[email protected] 3. Comparison of theory and experiment for aμ 20 ‡[email protected] C. Proton magnetic moment in nuclear magnetons §[email protected] μp=μN 20 0034-6861=2016=88(3)=035009(73) 035009-1 Published by the American Physical Society Peter J. Mohr, David B. Newell, and Barry N. Taylor: CODATA recommended values of the fundamental ... D. Atomic g-factors in hydrogenic 12C and 28Si A. Comparison of 2014 and 2010 CODATA and Ar e 21 recommended values 64 1. Theoryð Þ of the bound-electron g-factor 22 B. Some implications of the 2014 CODATA 12 5 28 13 2. Measurements of g C þ and g Si þ 24 recommended values and adjustment for VI. Magnetic-moment Ratios andð the Muon-electronÞ ð Þ metrology and physics 65 Mass Ratio 25 1. Conventional electrical units 65 A. Theoretical ratios of atomic bound-particle to 2. Josephson and quantum-Hall effects 66 free-particle g-factors 26 3. The new SI 66 1. Ratio measurements 26 4. Proton radius 66 B. Muonium transition frequencies, the muon-proton 5. Muon magnetic-moment anomaly 66 magnetic-moment ratio μμ=μp, and muon-electron 6. Electron magnetic-moment anomaly, mass ratio mμ=me 27 fine-structure constant, and QED 66 1. Theory of the muonium ground-state C. Suggestions for future work 66 hyperfine splitting 28 List of Symbols and Abbreviations 67 2. Measurements of muonium transition frequencies Acknowledgments 69 and values of μμ=μp and mμ=me 29 References 69 VII. Quotient of Planck Constant and Particle Mass h=m X and α 30 I. INTRODUCTION VIII. Electricalð MeasurementsÞ 31 A. NPL watt balance 31 This report describes work carried out under the auspices of B. METAS watt balance 32 the Task Group on Fundamental Constants, one of several task C. LNE watt balance 32 groups of the Committee on Data for Science and Technology D. NIST watt balance 32 (CODATA) founded in 1966 as an interdisciplinary committee E. NRC watt balance 33 of the International Council for Science (ICSU). It gives a IX. Measurements Involving Silicon Crystals 33 detailed account of the 2014 CODATA multivariate least- A. Measurements with natural silicon 33 squares adjustment of the values of the constants as well as the B. Determination of NA with enriched silicon 34 X. Thermal Physical Quantities 35 resulting 2014 set of over 300 self-consistent recommended A. Molar gas constant R, acoustic gas thermometry 35 values. The cutoff date for new data to be considered for 1. New values 35 possible inclusion in the 2014 adjustment was at the close of a. NIM 2013 35 31 December 2014, and the new set of values first became b. NPL 2013 36 available on 25 June 2015 at physics.nist.gov/constants, part c. LNE 2015 36 of the website of the Fundamental Constants Data Center of 2. Updated values 36 the National Institute of Standards and Technology (NIST), a. Molar mass of argon 36 Gaithersburg, Maryland, USA. b. Molar mass of helium 37 c. Thermal conductivity of argon 37 A. Background B. Quotient k=h, Johnson noise thermometry 37 C. Quotient Aϵ=R, dielectric-constant gas thermometry 37 The compilation of a carefully reviewed set of values of the D. Other data 38 fundamental constants of physics and chemistry arguably E. Stefan-Boltzmann constant σ 38 began over 85 years ago with the paper of Birge (1929). In XI. Newtonian Constant of Gravitation G 38 1969, 40 years after the publication of Birge’s paper, the A. Updated values 38 CODATA Task Group on Fundamental Constants was estab- 1. Huazhong University of Science and Technology 38 lished for the following purpose: to periodically provide B. New values 39 the scientific and technological communities with a self- 1. International Bureau of Weights and Measures 39 consistent set of internationally recommended values of the 2. European Laboratory for Non-Linear basic constants and conversion factors of physics and chem- Spectroscopy, University of Florence 39 istry based on all the data available at a given point in time. 3. University of California, Irvine 40 The Task Group first met this responsibility with its 1973 XII. Electroweak Quantities 41 multivariate least-squares adjustment of the values of the XIII. Analysis of Data 41 A. Comparison of data through inferred values of constants (Cohen and Taylor, 1973), which was followed α, h, and k 41 13 years later by the 1986 adjustment (Cohen and Taylor, B. Multivariate analysis of data 43 1987). Starting with its third adjustment in 1998 the Task 1. Data related to the Newtonian constant of Group has carried them out every 4 years; if the 1998 gravitation G 46 adjustment is counted as the first of the new 4-year cycle, 2. Data related to all other constants 48 the 2014 adjustment described in this report is the 5th of the 3. Test of the Josephson and quantum-Hall-effect cycle. Throughout this article we refer to the detailed relations 53 reports describing the 1998, 2002, 2006, 2010, and 2014 XIV. The 2014 CODATA Recommended Values 55 adjustments, or sometimes the adjustments themselves, as A. Calculational details 55 CODATA-XX, where XX is 98, 02, 06, 10, or 14 (Mohr and B. Tables of values 63 Taylor, 2000, 2005; Mohr, Taylor, and Newell, 2008a, 2008b, XV. Summary and Conclusion 64 2012a, 2012b). Rev. Mod. Phys., Vol. 88, No. 3, July–September 2016 035009-2 Peter J. Mohr, David B. Newell, and Barry N. Taylor: CODATA recommended values of the fundamental ... To help keep this report to a reasonable length, our data B. Highlights of the CODATA 2014 adjustment review focuses on the new results that became available We summarize here the most significant advances made, or between the 31 December 2010 and 31 December 2014 lack thereof, in our knowledge of the values of the funda- closing dates of the 2010 and 2014 adjustments (in this paper the term “past 4 years” means this time interval); our previous mental constants in the past 4 years and, where appropriate, reports should be consulted for discussions of the older data.
Recommended publications
  • Chapter 16 – Electrostatics-I

    Chapter 16 – Electrostatics-I

    Chapter 16 Electrostatics I Electrostatics – NOT Really Electrodynamics Electric Charge – Some history •Historically people knew of electrostatic effects •Hair attracted to amber rubbed on clothes •People could generate “sparks” •Recorded in ancient Greek history •600 BC Thales of Miletus notes effects •1600 AD - William Gilbert coins Latin term electricus from Greek ηλεκτρον (elektron) – Greek term for Amber •1660 Otto von Guericke – builds electrostatic generator •1675 Robert Boyle – show charge effects work in vacuum •1729 Stephen Gray – discusses insulators and conductors •1730 C. F. du Fay – proposes two types of charges – can cancel •Glass rubbed with silk – glass charged with “vitreous electricity” •Amber rubbed with fur – Amber charged with “resinous electricity” A little more history • 1750 Ben Franklin proposes “vitreous” and “resinous” electricity are the same ‘electricity fluid” under different “pressures” • He labels them “positive” and “negative” electricity • Proposaes “conservation of charge” • June 15 1752(?) Franklin flies kite and “collects” electricity • 1839 Michael Faraday proposes “electricity” is all from two opposite types of “charges” • We call “positive” the charge left on glass rubbed with silk • Today we would say ‘electrons” are rubbed off the glass Torsion Balance • Charles-Augustin de Coulomb - 1777 Used to measure force from electric charges and to measure force from gravity = - - “Hooks law” for fibers (recall F = -kx for springs) General Equation with damping - angle I – moment of inertia C – damping
  • 2019 Redefinition of SI Base Units

    2019 Redefinition of SI Base Units

    2019 redefinition of SI base units A redefinition of SI base units is scheduled to come into force on 20 May 2019.[1][2] The kilogram, ampere, kelvin, and mole will then be defined by setting exact numerical values for the Planck constant (h), the elementary electric charge (e), the Boltzmann constant (k), and the Avogadro constant (NA), respectively. The metre and candela are already defined by physical constants, subject to correction to their present definitions. The new definitions aim to improve the SI without changing the size of any units, thus ensuring continuity with existing measurements.[3][4] In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes,[5][6] which the International Committee for Weights and Measures (CIPM) had proposed earlier that year.[7]:23 The previous major change of the metric system was in 1960 when the International System of Units (SI) was formally published. The SI is a coherent system structured around seven base units whose definitions are unconstrained by that of any other unit and another twenty-two named units derived from these base units. The metre was redefined in terms of the wavelength of a spectral line of a The SI system after the 2019 redefinition: krypton-86 radiation,[Note 1] making it derivable from universal natural Dependence of base unit definitions onphysical constants with fixed numerical values and on other phenomena, but the kilogram remained defined in terms of a physical prototype, base units. leaving it the only artefact upon which the SI unit definitions depend. The metric system was originally conceived as a system of measurement that was derivable from unchanging phenomena,[8] but practical limitations necessitated the use of artefacts (the prototype metre and prototype kilogram) when the metric system was first introduced in France in 1799.
  • APPENDICES 206 Appendices

    APPENDICES 206 Appendices

    AAPPENDICES 206 Appendices CONTENTS A.1 Units 207-208 A.2 Abbreviations 209 SUMMARY A description is given of the units used in this thesis, and a list of frequently used abbreviations with the corresponding term is given. Units Description of units used in this thesis and conversion factors for A.1 transformation into other units The formulas and properties presented in this thesis are reported in atomic units unless explicitly noted otherwise; the exceptions to this rule are energies, which are most frequently reported in kcal/mol, and distances that are normally reported in Å. In the atomic units system, four frequently used quantities (Planck’s constant h divided by 2! [h], mass of electron [me], electron charge [e], and vacuum permittivity [4!e0]) are set explicitly to 1 in the formulas, making these more simple to read. For instance, the Schrödinger equation for the hydrogen atom is in SI units: È 2 e2 ˘ Í - h —2 - ˙ f = E f (1) ÎÍ 2me 4pe0r ˚˙ In atomic units, it looks like: È 1 1˘ - —2 - f = E f (2) ÎÍ 2 r ˚˙ Before a quantity can be used in the atomic units equations, it has to be transformed from SI units into atomic units; the same is true for the quantities obtained from the equations, which can be transformed from atomic units into SI units. For instance, the solution of equation (2) for the ground state of the hydrogen atom gives an energy of –0.5 atomic units (Hartree), which can be converted into other units quite simply by multiplying with the appropriate conversion factor (see table A.1.1).
  • Gauss' Theorem (See History for Rea- Son)

    Gauss' Theorem (See History for Rea- Son)

    Gauss’ Law Contents 1 Gauss’s law 1 1.1 Qualitative description ......................................... 1 1.2 Equation involving E field ....................................... 1 1.2.1 Integral form ......................................... 1 1.2.2 Differential form ....................................... 2 1.2.3 Equivalence of integral and differential forms ........................ 2 1.3 Equation involving D field ....................................... 2 1.3.1 Free, bound, and total charge ................................. 2 1.3.2 Integral form ......................................... 2 1.3.3 Differential form ....................................... 2 1.4 Equivalence of total and free charge statements ............................ 2 1.5 Equation for linear materials ...................................... 2 1.6 Relation to Coulomb’s law ....................................... 3 1.6.1 Deriving Gauss’s law from Coulomb’s law .......................... 3 1.6.2 Deriving Coulomb’s law from Gauss’s law .......................... 3 1.7 See also ................................................ 3 1.8 Notes ................................................. 3 1.9 References ............................................... 3 1.10 External links ............................................. 3 2 Electric flux 4 2.1 See also ................................................ 4 2.2 References ............................................... 4 2.3 External links ............................................. 4 3 Ampère’s circuital law 5 3.1 Ampère’s original
  • Arxiv:0801.0028V1 [Physics.Atom-Ph] 29 Dec 2007 § ‡ † (People’S China Metrology, Of) of Lic Institute Canada National Council, Zhang, Research Z

    Arxiv:0801.0028V1 [Physics.Atom-Ph] 29 Dec 2007 § ‡ † (People’S China Metrology, Of) of Lic Institute Canada National Council, Zhang, Research Z

    CODATA Recommended Values of the Fundamental Physical Constants: 2006∗ Peter J. Mohr†, Barry N. Taylor‡, and David B. Newell§, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8420, USA (Dated: March 29, 2012) This paper gives the 2006 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. Further, it describes in detail the adjustment of the values of the constants, including the selection of the final set of input data based on the results of least-squares analyses. The 2006 adjustment takes into account the data considered in the 2002 adjustment as well as the data that became available between 31 December 2002, the closing date of that adjustment, and 31 December 2006, the closing date of the new adjustment. The new data have led to a significant reduction in the uncertainties of many recommended values. The 2006 set replaces the previously recommended 2002 CODATA set and may also be found on the World Wide Web at physics.nist.gov/constants. Contents 3. Cyclotron resonance measurement of the electron relative atomic mass Ar(e) 8 Glossary 2 4. Atomic transition frequencies 8 1. Introduction 4 1. Hydrogen and deuterium transition frequencies, the 1. Background 4 Rydberg constant R∞, and the proton and deuteron charge radii R , R 8 2. Time variation of the constants 5 p d 1. Theory relevant to the Rydberg constant 9 3. Outline of paper 5 2. Experiments on hydrogen and deuterium 16 3.
  • Conventioral Standards?* JESSE W

    Conventioral Standards?* JESSE W

    156 IRE TRANSACTIONS ON INSTRUMENTATION December Present Status of Precise Information on the Universal Physical Constants. Has the Time Arrived for Their Adoption to Replace Our Present Arbitrary Conventioral Standards?* JESSE W. M. DuMONDt INTRODUCTION this subject that the experimentally measured data r HREE years ago Dr. E. R. Cohen and I prepared often do not give the desired unknowns directly but and published our latest (1955) least-squares ad- instead give functions of the unknowns. justment of all the most reliable data then avail- Seven different functions of these above four un- able bearing on the universal constants of physics and knowns have been measured by experimental methods chemistry. Since then new data and information have which we feel are sufficiently precise and reliable to been accumulating so that a year or two from now the qualify them as input data in a least-squares adjust- time may perhaps be propitious for us to prepare a new ment. These seven experimentally determined numeri- adjustment taking the newly-gained knowledge into cal values are not only functions of the unknowns,ae, account. At present it is too early to attempt such a e, N, and A, but also of the above-mentioned experi re-evaluation since many of the investigations and re- mentally determined auxiliary constants, of which five determinations now under way are still far from com- different kinds are listed in Table I. Another of these pleted. I shall be obliged, therefore, to content myself auxiliary constants I find it expedient to recall to your in this talk with a description of the sources of informa- attention at the very beginning to avoid any possibility tion upon which our 1955 evaluation was based, men- of confusion.
  • The Discovery of Thermodynamics

    The Discovery of Thermodynamics

    Philosophical Magazine ISSN: 1478-6435 (Print) 1478-6443 (Online) Journal homepage: https://www.tandfonline.com/loi/tphm20 The discovery of thermodynamics Peter Weinberger To cite this article: Peter Weinberger (2013) The discovery of thermodynamics, Philosophical Magazine, 93:20, 2576-2612, DOI: 10.1080/14786435.2013.784402 To link to this article: https://doi.org/10.1080/14786435.2013.784402 Published online: 09 Apr 2013. Submit your article to this journal Article views: 658 Citing articles: 2 View citing articles Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=tphm20 Philosophical Magazine, 2013 Vol. 93, No. 20, 2576–2612, http://dx.doi.org/10.1080/14786435.2013.784402 COMMENTARY The discovery of thermodynamics Peter Weinberger∗ Center for Computational Nanoscience, Seilerstätte 10/21, A1010 Vienna, Austria (Received 21 December 2012; final version received 6 March 2013) Based on the idea that a scientific journal is also an “agora” (Greek: market place) for the exchange of ideas and scientific concepts, the history of thermodynamics between 1800 and 1910 as documented in the Philosophical Magazine Archives is uncovered. Famous scientists such as Joule, Thomson (Lord Kelvin), Clau- sius, Maxwell or Boltzmann shared this forum. Not always in the most friendly manner. It is interesting to find out, how difficult it was to describe in a scientific (mathematical) language a phenomenon like “heat”, to see, how long it took to arrive at one of the fundamental principles in physics: entropy. Scientific progress started from the simple rule of Boyle and Mariotte dating from the late eighteenth century and arrived in the twentieth century with the concept of probabilities.
  • Ee334lect37summaryelectroma

    Ee334lect37summaryelectroma

    EE334 Electromagnetic Theory I Todd Kaiser Maxwell’s Equations: Maxwell’s equations were developed on experimental evidence and have been found to govern all classical electromagnetic phenomena. They can be written in differential or integral form. r r r Gauss'sLaw ∇ ⋅ D = ρ D ⋅ dS = ρ dv = Q ∫∫ enclosed SV r r r Nomagneticmonopoles ∇ ⋅ B = 0 ∫ B ⋅ dS = 0 S r r ∂B r r ∂ r r Faraday'sLaw ∇× E = − E ⋅ dl = − B ⋅ dS ∫∫S ∂t C ∂t r r r ∂D r r r r ∂ r r Modified Ampere'sLaw ∇× H = J + H ⋅ dl = J ⋅ dS + D ⋅ dS ∫ ∫∫SS ∂t C ∂t where: E = Electric Field Intensity (V/m) D = Electric Flux Density (C/m2) H = Magnetic Field Intensity (A/m) B = Magnetic Flux Density (T) J = Electric Current Density (A/m2) ρ = Electric Charge Density (C/m3) The Continuity Equation for current is consistent with Maxwell’s Equations and the conservation of charge. It can be used to derive Kirchhoff’s Current Law: r ∂ρ ∂ρ r ∇ ⋅ J + = 0 if = 0 ∇ ⋅ J = 0 implies KCL ∂t ∂t Constitutive Relationships: The field intensities and flux densities are related by using the constitutive equations. In general, the permittivity (ε) and the permeability (µ) are tensors (different values in different directions) and are functions of the material. In simple materials they are scalars. r r r r D = ε E ⇒ D = ε rε 0 E r r r r B = µ H ⇒ B = µ r µ0 H where: εr = Relative permittivity ε0 = Vacuum permittivity µr = Relative permeability µ0 = Vacuum permeability Boundary Conditions: At abrupt interfaces between different materials the following conditions hold: r r r r nˆ × (E1 − E2 )= 0 nˆ ⋅(D1 − D2 )= ρ S r r r r r nˆ × ()H1 − H 2 = J S nˆ ⋅ ()B1 − B2 = 0 where: n is the normal vector from region-2 to region-1 Js is the surface current density (A/m) 2 ρs is the surface charge density (C/m ) 1 Electrostatic Fields: When there are no time dependent fields, electric and magnetic fields can exist as independent fields.
  • Fundamental Physical Constants — Extensive Listing Relative Std

    Fundamental Physical Constants — Extensive Listing Relative Std

    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
  • Fundamental Constants

    Fundamental Constants

    Appendix A Fundamental Constants Table A.1 Fundamental constants Quantity & symbol CGS MKS (SI) Speed of light in vacuum c 2.997925 1010 cm sec−1 108 ms−1 −7 −6 −1 Magnetic constant μ0 = 4π × 10 1.25664 10 Hm (permeability of free space) 2 −12 −1 Electric constant 0 = 1/μ0c 8.8541853 10 Fm (permittivity of free space) Electron charge e 1.60219 10−19 C 4.80324 10−10 esu Electron volt eV 1.60219 10−12 erg eV−1 10−19 JeV−1 −28 −31 Electron rest mass m0 9.10956 10 gm 10 kg Planck’s constant h 6.626196 10−27 erg sec 10−34 Js Planck’s constant = h/2π 1.05459 10−27 erg sec 10−34 Js 2 2 −8 −10 Bohr radius a0 = 4π0 /m0e 0.529177 10 cm 10 m = 2 2 Rydberg constant Ry /2m0a0 13.6058 eV eV Fine structure constant 7.297351 10−3 10−3 2 α = e /20hc 23 −1 23 −1 Avogadro’s constant L,NA 6.022169 10 mol 10 mol 25 −3 Loschmidt’s constant NL 2.68719 10 m −16 −1 −23 −1 Boltzmann’s constant kB = R/L 1.380622 10 erg K 10 JK Faraday constant F = Le 9.64867 104 Cmol−1 7 −1 −1 −1 −1 Universal gas constant R = LkB 8.31435 10 erg K mol JK mol Mechanical equivalent of heat 4.184 107 erg cal−1 J cal−1 −21 −1 −24 −1 Bohr magneton μB = e/2m0c 9.2741 10 erg G 10 JT −24 −27 Proton rest mass mp 1.67251 10 gm 10 kg −24 −1 −27 −1 Nuclear magneton μN = e/2mpc 5.0508 10 erg G 10 JT −24 −27 Neutron rest mass mn 1.67492 10 gm 10 kg Stefan-Boltzmann constant 5.6697 10−8 Wm−2 K−4 = 5 4 3 2 σ 2π kB /15h c Y.
  • Lesson 9: Coulomb's Law

    Lesson 9: Coulomb's Law

    Lesson 9: Coulomb's Law Charles Augustin de Coulomb Before getting into all the hardcore physics that surrounds him, it’s a good idea to understand a little about Coulomb. ● He was born in 1736 in Angoulême, France. ● He received the majority of his higher education at the Ecole du Genie at Mezieres (a french military university with a very high reputation, similar to universities like Oxford, Harvard, etc.) from which he graduated in 1761. ● He then spent some time serving as a military engineer in the West Indies and other French outposts, until 1781 when he was permanently stationed in Illustration 1: Paris and was able to devote more time to scientific research. Charles Coulomb Between 1785-91 he published seven memoirs (papers) on physics. ● One of them, published in 1785, discussed the inverse square law of forces between two charged particles. This just means that as you move charges apart, the force between them starts to decrease faster and faster (exponentially). ● In a later memoir he showed that the force is also proportional to the product of the charges, a relationship now called “Coulomb’s Law”. ● For his work, the unit of electrical charge is named after him. This is interesting in that Coulomb was one of the first people to help create the metric system. ● He died in 1806. The Torsion Balance When Coulomb was doing his original experiments he decided to use a torsion balance to measure the forces between charges. ● You already learned about a torsion balance in Physics 20 when you discussed Henry Cavendish’s experiment to measure the value of “G” , the universal gravitational constant.
  • Lecture 12 Molecular Dynamics

    Lecture 12 Molecular Dynamics

    Lecture 12 Molecular Dynamics Required reading: Chapter 6: 6.22 –6.23 Karplus, M., and Petsko, G. A. (1990) Molecular dynamics simulations in biology. Nature 347: 631‐639. For further reading on the 2013 Nobel Prize, history and current state of computational methods like MD: Smith and Roux. Structure 21: 2102‐2105. Wednesday: Midterm 1 Reading for Friday: Chapter 7, sections 7.1‐7.19 MCB65 2/22/16 1 Today’s goals • Explain how solvent influences electrostatics • Dielectric constant models polarizability of solvent • Electrostatics influence interactions of ligands • Describe the basic principles behind to molecular dynamics (MD) • Computational simulation of motions of molecules • Challenges and limitations of MD • Examples of insights into protein function from MD MCB65 2/22/16 2 Energy of macromolecules • Component energy terms are assumed to be additive • parameter values – typically pulled from data on small molecules –are assumed to be transferable • Assumptions are likely reasonable for van der Waals and bonded energy terms, but less so for electrostatics Utotal Ubonds U angles U dihedrals U vdw U elec MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/22/16 3 Solvent effects • Measurements of H‐bonds in gases: • ~10‐20 kJ mol‐1 • ~40 kJ mol‐1 when one partner is charged • Calculations for peptide bond to peptide bond H‐bond in vacuum: • ~20 kJ mol‐1 • Measurement of H‐bond energy in proteins in aqueous buffer: • ~2‐4 kJ mol‐1 • ~4‐8 kJ mol‐1 when one partner is charged • Where does the difference come from? • MCB65 Solvent effect – competition with water 2/22/16 4 Interactions with water weaken H‐bonds • H‐bond energy in solvated proteins: • ~2‐4 kJ mol‐1 (~4‐8 kJ mol‐1 when one partner is charged) • Energy difference between H‐bond with water vs.