1.PREFACE This is the first edition of the CRC Handbook of Chemistry and Physics for the 21st Century (as century is officially defined). Few would dispute that the 20th Century was the century of science; major paradigm shifts took place first in physics and chemistry and, in the second half of the century, in biology. The Rubber Handbook, socalled after the original name of its publisher, the Chemical Rubber Company, was a fixture for almost all of that eventful century. When the first edition appeared in 1913, the electron had been known for only 17 years, there were 81 elements, and the Bohr theory of the hydrogen atom was still in press. The Handbook was a significant innovation. While systematic compilation of data from the chemistry and physics literature had begun earlier, especially in Germany, the massive tomes that were published by Beilstein, Gmelin, and Landolt-Brnstein were strictly for libraries. The Rubber Handbook appears to have been the first compact, low-price volume of reference data suitable for students and individual researchers to keep on their desk or laboratory bench. It quickly became a standard and grew from its original 116 pages to the present size of over 2500 pages. Generations of students have relied on the CRC Handbook as a resource in their studies, but the impact has been much broader. Senior research scientists, engineers, and workers in other fields have used the book extensively. Linus Pauling, perhaps the most influential chemist of the 20th century, made the following comments a few years before his death: People who have interviewed me have commented on the extensive knowledge that I have about the properties of substances, especially inorganic compounds, including minerals. I attribute this knowledge in part to the fact that I possessed the Rubber Handbook. I remember clearly the five summers, beginning in 1919, when I worked as a paving-plant inspector, supervising the laying of bituminous pavement in the mountainous region of southern Oregon. For much of the time I was free to read, just keeping an eye on the operation of the paving plant. I remember the book that I read over and over was the Rubber Handbook. I puzzled over the tables of properties - hardness, color, melting and boiling point, density, magnetic properties, and others - trying to think of reasonable explanations of the empirical data. Only in the 1920s and 1930s did I have some success in this effort. Paulings success was the first step in our ability to relate the physical and chemical behavior of bulk materials to their molecular structure in a quantitative manner. One factor in the success of the Handbook has been its annual revisions. This practice, followed throughout the century except for a few wartime years, permitted the replacement of old data with new and more accurate values, as well as the introduction of new topics that became important as science moved forward. This policy has helped the Handbook meet the needs of the scientific community in a timely fashion.

2. The 82nd Edition continues the tradition of updates and improvements. The major change is a revised and expanded table of Physical Constants of Inorganic Compounds. The number of compounds has been increased by 12%, the format improved, and the constants updated. In addition, quantitative data on solubility in water are now included in the table, and a formula index has been added. Other tables that have been expanded and updated include: Critical Constants Aqueous Solubility and Henrys Law Constants of Organic Compounds Chemical Carcinogens Threshold Limits for Airborne Contaminants Nomenclature for Organic Polymers Standard Atomic Weights Atomic Masses and Abundances Table of the Isotopes New topics covered in this edition include: Surface Tension of Aqueous Mixtures Viscosity of Carbon Dioxide along the Saturation Line Gibbs Energy of Formation for Important Biological Species Optical Properties of Inorganic and Organic Solids Interstellar Molecules Allocation of Frequencies in the Radio Spectrum Units for Magnetic Properties This electronic version of the Handbook of Chemistry and Physics contains all the material from the print version of the 82nd Edition, as well as some additional data that could not be accommodated in the printed book. Powerful search capabilities, which are explained in the Help messages, greatly facilitate the task of locating the data. The Editor will appreciate suggestions on new topics for the Handbook and notification of any errors. Address all comments to Editor, Handbook of Chemistry and Physics, CRC Press, Inc., 2000 Corporate Blvd. N. W., Boca Raton, FL 33431. Comments may also be sent by electronic mail to drlide@post.harvard.edu. The Handbook of Chemistry and Physics is dependent on the efforts of many contributors throughout the world. I appreciate the valuable suggestions that have come from the Editorial Advisory Board and from many users. I should also like to thank Susan Fox and the rest of the production team at CRC Press for their excellent support. David R. Lide January 1, 2001 This Edition is Dedicated to the Memory of David Reynolds Lide (1901-1976) and Kate Simmons Lide (1896-1991) 3. This work contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot accept responsibility for the validity of all materials or for the consequences of their use. Copyright CRC Press LLC 2002 4. FUNDAMENTAL PHYSICAL CONSTANTS Peter J. Mohr and Barry N. Taylor These tables give the 1998 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. The 1998 set replaces the previous set of constants recommended by CODATA in 1986; assigned uncertainties have been reduced by a factor of 1/5 to 1/12 (and sometimes even greater) relative to the 1986 uncertainties. The recommended set is based on a least-squares adjustment involving all of the relevant experimental and theoretical data available through December 31, 1998. Full details of the input data and the adjustment procedure are given in Reference 1. The 1998 adjustment was carried out by P. J. Mohr and B. N. Taylor of the National Institute of Standards and Technology (NIST) under the auspices of the CODATA Task Group on Fundamental Constants. The Task Group was established in 1969 with the aim of periodically providing the scientific and technological communities with a self-consistent set of internationally recommended values of the fundamental physical constants based on all applicable information available at a given point in time. The first set was published in 1973 and was followed by a revised set first published in 1986; the current 1998 set first appeared in 1999. In the future, the CODATA Task Group plans to take advantage of the high level of automation developed for the current set in order to issue a new set of recommended values at least every four years. At the time of completion of the 1998 adjustment, the membership of the Task Group was as follows: F. Cabiati, Istituto Elettrotecnico Nazionale Galileo Ferraris, Italy E. R. Cohen, Science Center, Rockwell International (retired), United States of America T. Endo, Electrotechnical Laboratory, Japan R. Liu, National Institute of Metrology, China (Peoples Republic of) B. A. Mamyrin, A. F. Ioffe Physical-Technical Institute, Russian Federation P. J. Mohr, National Institute of Standards and Technology, United States of America F. Nez, Laboratoire Kastler-Brossel, France B. W. Petley, National Physical Laboratory, United Kingdom T. J. Quinn, Bureau International des Poids et Mesures B. N. Taylor, National Institute of Standards and Technology, United States of America V. S. Tuninsky, D. I. Mendeleyev All-Russian Research Institute for Metrology, Russian Federation W. Wger, Physikalisch-Technische Bundesanstalt, Germany B. M. Wood, National Research Council, Canada REFERENCES 1. Mohr, Peter J., and Taylor, Barry N., J. Phys Chem. Ref. Data 28, 1713, 1999; Rev. Mod. Phys. 72, 351, 2000. The 1998 set of recommended values is also available at the Web site of the Fundamental Constants Data Center of the NIST Physics Laboratory: http://physics.nist.gov/constants. 5. Fundamental Physical Constants QuantitySymbolValueUnitRelative std. uncert. u rUNIVERSAL m s1 N A2 N A2 F m1speed of light in vacuum magnetic constantc, c0 0electric constant 1/0 c2 characteristic impedance of vacuum 0 / 0 = 0 c0299 792 458 4 107 = 12.566 370 614... 107 8.854 187 817... 1012Z0376.730 313 461...G G/ c h6.673(10) 1011 6.707(10) 1039 6.626 068 76(52) 1034 4.135 667 27(16) 1015 1.054 571 596(82) 1034 6.582 118 89(26) 1016m3 kg1 s2 (GeV/c2 )2 Js eV s Js eV s1.5 103 1.5 103 7.8 108 3.9 108 7.8 108 3.9 108mP lP tP2.1767(16) 108 1.6160(12) 1035 5.3906(40) 1044kg m s7.5 104 7.5 104 7.5 1041.602 176 462(63) 1019 2.417 989 491(95) 1014C A J13.9 108 3.9 108G0 G 1 0 KJ2.067 833 636(81) 1015 7.748 091 696(28) 105 12 906.403 786(47) 483 597.898(19) 109Wb S3.9 108 3.7 109 3.7 109 3.9 108RK25 812.807 572(95)B927.400 899(37) 1026 5.788 381 749(43) 105 13.996 246 24(56) 109 46.686 4521(19) 0.671 7131(12)J T1 eV T1 Hz T1 m1 T1 K T14.0 108 7.3 109 4.0 108 4.0 108 1.7 1065.050 783 17(20) 1027 3.152 451 238(24) 108 7.622 593 96(31) 2.542 623 66(10) 102 3.658 2638(64) 104J T1 eV T1 MHz T1 m1 T1 K T14.0 108 7.6 109 4.0 108 4.0 108 1.7 106Newtonian constant of gravitation Planck constant in eV s h/2 in eV s Planck mass ( c/G)1/2 Planck length /m P c = ( G/c3 )1/2 Planck time lP /c = ( G/c5 )1/2(exact) (exact) (exact) (exact)ELECTROMAGNETIC elementary chargemagnetic ux quantum h/2e conductance quantum 2e2/ h inverse of conductance quantum Josephson constanta 2e/ h von Klitzing constantb h/e2 = 0 c/2 Bohr magneton e /2m e in eV T1e e/ h 0B / h B / hc B /k nuclear magneton e /2m p in eV T1N N / h N / hc N /kHz V13.7 109ATOMIC AND NUCLEAR General ne-structure constant e2/4 0 c inverse ne-structure constant 17.297 352 533(27) 103 137.035 999 76(50)3.7 109 3.7 109 6. Fundamental Physical Constants QuantityRydberg constant 2 m e c/2hSymbolUnitRelative std. uncert. u rR R c R hc10 973 731.568 549(83) 3.289 841 960 368(25) 1015 2.179 871 90(17) 1018 13.605 691 72(53)m1 Hz J eV7.6 1012 7.6 1012 7.8 108 3.9 108a00.529 177 2083(19) 1010m3.7 109Eh4.359 743 81(34) 1018 27.211 3834(11) 3.636 947 516(27) 104 7.273 895 032(53) 104J eV m2 s1 m2 s17.8 108 3.9 108 7.3 109 7.3 109GeV28.6 106R hc in eV Bohr radius /4 R = 4 0 2/m e e2 Hartree energy e2/40 a0 = 2R hc = 2 m e c2 in eV quantum of circulationValueh/2m e h/m eElectroweak Fermi coupling constantc weak mixing angled W (on-shell scheme) 2 sin2 W = sW 1 (m W /m Z )2G F /( c)31.166 39(1) 105sin2 W0.2224(19)8.7 103Electron, e 9.109 381 88(72) 1031kg7.9 108c25.485 799 110(12) 104 8.187 104 14(64) 1014 0.510 998 902(21)u J MeV2.1 109 7.9 108 4.0 108electron-muon mass ratio electron-tau mass ratio electron-proton mass ratio electron-neutron mass ratio electron-deuteron mass ratio electron to alpha particle mass ratiom e /m m e /m m e /m p m e /m n m e /m d m e /m 4.836 332 10(15) 103 2.875 55(47) 104 5.446 170 232(12) 104 5.438 673 462(12) 104 2.724 437 1170(58) 104 1.370 933 5611(29) 104electron charge to mass quotient electron molar mass NA m e Compton wavelength h/m e c C /2 = a0 = 2/4 R classical electron radius 2 a0 2 Thomson cross section (8/3)ree/m e M(e), Me C re e1.758 820 174(71) 1011 5.485 799 110(12) 107 2.426 310 215(18) 1012 386.159 2642(28) 1015 2.817 940 285(31) 1015 0.665 245 854(15) 1028C kg1 kg mol1 m m m m24.0 108 2.1 109 7.3 109 7.3 109 1.1 108 2.2 108e e /B e /N928.476 362(37) 1026 1.001 159 652 1869(41) 1 838.281 9660(39)J T14.0 108 4.1 1012 2.1 109ae ge1.159 652 1869(41) 103 2.002 319 304 3737(82)3.5 109 4.1 1012e /206.766 9720(63)3.0 108electron mass in u, m e = Ar (e) u (electron relative atomic mass times u) energy equivalent in MeVelectron magnetic moment to Bohr magneton ratio to nuclear magneton ratio electron magnetic moment anomaly |e |/B 1 electron g-factor 2(1 + ae ) electron-muon magnetic moment ratiomemeC3.0 108 1.6 104 2.1 109 2.2 109 2.1 109 2.1 109 7. Fundamental Physical Constants Quantity electron-proton magnetic moment ratio electron to shielded proton magnetic moment ratio (H2 O, sphere, 25 C) electron-neutron magnetic moment ratio electron-deuteron magnetic moment ratio electron to shielded helione magnetic moment ratio (gas, sphere, 25 C) electron gyromagnetic ratio 2|e |/SymbolValueUnitRelative std. uncert. u re /p 658.210 6875(66)1.0 108e /p 658.227 5954(71)1.1 108e /n960.920 50(23)2.4 107e /d2 143.923 498(23)1.1 108e /h864.058 255(10)1.2 108e e /21.760 859 794(71) 1011 28 024.9540(11)s1 T1 MHz T14.0 108 4.0 1081.883 531 09(16) 1028kg8.4 1080.113 428 9168(34) 1.692 833 32(14) 1011 105.658 3568(52)u J MeV3.0 108 8.4 108 4.9 108kg mol13.0 108 1.6 104 3.0 108 3.0 108 3.0 108Muon, muon mass in u, m = Ar () u (muon relative atomic mass times u) energy equivalent in MeVmmc2muon-electron mass ratio muon-tau mass ratio muon-proton mass ratio muon-neutron mass ratio muon molar mass NA m m /m e m /m m /m p m /m n M(), M206.768 2657(63) 5.945 72(97) 102 0.112 609 5173(34) 0.112 454 5079(34) 0.113 428 9168(34) 103muon Compton wavelength h/m c C, /2 muon magnetic moment to Bohr magneton ratio to nuclear magneton ratioC, /B /N11.734 441 97(35) 1015 1.867 594 444(55) 1015 4.490 448 13(22) 1026 4.841 970 85(15) 103 8.890 597 70(27)a g1.165 916 02(64) 103 2.002 331 8320(13)5.5 107 6.4 1010 /p3.183 345 39(10)3.2 108muon magnetic moment anomaly | |/(e /2m ) 1 muon g-factor 2(1 + a ) muon-proton magnetic moment ratioC,m m J T12.9 108 2.9 108 4.9 108 3.0 108 3.0 108Tau, tau massf in u, m = Ar () u (tau relative atomic mass times u) energy equivalent in MeV3.167 88(52) 1027mmc2kg1.6 1041.907 74(31) 2.847 15(46) 1010 1 777.05(29)u J MeV1.6 104 1.6 104 1.6 104 8. Fundamental Physical Constantsm /m e m /m m /m p m /m n M(), Mtau Compton wavelength h/m c C, /2C,Relative std. uncert. u r3 477.60(57) 16.8188(27) 1.893 96(31) 1.891 35(31) 1.907 74(31) 103kg mol11.6 104 1.6 104 1.6 104 1.6 104 1.6 1040.697 70(11) 1015 0.111 042(18) 1015m m1.6 104 1.6 104kg7.9 1081.007 276 466 88(13) 1.503 277 31(12) 1010 938.271 998(38)u J MeV1.3 1010 7.9 108 4.0 108C kg1 kg mol12.1 109 3.0 108 1.6 104 5.8 1010 4.0 108 1.3 1010Symboltau-electron mass ratio tau-muon mass ratio tau-proton mass ratio tau-neutron mass ratio tau molar mass NA m Unit1.672 621 58(13) 1027QuantityC,ValueProton, p proton mass in u, m p = Ar (p) u (proton relative atomic mass times u) energy equivalent in MeVmpmpc2proton-electron mass ratio proton-muon mass ratio proton-tau mass ratio proton-neutron mass ratio proton charge to mass quotient proton molar mass NA m pm p /m e m p /m m p /m m p /m n e/m p M(p), Mp1 836.152 6675(39) 8.880 244 08(27) 0.527 994(86) 0.998 623 478 55(58) 9.578 834 08(38) 107 1.007 276 466 88(13) 103proton Compton wavelength h/m p c C,p /2 proton magnetic moment to Bohr magneton ratio to nuclear magneton ratio proton g-factor 2p /NC,p p p /B p /N gp1.321 409 847(10) 1015 0.210 308 9089(16) 1015 1.410 606 633(58) 1026 1.521 032 203(15) 103 2.792 847 337(29) 5.585 694 675(57)p /n p1.459 898 05(34) 1.410 570 399(59) 1026p /B p /N1.520 993 132(16) 103 2.792 775 597(31)1.1 108 1.1 108p25.687(15) 1065.7 104p p /22.675 222 12(11) 108 42.577 4825(18)s1 T1 MHz T14.1 108 4.1 108p2.675 153 41(11) 108s1 T14.2 108p /242.576 3888(18)MHz T14.2 108proton-neutron magnetic moment ratio shielded proton magnetic moment (H2 O, sphere, 25 C) to Bohr magneton ratio to nuclear magneton ratio proton magnetic shielding correction 1 p /p (H2 O, sphere, 25 C) proton gyromagnetic ratio 2p / shielded proton gyromagnetic ratio 2p / (H2 O, sphere, 25 C)C,pNeutron, nm m J T1J T17.6 109 7.6 109 4.1 108 1.0 108 1.0 108 1.0 108 2.4 107 4.2 108 9. Fundamental Physical Constants QuantitySymbolValueUnitRelative std. uncert. u rmn1.674 927 16(13) 1027kg7.9 108m n c21.008 664 915 78(55) 1.505 349 46(12) 1010 939.565 330(38)u J MeV5.4 1010 7.9 108 4.0 108neutron-electron mass ratio neutron-muon mass ratio neutron-tau mass ratio neutron-proton mass ratio neutron molar mass NA m nm n /m e m n /m m n /m m n /m p M(n), Mn1 838.683 6550(40) 8.892 484 78(27) 0.528 722(86) 1.001 378 418 87(58) 1.008 664 915 78(55) 103kg mol12.2 109 3.0 108 1.6 104 5.8 1010 5.4 1010neutron Compton wavelength h/m n c C,n /2 neutron magnetic moment to Bohr magneton ratio to nuclear magneton ratioC,n n n /B n /N1.319 590 898(10) 1015 0.210 019 4142(16) 1015 0.966 236 40(23) 1026 1.041 875 63(25) 103 1.913 042 72(45)gn3.826 085 45(90)2.4 107n /e1.040 668 82(25) 1032.4 107n /p0.684 979 34(16)2.4 107n /p0.684 996 94(16)2.4 107n n /21.832 471 88(44) 108 29.164 6958(70)neutron mass in u, m n = Ar (n) u (neutron relative atomic mass times u) energy equivalent in MeVneutron g-factor 2n /N neutron-electron magnetic moment ratio neutron-proton magnetic moment ratio neutron to shielded proton magnetic moment ratio (H2 O, sphere, 25 C) neutron gyromagnetic ratio 2|n |/C,nm m J T17.6 109 7.6 109 2.4 107 2.4 107 2.4 107s1 T1 MHz T12.4 107 2.4 1073.343 583 09(26) 1027kg7.9 1082.013 553 212 71(35) 3.005 062 62(24) 1010 1 875.612 762(75)u J MeV1.7 1010 7.9 108 4.0 108kg mol12.1 109 2.0 1010 1.7 1010Deuteron, d deuteron mass in u, m d = Ar (d) u (deuteron relative atomic mass times u) energy equivalent in MeVmdmdc2deuteron-electron mass ratio deuteron-proton mass ratio deuteron molar mass NA m dm d /m e m d /m p M(d), Md3 670.482 9550(78) 1.999 007 500 83(41) 2.013 553 212 71(35) 103deuteron magnetic moment to Bohr magneton ratio to nuclear magneton ratiod d /B d /N0.433 073 457(18) 1026 0.466 975 4556(50) 103 0.857 438 2284(94)d /e4.664 345 537(50) 1041.1 108d /p0.307 012 2083(45)1.5 108deuteron-electron magnetic moment ratio deuteron-proton magnetic moment ratioJ T14.2 108 1.1 108 1.1 108 10. Fundamental Physical Constants Quantity deuteron-neutron magnetic moment ratioSymbolValued /nUnitRelative std. uncert. u r2.4 1070.448 206 52(11) Helion, hhelion masse in u, m h = Ar (h) u (helion relative atomic mass times u) energy equivalent in MeV5.006 411 74(39) 1027mhc2kg7.9 1083.014 932 234 69(86) 4.499 538 48(35) 1010 2 808.391 32(11)mhu J MeV2.8 1010 7.9 108 4.0 108kg mol1 J T12.1 109 3.1 1010 2.8 1010 4.2 108shielded helion to shielded proton magnetic moment ratio (gas/H2 O, spheres, 25 C) shielded helion gyromagnetic ratio 2|h |/ (gas, sphere, 25 C)m h /m e m h /m p M(h), Mh h5 495.885 238(12) 2.993 152 658 50(93) 3.014 932 234 69(86) 103 1.074 552 967(45) 1026h /B h /N1.158 671 474(14) 103 2.127 497 718(25)1.2 108 1.2 108h /p0.761 766 563(12)1.5 108h /p0.761 786 1313(33)4.3 109h2.037 894 764(85) 108s1 T14.2 108h /2helion-electron mass ratio helion-proton mass ratio helion molar mass NA m h shielded helion magnetic moment (gas, sphere, 25 C) to Bohr magneton ratio to nuclear magneton ratio shielded helion to proton magnetic moment ratio (gas, sphere, 25 C)32.434 1025(14)MHz T14.2 1086.644 655 98(52) 1027kg7.9 1084.001 506 1747(10) 5.971 918 97(47) 1010 3 727.379 04(15)u J MeV2.5 1010 7.9 108 4.0 108kg mol12.1 109 2.8 1010 2.5 1010Alpha particle, alpha particle mass in u, m = Ar () u (alpha particle relative atomic mass times u) energy equivalent in MeV alpha particle to electron mass ratio alpha particle to proton mass ratio alpha particle molar mass NA m mmc2m /m e m /m p M(), M7 294.299 508(16) 3.972 599 6846(11) 4.001 506 1747(10) 103PHYSICO-CHEMICAL Avogadro constant atomic mass constant 1 m u = 12 m(12 C) = 1 u = 103 kg mol1/NA energy equivalent in MeV Faraday constantg NA eNA , L6.022 141 99(47) 1023mol17.9 108mu1.660 538 73(13) 1027kg7.9 108m u c21.492 417 78(12) 1010 931.494 013(37) 96 485.3415(39)J MeV C mol17.9 108 4.0 108 4.0 108F 11. Fundamental Physical Constantsmolar Planck constant molar gas constant Boltzmann constant R/NA in eV K1molar volume of ideal gas RT / p T = 273.15 K, p = 101.325 kPa Loschmidt constant NA /Vm T = 273.15 K, p = 100 kPa Sackur-Tetrode constant (absolute entropy constant)h 5 2 3/2 kT / p ] 1 0 2 + ln[(2m u kT1 / h ) T1 = 1 K, p0 = 100 kPa T1 = 1 K, p0 = 101.325 kPa Stefan-Boltzmann constant ( 2 /60)k 4/ 3 c2 rst radiation constant 2hc2 rst radiation constant for spectral radiance 2hc2 second radiation constant hc/k Wien displacement law constant b = max T = c2 /4.965 114 231...ValueUnitRelative std. uncert. u rk/ h k/ hcQuantity3.990 312 689(30) 1010 0.119 626 564 92(91) 8.314 472(15) 1.380 6503(24) 1023 8.617 342(15) 105 2.083 6644(36) 1010 69.503 56(12)J s mol1 J m mol1 J mol1 K1 J K1 eV K1 Hz K1 m1 K17.6 109 7.6 109 1.7 106 1.7 106 1.7 106 1.7 106 1.7 106Vm n0 Vm22.413 996(39) 103 2.686 7775(47) 1025 22.710 981(40) 103m3 mol1 m3 m3 mol11.7 106 1.7 106 1.7 106S0 /R1.151 7048(44) 1.164 8678(44) c1 c1L c25.670 400(40) 108 3.741 771 07(29) 1016 1.191 042 722(93) 1016 1.438 7752(25) 102W m2 K4 W m2 W m2 sr1 mK7.0 106 7.8 108 7.8 108 1.7 106b2.897 7686(51) 103mK1.7 106SymbolNA h NA hc R k3.8 106 3.7 106a See the Adopted values table for the conventional value adopted internationally for realizing representations of the volt using the Joseph-son effect. b See the Adopted values table for the conventional value adopted internationally for realizing representations of the ohm using the quantum Halleffect. c Value recommended by the Particle Data Group, Caso et al., Eur. Phys. J. C 3(1-4), 1-794 (1998). d Based on the ratio of the masses of the W and Z bosons m /m recommended by the Particle Data Group (Caso et al., 1998). The value for W Z sin2 W they recommend, which is based on a particular variant of the modied minimal subtraction (MS) scheme, is sin2 W (MZ ) = 0.231 24(24). e The helion, symbol h, is the nucleus of the 3 He atom. f This and all other values involving m are based on the value of m c2 in MeV recommended by the Particle Data Group, Caso et al., Eur. Phys. J. C 3(1-4), 1-794 (1998), but with a standard uncertainty of 0.29 MeV rather than the quoted uncertainty of 0.26 MeV, +0.29 MeV. g The numerical value of F to be used in coulometric chemical measurements is 96 485.3432(76) [7.9108 ] when the relevant current is measured in terms of representations of the volt and ohm based on the Josephson and quantum Hall effects and the internationally adopted conventional values of the Josephson and von Klitzing constants K J90 and RK90 given in the Adopted values table. h The entropy of an ideal monoatomic gas of relative atomic mass A is given by S = S + 3 R ln A R ln( p/ p ) + 5 R ln(T/K). r r 0 0 2 2 12. Fundamental Physical Constants Adopted values Relative std. uncert. u rQuantitySymbolValueUnitmolar mass of 12 C molar mass constanta M(12 C)/12 conventional value of Josephson constantb conventional value of von Klitzing constantc standard atmosphere standard acceleration of gravityM(12 C) Mu12 103 1 103kg mol1 kg mol1(exact) (exact)K J90483 597.9GHz V1(exact)RK9025 812.807 101 325 9.806 65Pa m s2(exact) (exact) (exact)gn a The relative atomic mass A (X) of particle X with mass m(X) is dened by A (X) = m(X)/m , where m = m(12 C)/12 = M /N = 1 u is r r u u u A the atomic mass constant, NA is the Avogadro constant, and u is the atomic mass unit. Thus the mass of particle X in u is m(X) = A r (X) u and the molar mass of X is M(X) = Ar (X)Mu . b This is the value adopted internationally for realizing representations of the volt using the Josephson effect. c This is the value adopted internationally for realizing representations of the ohm using the quantum Hall effect. 13. Energy Equivalents Jkgm1Hz1J(1 J) = 1J(1 J)/c2 = 1.112 650 056 1017 kg(1 J)/hc = 5.034 117 62(39) 1024 m1(1 J)/h = 1.509 190 50(12) 1033 Hz1 kg(1 kg)c2 = 8.987 551 787 1016 J(1 kg) = 1 kg(1 kg)c/ h = 4.524 439 29(35) 1041 m1(1 kg)c2 / h = 1.356 392 77(11) 1050 Hz1 m1(1 m1 )hc = 1.986 445 44(16) 1025 J(1 m1 )h/c = 2.210 218 63(17) 1042 kg(1 m1 ) = 1 m1(1 m1 )c = 299 792 458 Hz1 Hz(1 Hz)h = 6.626 068 76(52) 1034 J(1 Hz)h/c2 = 7.372 495 78(58) 1051 kg(1 Hz)/c = 3.335 640 952 109 m1(1 Hz) = 1 Hz1K(1 K)k = 1.380 6503(24) 1023 J(1 K)k/c2 = 1.536 1807(27) 1040 kg(1 K)k/ hc = 69.503 56(12) m1(1 K)k/ h = 2.083 6644(36) 1010 Hz1 eV(1 eV) = 1.602 176 462(63) 1019 J(1 eV)/ hc = (1 eV)/c2 = 1.782 661 731(70) 1036 kg 8.065 544 77(32) 105 m11u(1 u)c2 = 1.492 417 78(12) 1010 J(1 u) = 1.660 538 73(13) 1027 kg(1 u)c/ h = 7.513 006 658(57) 1014 m1(1 u)c2 / h = 2.252 342 733(17) 1023 Hz1 Eh(1 E h ) = 4.359 743 81(34) 1018 J(1 E h )/c2 = 4.850 869 19(38) 1035 kg(1 E h )/ hc = 2.194 746 313 710(17) 107 m1(1 E h )/ h = 6.579 683 920 735(50) 1015 Hz(1 eV)/ h = 2.417 989 491(95) 1014 HzDerived from the relations E = mc2 = hc/ = h = kT , and based on the 1998 CODATA adjustment of the values of the constants; 1 1 eV = (e/C) J, 1 u = m u = 12 m(12 C) = 103 kg mol1/NA , and E h = 2R hc = 2 m e c2 is the Hartree energy (hartree). 14. Energy Equivalents KeVuEh1J(1 J)/k = 7.242 964(13) 1022 K(1 J) = 6.241 509 74(24) 1018 eV(1 J)/c2 = 6.700 536 62(53) 109 u(1 J) = 2.293 712 76(18) 1017 E h1 kg(1 kg)c2/k = 6.509 651(11) 1039 K(1 kg)c2 = 5.609 589 21(22) 1035 eV(1 kg) = 6.022 141 99(47) 1026 u(1 kg)c2 = 2.061 486 22(16) 1034 E h1 m1(1 m1 )hc/k = 1.438 7752(25) 102 K(1 m1 )hc = (1 m1 )h/c = (1 m1 )hc = 6 eV 1.331 025 042(10) 1015 u 4.556 335 252 750(35) 108 E 1.239 841 857(49) 10 h1 Hz(1 Hz)h/k = (1 Hz)h = 4.799 2374(84) 1011 K 4.135 667 27(16) 1015 eV(1 Hz)h/c2 = (1 Hz)h = 4.439 821 637(34) 1024 u 1.519 829 846 003(12) 1016 E h1K(1 K) = 1K(1 K)k = 8.617 342(15) 105 eV(1 K)k/c2 = 9.251 098(16) 1014 u(1 K)k = 3.166 8153(55) 106 E h1 eV(1 eV)/k = 1.160 4506(20) 104 K(1 eV) = 1 eV(1 eV)/c2 = 1.073 544 206(43) 109 u(1 eV) = 3.674 932 60(14) 102 E h1u(1 u)c2/k = 1.080 9528(19) 1013 K(1 u)c2 = 931.494 013(37) 106 eV(1 u) = 1u(1 u)c2 = 3.423 177 709(26) 107 E h1 Eh(1 E h )/k = 3.157 7465(55) 105 K(1 E h ) = 27.211 3834(11) eV(1 E h )/c2 = 2.921 262 304(22) 108 u(1 E h ) = 1 EhDerived from the relations E = mc2 = hc/ = h = kT , and based on the 1998 CODATA adjustment of the values of the constants; 1 1 eV = (e/C) J, 1 u = m u = 12 m(12 C) = 103 kg mol1/NA , and E h = 2R hc = 2 m e c2 is the Hartree energy (hartree). 15. STANDARD ATOMIC WEIGHTS (1997) This table of atomic weights is reprinted from the 1997 report of the IUPAC Commission on Atomic Weights and Isotopic Abundances. The Standard Atomic Weights apply to the elements as they exist naturally on Earth, and the uncertainties take into account the isotopic variation found in most laboratory samples. Further comments on the variability are given in the footnotes. The number in parentheses following the atomic weight value gives the uncertainty in the last digit. An entry in brackets indicates the mass number of the longest-lived isotope of an element that has no stable isotopes and for which a Standard Atomic Weight cannot be defined because of wide variability in isotopic composition (or complete absence) in nature. REFERENCE Vocke, R. D. (for IUPAC Commission on Atomic Weights and Isotopic Abundances), Atomic Weights of the Elements 1997, Pure Appl. Chem., 71, 1593, 1999.Name Actinium Aluminum Americium Antimony Argon Arsenic Astatine Barium Berkelium Beryllium Bismuth Bohrium Boron Bromine Cadmium Calcium Californium Carbon Cerium Cesium Chlorine Chromium Cobalt Copper Curium Dubnium Dysprosium Einsteinium Erbium Europium Fermium Fluorine Francium Gadolinium Gallium Germanium Gold Hafnium Hassium Helium Holmium Hydrogen Indium IodineSymbolAt. no.Atomic WeightAc Al Am Sb Ar As At Ba Bk Be Bi Bh B Br Cd Ca Cf C Ce Cs Cl Cr Co Cu Cm Db Dy Es Er Eu Fm F Fr Gd Ga Ge Au Hf Hs He Ho H In I89 13 95 51 18 33 85 56 97 4 83 107 5 35 48 20 98 6 58 55 17 24 27 29 96 105 66 99 68 63 100 9 87 64 31 32 79 72 108 2 67 1 49 53[227] 26.981538(2) [243] 121.760(1) 39.948(1) 74.92160(2) [210] 137.327(7) [247] 9.012182(3) 208.98038(2) [264] 10.811(7) 79.904(1) 112.411(8) 40.078(4) [251] 12.0107(8) 140.116(1) 132.90545(2) 35.4527(9) 51.9961(6) 58.933200(9) 63.546(3) [247] [262] 162.50(3) [252] 167.26(3) 151.964(1) [257] 18.9984032(5) [223] 157.25(3) 69.723(1) 72.61(2) 196.96655(2) 178.49(2) [269] 4.002602(2) 164.93032(2) 1.00794(7) 114.818(3) 126.90447(3)1-12Footnotesg ggrmrg g g grmrg g ggg gr mr 16. STANDARD ATOMIC WEIGHTS (1997) (continued)NameSymbolAt. no.Iridium Iron Krypton Lanthanum Lawrencium Lead Lithium Lutetium Magnesium Manganese Meitnerium Mendelevium Mercury Molybdenum Neodymium Neon Neptunium Nickel Niobium Nitrogen Nobelium Osmium Oxygen Palladium Phosphorus Platinum Plutonium Polonium Potassium Praseodymium Promethium Protactinium Radium Radon Rhenium Rhodium Rubidium Ruthenium Rutherfordium Samarium Scandium Seaborgium Selenium Silicon Silver Sodium Strontium Sulfur Tantalum Technetium Tellurium Terbium Thallium Thorium Thulium Tin Titanium TungstenIr Fe Kr La Lr Pb Li Lu Mg Mn Mt Md Hg Mo Nd Ne Np Ni Nb N No Os O Pd P Pt Pu Po K Pr Pm Pa Ra Rn Re Rh Rb Ru Rf Sm Sc Sg Se Si Ag Na Sr S Ta Tc Te Tb Tl Th Tm Sn Ti W77 26 36 57 103 82 3 71 12 25 109 101 80 42 60 10 93 28 41 7 102 76 8 46 15 78 94 84 19 59 61 91 88 86 75 45 37 44 104 62 21 106 34 14 47 11 38 16 73 43 52 65 81 90 69 50 22 74Atomic Weight 192.217(3) 55.845(2) 83.80(1) 138.9055(2) [262] 207.2(1) 6.941(2)* 174.967(1) 24.3050(6) 54.938049(9) [268] [258] 200.59(2) 95.94(1) 144.24(3) 20.1797(6) [237] 58.6934(2) 92.90638(2) 14.00674(7) [259] 190.23(3) 15.9994(3) 106.42(1) 30.973761(2) 195.078(2) [244] [209] 39.0983(1) 140.90765(2) [145] 231.03588(2) [226] [222] 186.207(1) 102.90550(2) 85.4678(3) 101.07(2) [261] 150.36(3) 44.955910(8) [266] 78.96(3) 28.0855(3) 107.8682(2) 22.989770(2) 87.62(1) 32.066(6) 180.9479(1) [98] 127.60(3) 158.92534(2) 204.3833(2) 232.0381(1) 168.93421(2) 118.710(7) 47.867(1) 183.84(1)1-13Footnotesg g g g gg g gmmr rmgrg g grgg g gr g g ggg gr r 17. STANDARD ATOMIC WEIGHTS (1997) (continued) Name Uranium Vanadium Xenon Ytterbium Yttrium Zinc Zirconium * g m rSymbolAt. no.Atomic WeightU V Xe Yb Y Zn Zr92 23 54 70 39 30 40238.0289(1) 50.9415(1) 131.29(2) 173.04(3) 88.90585(2) 65.39(2) 91.224(2)Footnotes gmg gmgCommercially available Li materials have atomic weights that are known to range between 6.939 and 6.996; if a more accurate value is required, it must be determined for the specific material. geological specimens are known in which the element has an isotopic composition outside the limits for normal material. The difference between the atomic weight of the element in such specimens and that given in the table may exceed the stated uncertainty. modified isotopic compositions may be found in commercially available material because it has been subjected to an undisclosed or inadvertent isotopic fractionation. Substantial deviations in atomic weight of the element from that given the table can occur. range in isotopic composition of normal terrestrial material prevents a more precise atomic weight being given; the tabulated atomic weight value should be applicable to any normal material.1-14 18. ATOMIC MASSES AND ABUNDANCES This table lists the mass (in atomic mass units, symbol u) and the natural abundance (in percent) of the stable nuclides and a few important radioactive nuclides. A complete table of all nuclides may be found in Section 11 (Table of the Isotopes). The atomic masses are based on the 1995 evaluation of Audi and Wapstra (Reference 2). The number in parentheses following the mass value is the uncertainty in the last digit(s) given. Natural abundance values are also followed by uncertainties in the last digit(s) of the stated values. This uncertainty includes both the estimated measurement uncertainty and the reported range of variation in different terrestrial sources of the element (see Reference 3 and 4 for more details). The absence of an entry in the Abundance column indicates a radioactive nuclide not present in nature or an element whose isotopic composition varies so widely that a meaningful natural abundance cannot be defined. An electronic version of these data is available on the Web site of the NIST Physics Laboratory (Reference 5). REFERENCES 1. Holden, N. E., Table of the Isotopes, in Lide, D. R., Ed., CRC Handbook of Chemistry and Physics, 82nd Ed., CRC Press, Boca Raton FL, 2001. 2. Audi, G., and Wapstra, A. H., Nucl. Phys., A595, 409, 1995. 3. Rosman, K. J. R., and Taylor, P. D. P., J. Phys. Chem. Ref. Data, 27, 1275, 1998. 4. R. D. Vocke (for IUPAC Commission on Atomic Weights and Isotopic Abundances), Pure Appl. Chem., 71, 1593, 1999. 5. Coursey, J. S., and Dragoset, R. A., Atomic Weights and Isotopic Compositions (version 2.1). Available: http://physics.nist.gov/Compositions/ National Institute of Standards and Technology, Gaithersburg, MD. Z 1Isotope 1H 2D 3T23He 4He36Li 7Li4 59Be 10B 11B612C 13C714N 15N816O 17O 18O9 1019F 20Ne 21Ne 22Ne11 1223Na 24Mg 25Mg 26Mg13 1427Al 28Si 29Si 30Si15 1631P 32S 33S 34S 36S1735Cl 37Cl1836Ar 38ArMass in u 1.0078250321(4) 2.0141017780(4) 3.0160492675(11) 3.0160293097(9) 4.0026032497(10) 6.0151223(5) 7.0160040(5) 9.0121821(4) 10.0129370(4) 11.0093055(5) 12.0000000(0) 13.0033548378(10) 14.0030740052(9) 15.0001088984(9) 15.9949146221(15) 16.99913150(22) 17.9991604(9) 18.99840320(7) 19.9924401759(20) 20.99384674(4) 21.99138551(23) 22.98976967(23) 23.98504190(20) 24.98583702(20) 25.98259304(21) 26.98153844(14) 27.9769265327(20) 28.97649472(3) 29.97377022(5) 30.97376151(20) 31.97207069(12) 32.97145850(12) 33.96786683(11) 35.96708088(25) 34.96885271(4) 36.96590260(5) 35.96754628(27) 37.9627322(5)Abundance in %ZIsotope 40Ar99.9850(70) 0.0115(70)1939K 40K 41K0.000137(3) 99.999863(3) 7.59(4) 92.41(4) 100 19.9(7) 80.1(7) 98.93(8) 1.07(8) 99.632(7) 0.368(7) 99.757(16) 0.038(1) 0.205(14) 100 90.48(3) 0.27(1) 9.25(3) 100 78.99(4) 10.00(1) 11.01(3) 100 92.2297(7) 4.6832(5) 3.0872(5) 100 94.93(31) 0.76(2) 4.29(28) 0.02(1) 75.78(4) 24.22(4) 0.3365(30) 0.0632(5)2040Ca 42Ca 43Ca 44Ca 46Ca 48Ca21 2245Sc 46Ti 47Ti 48Ti 49Ti 50Ti2350V 51V2450Cr 52Cr 53Cr 54Cr25 2655Mn 54Fe 56Fe 57Fe 58Fe27 2859Co 58Ni 60Ni 61Ni 62Ni 64Ni2963Cu 65Cu3064Zn 66Zn 67Zn1-15Mass in u 39.962383123(3) 38.9637069(3) 39.96399867(29) 40.96182597(28) 39.9625912(3) 41.9586183(4) 42.9587668(5) 43.9554811(9) 45.9536928(25) 47.952534(4) 44.9559102(12) 45.9526295(12) 46.9517638(10) 47.9479471(10) 48.9478708(10) 49.9447921(11) 49.9471628(14) 50.9439637(14) 49.9460496(14) 51.9405119(15) 52.9406538(15) 53.9388849(15) 54.9380496(14) 53.9396148(14) 55.9349421(15) 56.9353987(15) 57.9332805(15) 58.9332002(15) 57.9353479(15) 59.9307906(15) 60.9310604(15) 61.9283488(15) 63.9279696(16) 62.9296011(15) 64.9277937(19) 63.9291466(18) 65.9260368(16) 66.9271309(17)Abundance in % 99.6003(30) 93.2581(44) 0.0117(1) 6.7302(44) 96.941(156) 0.647(23) 0.135(10) 2.086(110) 0.004(3) 0.187(21) 100 8.25(3) 7.44(2) 73.72(3) 5.41(2) 5.18(2) 0.250(4) 99.750(4) 4.345(13) 83.789(18) 9.501(17) 2.365(7) 100 5.845(35) 91.754(36) 2.119(10) 0.282(4) 100 68.0769(89) 26.2231(77) 1.1399(6) 3.6345(17) 0.9256(9) 69.17(3) 30.83(3) 48.63(60) 27.90(27) 4.10(13) 19. ATOMIC MASSES AND ABUNDANCES (continued) ZIsotope 68Zn 70Zn3169Ga 71Ga3270Ge 72Ge 73Ge 74Ge 76Ge33 3475As 74Se 76Se 77Se 78Se 80Se 82Se3579Br 81Br3678Kr 80Kr 82Kr 83Kr 84Kr 86Kr3785Rb 87Rb3884Sr 86Sr 87Sr 88Sr39 4089Y 90Zr 91Zr 92Zr 94Zr 96Zr41 4293Nb 92Mo 94Mo 95Mo 96Mo 97Mo 98Mo 100Mo4397Tc 98Tc 99Tc4496Ru 98Ru 99Ru 100Ru 101Ru 102Ru 104Ru45 46103Rh 102Pd 104Pd 105PdMass in u 67.9248476(17) 69.925325(4) 68.925581(3) 70.9247050(19) 69.9242504(19) 71.9220762(16) 72.9234594(16) 73.9211782(16) 75.9214027(16) 74.9215964(18) 73.9224766(16) 75.9192141(16) 76.9199146(16) 77.9173095(16) 79.9165218(20) 81.9167000(22) 78.9183376(20) 80.916291(3) 77.920386(7) 79.916378(4) 81.9134846(28) 82.914136(3) 83.911507(3) 85.9106103(12) 84.9117893(25) 86.9091835(27) 83.913425(4) 85.9092624(24) 86.9088793(24) 87.9056143(24) 88.9058479(25) 89.9047037(23) 90.9056450(23) 91.9050401(23) 93.9063158(25) 95.908276(3) 92.9063775(24) 91.906810(4) 93.9050876(20) 94.9058415(20) 95.9046789(20) 96.9060210(20) 97.9054078(20) 99.907477(6) 96.906365(5) 97.907216(4) 98.9062546(21) 95.907598(8) 97.905287(7) 98.9059393(21) 99.9042197(22) 100.9055822(22) 101.9043495(22) 103.905430(4) 102.905504(3) 101.905608(3) 103.904035(5) 104.905084(5)Abundance in %ZIsotope 106Pd18.75(51) 0.62(3) 60.108(9) 39.892(9) 20.84(87) 27.54(34) 7.73(5) 36.28(73) 7.61(38) 100 0.89(4) 9.37(29) 7.63(16) 23.77(28) 49.61(41) 8.73(22) 50.69(7) 49.31(7) 0.35(1) 2.28(6) 11.58(14) 11.49(6) 57.00(4) 17.30(22) 72.17(2) 27.83(2) 0.56(1) 9.86(1) 7.00(1) 82.58(1) 100 51.45(40) 11.22(5) 17.15(8) 17.38(28) 2.80(9) 100 14.84(35) 9.25(12) 15.92(13) 16.68(2) 9.55(8) 24.13(31) 9.63(23)108Pd 110Pd47107Ag 109Ag48106Cd 108Cd 110Cd 111Cd 112Cd 113Cd 114Cd 116Cd49113In 115In50112Sn 114Sn 115Sn 116Sn 117Sn 118Sn 119Sn 120Sn 122Sn 124Sn51121Sb 123Sb52120Te 122Te 123Te 124Te 125Te 126Te 128Te 130Te53 54127I 124Xe 126Xe 128Xe 129Xe 130Xe 131Xe 132Xe 134Xe 136Xe55 56133Cs 130Ba 132Ba5.54(14) 1.87(3) 12.76(14) 12.60(7) 17.06(2) 31.55(14) 18.62(27) 100 1.02(1) 11.14(8) 22.33(8)134Ba 135Ba 136Ba 137Ba 138Ba57138La 139La58136Ce 138Ce 140Ce1-16Mass in u 105.903483(5) 107.903894(4) 109.905152(12) 106.905093(6) 108.904756(3) 105.906458(6) 107.904183(6) 109.903006(3) 110.904182(3) 111.9027572(30) 112.9044009(30) 113.9033581(30) 115.904755(3) 112.904061(4) 114.903878(5) 111.904821(5) 113.902782(3) 114.903346(3) 115.901744(3) 116.902954(3) 117.901606(3) 118.903309(3) 119.9021966(27) 121.9034401(29) 123.9052746(15) 120.9038180(24) 122.9042157(22) 119.904020(11) 121.9030471(20) 122.9042730(19) 123.9028195(16) 124.9044247(20) 125.9033055(20) 127.9044614(19) 129.9062228(21) 126.904468(4) 123.9058958(21) 125.904269(7) 127.9035304(15) 128.9047795(9) 129.9035079(10) 130.9050819(10) 131.9041545(12) 133.9053945(9) 135.907220(8) 132.905447(3) 129.906310(7) 131.905056(3) 133.904503(3) 134.905683(3) 135.904570(3) 136.905821(3) 137.905241(3) 137.907107(4) 138.906348(3) 135.907140(50) 137.905986(11) 139.905434(3)Abundance in % 27.33(3) 26.46(9) 11.72(9) 51.839(8) 48.161(8) 1.25(6) 0.89(3) 12.49(18) 12.80(12) 24.13(21) 12.22(12) 28.73(42) 7.49(18) 4.29(5) 95.71(5) 0.97(1) 0.66(1) 0.34(1) 14.54(9) 7.68(7) 24.22(9) 8.59(4) 32.58(9) 4.63(3) 5.79(5) 57.21(5) 42.79(5) 0.09(1) 2.55(12) 0.89(3) 4.74(14) 7.07(15) 18.84(25) 31.74(8) 34.08(62) 100 0.09(1) 0.09(1) 1.92(3) 26.44(24) 4.08(2) 21.18(3) 26.89(6) 10.44(10) 8.87(16) 100 0.106(1) 0.101(1) 2.417(18) 6.592(12) 7.854(24) 11.232(24) 71.698(42) 0.090(1) 99.910(1) 0.185(2) 0.251(2) 88.450(51) 20. ATOMIC MASSES AND ABUNDANCES (continued) ZIsotope 142Ce59 60141Pr 142Nd 143Nd 144Nd 145Nd 146Nd 148Nd 150Nd61145Pm 147Pm62144Sm 147Sm 148Sm 149Sm 150Sm 152Sm 154Sm63151Eu 153Eu64152Gd 154Gd 155Gd 156Gd 157Gd 158Gd 160Gd65 66159Tb 156Dy 158Dy 160Dy 161Dy 162Dy 163Dy 164Dy67 68165Ho 162Er 164Er 166Er 167Er 168Er 170Er69 70169Tm 168Yb 170Yb 171Yb 172Yb 173Yb 174Yb 176Yb71175Lu 176Lu72174Hf 176Hf 177Hf 178Hf 179Hf 180HfMass in u 141.909240(4) 140.907648(3) 141.907719(3) 142.909810(3) 143.910083(3) 144.912569(3) 145.913112(3) 147.916889(3) 149.920887(4) 144.912744(4) 146.915134(3) 143.911995(4) 146.914893(3) 147.914818(3) 148.917180(3) 149.917271(3) 151.919728(3) 153.922205(3) 150.919846(3) 152.921226(3) 151.919788(3) 153.920862(3) 154.922619(3) 155.922120(3) 156.923957(3) 157.924101(3) 159.927051(3) 158.925343(3) 155.924278(7) 157.924405(4) 159.925194(3) 160.926930(3) 161.926795(3) 162.928728(3) 163.929171(3) 164.930319(3) 161.928775(4) 163.929197(4) 165.930290(3) 166.932045(3) 167.932368(3) 169.935460(3) 168.934211(3) 167.933894(5) 169.934759(3) 170.936322(3) 171.9363777(30) 172.9382068(30) 173.9388581(30) 175.942568(3) 174.9407679(28) 175.9426824(28) 173.940040(3) 175.9414018(29) 176.9432200(27) 177.9436977(27) 178.9458151(27) 179.9465488(27)Abundance in %Z11.114(51) 100 27.2(5) 12.2(2) 23.8(3) 8.3(1) 17.2(3) 5.7(1) 5.6(2)73Isotope 180Ta 181Ta74180W 182W 183W 184W 186W75185Re 187Re76184Os 186Os 187Os3.07(7) 14.99(18) 11.24(10) 13.82(7) 7.38(1) 26.75(16) 22.75(29) 47.81(3) 52.19(3) 0.20(1) 2.18(3) 14.80(12) 20.47(9) 15.65(2) 24.84(7) 21.86(19) 100 0.06(1) 0.10(1) 2.34(8) 18.91(24) 25.51(26) 24.90(16) 28.18(37) 100 0.14(1) 1.61(3) 33.61(35) 22.93(17) 26.78(26) 14.93(27) 100 0.13(1) 3.04(15) 14.28(57) 21.83(67) 16.13(27) 31.83(92) 12.76(41) 97.41(2) 2.59(2) 0.16(1) 5.26(7) 18.60(9) 27.28(7) 13.62(2) 35.08(16)188Os 189Os 190Os 192Os77191Ir 193Ir78190Pt 192Pt 194Pt 195Pt 196Pt 198Pt79 80197Au 196Hg 198Hg 199Hg 200Hg 201Hg 202Hg 204Hg81203Tl 205Tl82204Pb 206Pb 207Pb 208Pb83 84209Bi 209Po 210Po85210At 211At86211Rn 220Rn 222Rn87 88223Fr 223Ra 224Ra 226Ra 228Ra89 90227Ac 230Th 232Th91 92231Pa 233U 234U 235U1-17Mass in u 179.947466(3) 180.947996(3) 179.946706(5) 181.948206(3) 182.9502245(29) 183.9509326(29) 185.954362(3) 184.9529557(30) 186.9557508(30) 183.952491(3) 185.953838(3) 186.9557479(30) 187.9558360(30) 188.9581449(30) 189.958445(3) 191.961479(4) 190.960591(3) 192.962924(3) 189.959930(7) 191.961035(4) 193.962664(3) 194.964774(3) 195.964935(3) 197.967876(4) 196.966552(3) 195.965815(4) 197.966752(3) 198.968262(3) 199.968309(3) 200.970285(3) 201.970626(3) 203.973476(3) 202.972329(3) 204.974412(3) 203.973029(3) 205.974449(3) 206.975881(3) 207.976636(3) 208.980383(3) 208.982416(3) 209.982857(3) 209.987131(9) 210.987481(4) 210.990585(8) 220.0113841(29) 222.0175705(27) 223.0197307(29) 223.018497(3) 224.0202020(29) 226.0254026(27) 228.0310641(27) 227.0277470(29) 230.0331266(22) 232.0380504(22) 231.0358789(28) 233.039628(3) 234.0409456(21) 235.0439231(21)Abundance in % 0.012(2) 99.988(2) 0.12(1) 26.50(16) 14.31(4) 30.64(2) 28.43(19) 37.40(2) 62.60(2) 0.02(1) 1.59(3) 1.96(2) 13.24(8) 16.15(5) 26.26(2) 40.78(19) 37.3(2) 62.7(2) 0.014(1) 0.782(7) 32.967(99) 33.832(10) 25.242(41) 7.163(55) 100 0.15(1) 9.97(20) 16.87(22) 23.10(19) 13.18(9) 29.86(26) 6.87(15) 29.524(14) 70.476(14) 1.4(1) 24.1(1) 22.1(1) 52.4(1) 100100 100 0.0055(2) 0.7200(51) 21. ATOMIC MASSES AND ABUNDANCES (continued) ZIsotope236U 238U93237Np 239Np94238Pu 239Pu 240Pu 241Pu 242Pu 244Pu95241Am 243Am96243Cm 244Cm 245Cm 246Cm 247Cm 248Cm97247BkMass in u236.0455619(21) 238.0507826(21) 237.0481673(21) 239.0529314(23) 238.0495534(21) 239.0521565(21) 240.0538075(21) 241.0568453(21) 242.0587368(21) 244.064198(5) 241.0568229(21) 243.0613727(23) 243.0613822(24) 244.0627463(21) 245.0654856(29) 246.0672176(24) 247.070347(5) 248.072342(5) 247.070299(6)Abundance in %ZIsotope249Bk99.2745(106)98249Cf 250Cf 251Cf 252Cf99 100 101252Es 257Fm 256Md 258Md102 103 104 105 106 107 108 109 110 111259No 262Lr 261Rf 262Db 263Sg 264Bh 265Hs 268Mt 269Uun 272Uuu*Mass values derived not purely from experimental data, but at least partly from systematic trends.1-18Mass in u249.074980(3) 249.074847(3) 250.0764000(24) 251.079580(5) 252.081620(5) 252.082970(50) 257.095099(7) 256.094050(60) 258.098425(5) 259.101020(110)* 262.109690(320)* 261.108750(110)* 262.114150(200)* 263.118310(130)* 264.124730(300)* 265.130000(320)* 268.138820(340)* 269.145140(310)* 272.153480(360)*Abundance in % 22. ELECTRON CONFIGURATION OF NEUTRAL ATOMS IN THE GROUND STATE Atomic no.n= ElementK 1 sL 2 sp1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 21 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 21 2 3 4 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6sM 3 p dsN 4 p d1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 21 2 3 4 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 61 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 21 2 3 4 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 61 2 3 5* 5 6 7 8 10* 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 101-131 2 4* 5 5 7 8 10* 10 10 10 10 10 10 10 10 10 10O 5 fspdfs1 2 2 2 1 1 2 1 1 1 2 2 2 2 2 2 2 2 21 2 3 4 5 6 6 61 2P 6 p dQ 7 s 23. ELECTRON CONFIGURATION OF NEUTRAL ATOMS IN THE GROUND STATE (continued) Atomic no. 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 *n= ElementK 1 sL 2 spLa Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Rf2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 26 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6sM 3 p dsN 4 p d2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 26 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 62 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 26 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 610 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 1010 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10O 5 fs1* 3 4 5 6 7 7 9* 10 11 12 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 142 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2p 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6dfs2* 3 4 6* 7 7* 9 10 11 12 13 14 14 142 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 21 111 2 3 4 5 6 7 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10P 6 p d1 2 3 4 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6Note irregularity.REFERENCE W. L. Wiese and G. A. Martin, in A Physicists Desk Reference, American Institute of Physics, New York, 1989, 94.1-141 2 1 1 111 2Q 7 s1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 24. INTERNATIONAL TEMPERATURE SCALE OF 1990 (ITS-90) B. W. Mangum A new temperature scale, the International Temperature Scale of 1990 (ITS-90), was officially adopted by the Comit International des Poids et Mesures (CIPM), meeting 2628 September 1989 at the Bureau International des Poids et Mesures (BIPM). The ITS-90 was recommended to the CIPM for its adoption following the completion of the final details of the new scale by the Comit Consultatif de Thermomtrie (CCT), meeting 1214 September 1989 at the BIPM in its 17th Session. The ITS-90 became the official international temperature scale on 1 January 1990. The ITS90 supersedes the present scales, the International Practical Temperature Scale of 1968 (IPTS-68) and the 1976 Provisional 0.5 to 30 K Temperature Scale (EPT-76). The ITS-90 extends upward from 0.65 K, and temperatures on this scale are in much better agreement with thermodynamic values that are those on the IPTS-68 and the EPT-76. The new scale has subranges and alternative definitions in certain ranges that greatly facilitate its use. Furthermore, its continuity, precision, and reproducibility throughout its ranges are much improved over that of the present scales. The replacement of the thermocouple with the platinum resistance thermometer at temperatures below 961.78C resulted in the biggest improvement in reproducibility. The ITS-90 is divided into four primary ranges: 1. Between 0.65 and 3.2 K, the ITS-90 is defined by the vapor pressure-temperature relation of 3He, and between 1.25 and 2.1768 K (the point) and between 2.1768 and 5.0 K by the vapor pressure-temperature relations of 4He. T90 is defined by the vapor pressure equations of the form: 9[()T90 / K = A0 + Ai ln( p/ Pa ) B / C i =1]iThe values of the coefficients Ai, and of the constants Ao, B, and C of the equations are given below. 2. Between 3.0 and 24.5561 K, the ITS-90 is defined in terms of a 3He or 4He constant volume gas thermometer (CVGT). The thermometer is calibrated at three temperatures at the triple point of neon (24.5561 K), at the triple point of equilibrium hydrogen (13.8033 K), and at a temperature between 3.0 and 5.0 K, the value of which is determined by using either 3He or 4He vapor pressure thermometry. 3. Between 13.8033 K (259.3467C) and 1234.93 K (961.78C), the ITS-90 is defined in terms of the specified fixed points given below, by resistance ratios of platinum resistance thermometers obtained by calibration at specified sets of the fixed points, and by reference functions and deviation functions of resistance ratios which relate to T90 between the fixed points. 4. Above 1234.93 K, the ITS-90 is defined in terms of Plancks radiation law, using the freezing-point temperature of either silver, gold, or copper as the reference temperature. Full details of the calibration procedures and reference functions for various subranges are given in: The International Temperature Scale of 1990, Metrologia, 27, 3, 1990; errata in Metrologia, 27, 107, 1990.Defining Fixed Points of the ITS-90 MaterialaEquilibrium statebTemperature T90 (K)He e-H2 e-H2 (or He) e-H2 (or He) Nec O2 Ar Hgc H2O Gac Inc Sn Zn Alc Ag AuVP TP VP (or CVGT) VP (or CVGT) TP TP TP TP TP MP FP FP FP FP FP FPCuc3 to 5 13.8033 17 20.3 24.5561 54.3584 83.8058 234.3156 273.16 302.9146 429.7485 505.078 692.677 933.473 1234.93 1337.33FP1357.771-15t90 (C)270.15 to 268.15 259.3467 256.15 252.85 248.5939 218.7916 189.3442 38.8344 0.01 29.7646 156.5985 231.928 419.527 660.323 961.78 1064.18 1084.62 25. INTERNATIONAL TEMPERATURE SCALE OF 1990 (ITS-90) (continued) Defining Fixed Points of the ITS-90 (continued) abce-H2 indicates equilibrium hydrogen, that is, hydrogen with the equilibrium distribution of its ortho and para states. Normal hydrogen at room temperature contains 25% para hydrogen and 75% ortho hydrogen. VP indicates vapor pressure point; CVGT indicates constant volume gas thermometer point; TP indicates triple point (equilibrium temperature at which the solid, liquid, and vapor phases coexist); FP indicates freezing point, and MP indicates melting point (the equilibrium temperatures at which the solid and liquid phases coexist under a pressure of 101 325 Pa, one standard atmosphere). The isotopic composition is that naturally occurring. Previously, these were secondary fixed points.Values of Coefficients in the Vapor Pressure Equations for Helium Coef.or constant A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 B C3He 0.653.2 K4He 1.252.1768 K1.053 447 0.980 106 0.676 380 0.372 692 0.151 656 0.002 263 0.006 596 0.088 966 0.004 770 0.054 943 7.3 4.31.392 408 0.527 153 0.166 756 0.050 988 0.026 514 0.001 975 0.017 976 0.005 409 0.013 259 0 5.6 2.91-164He 2.17685.0 K3.146 631 1.357 655 0.413 923 0.091 159 0.016 349 0.001 826 0.004 325 0.004 973 0 0 10.3 1.9 26. CONVERSION OF TEMPERATURES FROM THE 1948 AND 1968 SCALES TO ITS-90 This table gives temperature corrections from older scales to the current International Temperature Scale of 1990 (see the preceding table for details on ITS-90). The first part of the table may be used for converting Celsius temperatures in the range -180 to 4000C from IPTS-68 or IPTS-48 to ITS90. Within the accuracy of the corrections, the temperature in the first column may be identified with either t68, t48, or t90. The second part of the table is designed for use at lower temperatures to convert values expressed in kelvins from EPT-76 or IPTS-68 to ITS-90. The references give analytical equations for expressing these relations. Note that Reference 1 supersedes Reference 2 with respect to corrections in the 630 to 1064C range. REFERENCES 1. Burns, G. W. et al., in Temperature: Its Measurement and Control in Science and Industry, Vol. 6, Schooley, J. F., Ed., American Institute of Physics, New York, 1993. 2. Goldberg, R. N. and Weir, R. D., Pure and Appl. Chem., 1545, 1992. t/Ct90-t68t90-t48t/Ct90-t68t90-t48t/Ct90-t68t90-t48-180 -170 -160 -150 -140 -130 -120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 2600.008 0.010 0.012 0.013 0.014 0.014 0.014 0.013 0.013 0.012 0.012 0.011 0.010 0.009 0.008 0.006 0.004 0.002 0.000 -0.002 -0.005 -0.007 -0.010 -0.013 -0.016 -0.018 -0.021 -0.024 -0.026 -0.028 -0.030 -0.032 -0.034 -0.036 -0.037 -0.038 -0.039 -0.039 -0.040 -0.040 -0.040 -0.040 -0.040 -0.040 -0.0400.020 0.017 0.007 0.000 0.001 0.008 0.017 0.026 0.035 0.041 0.045 0.045 0.042 0.038 0.032 0.024 0.016 0.008 0.000 -0.006 -0.012 -0.016 -0.020 -0.023 -0.026 -0.026 -0.027 -0.027 -0.026 -0.024 -0.023 -0.020 -0.018 -0.016 -0.012 -0.009 -0.005 -0.001 0.003 0.007 0.011 0.014 0.018 0.021 0.024270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710-0.039 -0.039 -0.039 -0.039 -0.039 -0.039 -0.040 -0.040 -0.041 -0.042 -0.043 -0.045 -0.046 -0.048 -0.051 -0.053 -0.056 -0.059 -0.062 -0.065 -0.068 -0.072 -0.075 -0.079 -0.083 -0.087 -0.090 -0.094 -0.098 -0.101 -0.105 -0.108 -0.112 -0.115 -0.118 -0.122 -0.125 -0.11 -0.10 -0.09 -0.07 -0.05 -0.04 -0.02 -0.010.028 0.030 0.032 0.034 0.035 0.036 0.036 0.037 0.036 0.035 0.034 0.032 0.030 0.028 0.024 0.022 0.019 0.015 0.012 0.009 0.007 0.004 0.002 0.000 -0.001 -0.002 -0.001 0.000 0.002 0.007 0.011 0.018 0.025 0.035 0.047 0.060 0.075 0.12 0.15 0.19 0.24 0.29 0.32 0.37 0.41720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1200 1300 1400 1500 1600 17000.00 0.02 0.03 0.03 0.04 0.05 0.05 0.05 0.05 0.05 0.04 0.04 0.03 0.02 0.01 0.00 -0.02 -0.03 -0.05 -0.06 -0.08 -0.10 -0.11 -0.13 -0.15 -0.16 -0.18 -0.19 -0.20 -0.22 -0.23 -0.23 -0.24 -0.25 -0.25 -0.25 -0.26 -0.26 -0.26 -0.30 -0.35 -0.39 -0.44 -0.49 -0.540.45 0.49 0.53 0.56 0.60 0.63 0.66 0.69 0.72 0.75 0.76 0.79 0.81 0.83 0.85 0.87 0.87 0.89 0.90 0.92 0.93 0.94 0.96 0.97 0.97 0.99 1.00 1.02 1.04 1.05 1.07 1.10 1.12 1.14 1.17 1.19 1.20 1.20 1.2 1.4 1.5 1.6 1.8 1.9 2.11-17 27. CONVERSION OF TEMPERATURES FROM THE 1948 AND 1968 SCALES TO ITS-90 (continued) t/Ct90-t68t90-t48T/K1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000-0.60 -0.66 -0.72 -0.79 -0.85 -0.93 -1.00 -1.07 -1.15 -1.24 -1.32 -1.41 -1.50 -1.59 -1.69 -1.78 -1.89 -1.99 -2.10 -2.21 -2.32 -2.43 -2.552.2 2.3 2.5 2.7 2.9 3.1 3.2 3.4 3.7 3.8 4.0 4.2 4.4 4.6 4.8 5.1 5.3 5.5 5.8 6.0 6.3 6.6 6.8T/KT90-T76T90-T68-0.0001 -0.0002 -0.0003 -0.0004 -0.0005 -0.0006 -0.0007 -0.0008 -0.0010 -0.0011 -0.0013 -0.0014 -0.0016 -0.0018 -0.0020 -0.0022 -0.0025 -0.0027 -0.0030 -0.0032 -0.0035 -0.0038 -0.0041-0.006 -0.003 -0.004 -0.006 -0.008 -0.009 -0.009 -0.008 -0.007 -0.007 -0.006 -0.005 -0.004 -0.00428 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 765 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 271-18T90-T68T/K-0.005 -0.006 -0.006 -0.007 -0.008 -0.008 -0.008 -0.007 -0.007 -0.007 -0.006 -0.006 -0.006 -0.006 -0.006 -0.006 -0.006 -0.007 -0.007 -0.007 -0.006 -0.006 -0.006 -0.005 -0.005 -0.004 -0.003 -0.002 -0.001 0.000 0.001 0.002 0.003 0.003 0.004 0.004 0.005 0.005 0.006 0.006 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.008 0.008T90-T7677 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 273.16 300 400 500 600 700 800 900T90-T76T90-T68 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.009 0.009 0.009 0.009 0.011 0.013 0.014 0.014 0.014 0.014 0.013 0.012 0.012 0.011 0.010 0.009 0.008 0.007 0.005 0.003 0.001 0.000 -0.006 -0.031 -0.040 -0.040 -0.055 -0.089 -0.124 28. INTERNATIONAL SYSTEM OF UNITS (SI) 1 SI base units Table 1 gives the seven base quantities, assumed to be mutually independent, on which the SI is founded; and the names and symbols of their respective units, called ``SI base units.' ' Definitions of the SI base units are given in Appendix A. The kelvin and its symbol K are also used to express the value of a temperature interval or a temperature difference.Table 1. SI base units SI base unit Base quantity length mass time electric current thermodynamic temperature amount of substance luminous intensityNameSymbolmeter kilogram second ampere kelvin mole candelam kg s A K mol cd2 SI deri ved units i Derived units are expressed algebraically in terms of base units or other derived units (including the radian and steradian which are the two supplementary units see Sec. 3). The symbols for derived units are obtained by means of the mathematical operations of multiplication and division. For example, the derived unit for the derived quantity molar mass (mass divided by amount of substance) is the kilogram per mole, symbol kg/mol. Additional examples of derived units expressed in terms of SI base units are given in Table 2.Table 2. Examples of SI derived units expressed in terms of SI base units SI derived unit Derived quantity area volume speed, velocity acceleration wave number mass density (density) specific volume current density magnetic field strength amount-of-substance concentration (concentration) luminance2.1NameSymbolsquare meter cubic meter meter per second meter per second squared reciprocal meter kilogram per cubic meter cubic meter per kilogram ampere per square meter ampere per meterm2 m3 m/s m/s 2 m1 kg/m 3 m 3 /kg A/m 2 A/mmole per cubic meter candela per square metermol/m 3 cd/m 2SI derived units with special names and symbolsCertain SI derived units have special names and symbols; these are given in Tables 3a and 3b. As discussed in Sec. 3, the radian and steradian, which are the two supplementary units, are included in Table 3a. 29. INTERNATIONAL SYSTEM OF UNITS (SI) (continued) Table 3a. SI derived units with special names and symbols, including the radian and steradian SI derived unit Derived quantitySpecial nameplane angle solid angle frequency force pressure, stress energy, work, quantity of heat power, radiant flux electric charge, quantity of electricity electric potential, potential difference, electromotive force capacitance electric resistance electric conductance magnetic flux magnetic flux density inductance Celsius temperature(a) luminous flux illuminance (a) (b)Special symbolExpression in terms of other SI unitsExpression in terms of SI base unitsradian steradian hertz newton pascalrad sr Hz N PaN/m2m m1 = 1 m 2 m2 = 1 s1 m kg s2 m1 kg s2joule wattJ WNm J/sm2 kg s2 m2 kg s3coulombCvolt farad ohm siemens weber tesla henry degree Celsius lumen luxV F S Wb T H C lm lxsA W/A C/V V/A A/V Vs Wb/m2 Wb/A cd sr lm/m2m2 kg s3 A1 m2 kg1 s4 A2 m2 kg s3 A2 m2 kg1 s3 A2 m2 kg s2 A1 kg s2 A1 m2 kg s2 A2 K cd sr (b) m2 cd sr (b)See Sec. 2.1.1. The steradian (sr) is not an SI base unit. However, in photometry the steradian (sr) is maintained in expressions for units (see Sec. 3).Table 3b. SI derived units with special names and symbols admitted for reasons of safeguarding human health (a) SI derived unit Derived quantitySpecial nameSpecial symbolExpression in terms of other SI unitsExpression in terms of SI base unitsactivity (of a radionuclide)becquerelBqabsorbed dose, specific energy (imparted), kermagrayGyJ/kgm2 s2dose equivalent, ambient dose equivalent, directional dose equivalent, personal dose equivalent, equivalent dosesievertSvJ/kgm2 s2(a)s1The derived quantities to be expressed in the gray and the sievert have been revised in accordance with the recommendations of the International Commission on Radiation Units and Measurements (ICRU).2.1.1 Degree Celsius In addition to the quantity thermodynamic temperature (symbol T ), expressed in the unit kelvin, use is also made of the quantity Celsius temperature (symbol t ) defined by the equation t = TT 0 , where T 0 = 273.15 K by definition. To express Celsius temperature, the unit degree Celsius, symbol C, which is equal in magnitude to the unit kelvin, is used; in this case, ``degree Celsius' ' is a special name used in place of ``kelvin.' ' An interval or difference of Celsius temperature can, however, be expressed in the unit kelvin as well as in the unit degree Celsius. (Note that the thermodynamic temperature T0 is exactly 0.01 K below the thermodynamic temperature of the triple point of water.) 30. INTERNATIONAL SYSTEM OF UNITS (SI) (continued) 2.2Use of SI derived units with special names and symbolsExamples of SI derived units that can be expressed with the aid of SI derived units having special names and symbols (including the radian and steradian) are given in Table 4. Table 4. Examples of SI derived units expressed with the aid of SI derived units having special names and symbols SI derived unit Derived quantity angular velocity angular acceleration dynamic viscosity moment of force surface tension heat flux density, irradiance radiant intensity radiance heat capacity, entropy specific heat capacity, specific entropy specific energy thermal conductivity energy density electric field strength electric charge density electric flux density permittivity permeability molar energy molar entropy, molar heat capacity exposure (x and rays) absorbed dose rate (a)NameSymbolExpression in terms of SI base unitsradian per second radian per second squared pascal second newton meter newton per meterrad/s rad/s 2 Pa s Nm N/mm m 1 s 1 = s 1 m m 1 s 2 = s 2 m1 kg s1 m 2 kg s2 kg s2watt per square meter watt per steradian watt per square meter steradian joule per kelvin joule per kilogram kelvin joule per kilogram watt per meter kelvin joule per cubic meter volt per meter coulomb per cubic meter coulomb per square meter farad per meter henry per meter joule per moleW/m 2 W/srkg s3 m 2 kg s 3 sr 1 (a)W/(m 2 sr) J/Kkg s 3 sr 1 (a) m 2 kg s2 K1J/(kg K) J/kg W/(m K) J/m 3 V/m C/m 3 C/m 2 F/m H/m J/molm 2 s2 K1 m 2 s2 m kg s3 K1 m1 kg s2 m kg s3 A1 m3 s A m2 s A m3 kg1 s4 A2 m kg s2 A2 m 2 kg s2 mol1joule per mole kelvin coulomb per kilogram gray per secondJ/(mol K) C/kg Gy/sm 2 kg s2 K1 mol1 kg1 s A m 2 s3The steradian (sr) is not an SI base unit. However, in radiometry the steradian (sr) is maintained in expressions for units (see Sec. 3).The advantages of using the special names and symbols of SI derived units are apparent in Table 4. Consider, for example, the quantity molar entropy: the unit J/(mol K) is obviously more easily understood than its SI base-unit equivalent, m 2 kg s 2 K 1 mol 1. Nevertheless, it should always be recognized that the special names and symbols exist for convenience; either the form in which special names or symbols are used for certain combinations of units or the form in which they are not used is correct. For example, because of the descriptive value implicit in the compound-unit form, communication is sometimes facilitated if magnetic flux (see Table 3a) is expressed in terms of the volt second (V s) instead of the weber (Wb). Tables 3a, 3b, and 4 also show that the values of several different quantities are expressed in the same SI unit. For example, the joule per kelvin (J/K) is the SI unit for heat capacity as well as for entropy. Thus the name of the unit is not sufficient to define the quantity measured. A derived unit can often be expressed in several different ways through the use of base units and derived units with special names. In practice, with certain quantities, preference is given to using certain units with special names, or combinations of units, to facilitate the distinction between quantities whose values have identical expressions in terms of SI base units. For example, the SI unit of frequency is specified as the hertz (Hz) rather than the reciprocal second (s 1 ), and the SI unit of moment of force is specified as the newton meter (N m) rather than the joule (J). 31. INTERNATIONAL SYSTEM OF UNITS (SI) (continued) Similarly, in the field of ionizing radiation, the SI unit of activity is designated as the becquerel (Bq) rather than the reciprocal second (s 1 ), and the SI units of absorbed dose and dose equivalent are designated as the gray (Gy) and the sievert (Sv), respectively, rather than the joule per kilogram (J/kg). 3 SI supplementary units As previously stated, there are two units in this class: the radian, symbol rad, the SI unit of the quantity plane angle; and the steradian, symbol sr, the SI unit of the quantity solid angle. Definitions of these units are given in Appendix A. The SI supplementary units are now interpreted as so-called dimensionless derived units for which the CGPM allows the freedom of using or not using them in expressions for SI derived units.3 Thus the radian and steradian are not given in a separate table but have been included in Table 3a together with other derived units with special names and symbols (seeSec.2.1). This interpretation of the supplementary units implies that plane angle and solid angle are considered derived quantities of dimension one (so-called dimensionless quantities), each of which has the which has the unit one, symbol 1, as its coherent SI unit. However, in practice, when one expresses the values of derived quantities involving plane angle or solid angle, it often aids understanding if the special names (or symbols) ``radian' ' (rad) or ``steradian' ' (sr) are used in place of the number 1. For example, although values of the derived quantity angular velocity (plane angle divided by time) may be expressed in the unit s1, such values are usually expressed in the unit rad/s. Because the radian and steradian are now viewed as so-called dimensionless derived units, the Consultative Committee for Units (CCU, Comit Consultatif des Units) of the CIPM as result of a 1993 request it received from ISO/TC12, recommended to the CIPM that it request the CGPM to abolish the class of supplementary units as a separate class in the SI. The CIPM accepted the CCU recommendation, and if the abolishment is approved by the CGPM as is likely (the question will be on the agenda of the 20th CGPM, October 1995), the SI will consist of only two classes of units: base units and derived units, with the radian and steradian subsumed into the class of derived units of the SI. (The option of using or not using them in expressions for SI derived units, as is convenient, would remain unchanged.) 4 Decimal multiples and submultiples of SI units: SI prefixes Table 5 gives the SI prefixes that are used to form decimal multiples and submultiples of SI units. They allow very large or very small numerical values to be avoided. A prefix attaches directly to the name of a unit, and a prefix symbol attaches directly to the symbol for a unit. For example, one kilometer, symbol 1 km, is equal to one thousand meters, symbol 1000 m or 103 m. When prefixes are attached to SI units, the units so formed are called ``multiples and submultiples of SI units' ' in order to distinguish them from the coherent system of SI units.Note:3Alternative definitions of the SI prefixes and their symbols are not permitted. For example, it is unacceptable to use kilo (k) to represent 2 10 = 1024, mega (M) to represent 2 20 = 1 048 576, or giga (G) to represent 2 30 = 1 073 741 824.This interpretation was given in 1980 by the CIPM . It was deemed necessary because Resolution 12 of the 11th CGPM, which established the SI in 1960 , did not specify the nature of the supplementary units. The interpretation is based on two principal considerations: that plane angle is generally expressed as the ratio of two lengths and solid angle as the ratio of an area and the square of a length, and are thus quantities of dimension one (so-called dimensionless quantities); and that treating the radian and steradian as SI base units a possibility not disallowed by Resolution 12 could compromise the internal coherence of the SI based on only seven base units. (See ISO 31-0 for a discussion of the concept of dimension.) 32. INTERNATIONAL SYSTEM OF UNITS (SI) (continued) Table 5. SI prefixes FactorPrefix10 24 10 21 10 18 10 15 10 12 10 9 10 6 10 3 10 2 10 1= = = = = = = =(10 3 ) 8 (10 3 ) 7 (10 3 ) 6 (10 3 ) 5 (10 3 ) 4 (10 3 ) 3 (10 3 ) 2 (10 3 ) 15SymbolFactor 101 102 103 106 109 1012 1015 1018 1021 1024PrefixSymbolUnits Outside the SIyotta zetta exa peta tera giga mega kilo hecto dekaY Z E P T G M k h da= = = = = = = =deci centi milli micro nano pico femto atto zepto yocto(10 3 ) 1 (10 3 ) 2 (10 3 ) 3 (10 3 ) 4 (10 3 ) 5 (10 3 ) 6 (10 3 ) 7 (10 3 ) 8d c m n p f a z yUnits that are outside the SI may be divided into three categories: those units that are accepted for use with the SI; those units that are temporarily accepted for use with the SI; and those units that are not accepted for use with the SI and thus must strictly be avoided. 5.1Units accepted for use with the SI The following sections discuss in detail the units that are acceptable for use with the SI.5.1.1Hour, degree, liter, and the likeCertain units that are not part of the SI are essential and used so widely that they are accepted by the CIPM for use with the SI. These units are given in Table 6. The combination of units of this table with SI units to form derived units should be restricted to special cases in order not to lose the advantages of the coherence of SI units. Additionally, it is recognized that it may be necessary on occasion to use time-related units other than those given in Table 6; in particular, circumstances may require that intervals of time be expressed in weeks, months, or years. In such cases, if a standardized symbol for the unit is not available, the name of the unit should be written out in full.Table 6. Units accepted for use with the SI NameSymbol minute hour time day degree minute plane angle second liter metric ton (c)min h d ' " l, L (b) tValue in SI units 1 min 1h 1d 1 1' 1" 1L 1t= = = = = = = =60 s 60 min = 3600 s 24 h = 86 400 s (/180) rad (1/60)=(/10 800) rad (1/60)' =(/648 000) rad 1 dm3 = 103 m3 10 3 kg(b)The alternative symbol for the liter, L, was adopted by the CGPM in order to avoid the risk of confusion between the letter l and the number 1 . Thus, although both l and L are internationally accepted symbols for the liter, to avoid this risk the symbol to be used in the United States is L . The script letter is not an approved symbol for the liter.(c)This is the name to be used for this unit in the United States; it is also used in some other English-speaking countries. However, ``tonne' ' is used in many countries. 33. INTERNATIONAL SYSTEM OF UNITS (SI) (continued) 5.1.2Neper, bel, shannon, and the likeThere are a few highly specialized units not listed in Table 6 that are given by the International Organization for Standardization (ISO) or the International Electrotechnical Commission (IEC) and which are also acceptable for use with the SI. They include the neper (Np), bel (B), octave, phon, and sone, and units used in information technology, including the baud (Bd), bit (bit), 4 erlang (E), hartley (Hart), and shannon (Sh). It is the position of NIST that the only such additional units that may be used with the SI are those given in either the International Standards on quantities and units of ISO or of IEC . 5.1.3Electronvolt and unified atomic mass unitThe CIPM also finds it necessary to accept for use with the SI the two units given in Table 7. These units are used in specialized fields; their values in SI units must be obtained from experiment and, therefore, are not known exactly.Note :In some fields the unified atomic mass unit is called the dalton, symbol Da; however, this name and symbol are not accepted by the CGPM, CIPM, ISO, or IEC for use with the SI. Similarly, AMU is not an acceptable unit symbol for the unified atomic mass unit. The only allowed name is ``unified atomic mass unit' ' and the only allowed symbol is u.Table 7. Units accepted for use with the SI whose values in SI units are obtained experimentally Name electronvolt unified atomic mass unit (a)Symbol eV uDefinition (a) (b)The electronvolt is the kinetic energy acquired by an electron in passing through a potential difference of 1 V in vacuum; 1 eV = 1.602 177 331019 J with a combined standard uncertainty of 0.000 000 491019 J . The unified atomic mass unit is equal to 1/12 of the mass of an atom of the nuclide 12 C; 1 u = 1.660 540 2 1027 kg with a combined standard uncertainty of 0.000 001 01027 kg .(b)5.1.4Natural and atomic unitsIn some cases, particularly in basic science, the values of quantities are expressed in terms of fundamental constants of nature or so-called natural units.The use of these units with the SI is permissible when it is necessary for the most effective communication of information. In such cases, the specific natural units that are used must be identified. This requirement applies even to the system of units customarily called ``atomicunits' ' used in theoretical atomic physics and chemistry, inasmuch as there are several different systems that have the appellation ``atomic units.'' Examples of physical quantities used as natural units are given in Table 8. NIST also takes the position that while theoretical results intended primarily for other theorists may be left in natural units, if they are also intended for experimentalists, they must also be given in acceptable units.4The symbol in parentheses following the name of the unit is its internationally accepted unit symbol, but the octave, phon, and sone have no such unit symbols. For additional information on the neper and bel, see Sec. 0.5 of ISO 31-2. The question of the byte (B) is under international consideration. 34. INTERNATIONAL SYSTEM OF UNITS (SI) (continued) Table 8. Examples of physical quantities sometimes used as natural units Kind of quantityPhysical quantity used as a unitaction electric charge energy length length magnetic flux magnetic moment magnetic moment mass mass speedPlanck constant divided by 2 elementary charge Hartree energy Bohr radius Compton wavelength (electron) magnetic flux quantum Bohr magneton nuclear magneton electron rest mass proton rest mass speed of electromagnetic waves in vacuum5.2Symbolh e Eh a0 C 0 B N me mp cUnits temporarily accepted for use with the SIBecause of existing practice in certain fields or countries, in 1978 the CIPM considered that it was permissible for the units given in Table 9 to continue to be used with the SI until the CIPM considers that their use is no longer necessary. However, these units must not be introduced where they are not presently used. Further, NIST strongly discourages the continued use of these units except for the nautical mile, knot, are, and hectare; and except for the curie, roentgen, rad, and rem until the year 2000 (the cessation date suggested by the Committee for Ineragency Radiation Research and Policy Coordination or CIRRPC, a United States Government interagency group). 5 Table 9. Units temporarily accepted for use with the SI (a) Name nautical mile knot ngstrm are(b) hectare(b) barn bar gal curie roentgen rad rem (a) (b) (c)Symbol a ha b bar Gal Ci R rad (c) remValue in SI units 1 nautical mile = 1852 m 1 nautical mile per hour = (1852/3600) m/s 1 = 0.1 nm = 1010 m 1 a = 1 dam2 = 10 2 m2 1 ha = 1 hm2 = 10 4 m2 1 b = 100 fm2 = 1028 m2 1 bar=0.1 MPa=100 kPa=1000 hPa=10 5 Pa 1 Gal = 1 cm/s 2 = 102 m/s 2 1 Ci = 3.71010 Bq 1 R = 2.58104 C/kg 1 rad = 1 cGy = 102 Gy 1 rem = 1 cSv = 102 SvSee Sec. 5.2 regarding the continued use of these units. This unit and its symbol are used to express agrarian areas. When there is risk of confusion with the symbol for the radian, rd may be used as the symbol for rad.5 In 1993 the CCU (see Sec. 3) was requested by ISO/TC 12 to consider asking the CIPM to deprecate the use of the units of Table 9 except for the nautical mile and knot, and possibly the are and hectare. The CCU discussed this request at its February 1995 meeting. 35. INTERNATIONAL SYSTEM OF UNITS (SI) (continued)Appendix A. A.1Definitions of the SI Base Units and the Radian and SteradianIntroductionThe following definitions of the SI base units are taken from NIST SP 330; the definitions of the SI supplementary units, the radian and steradian, which are now interpreted as SI derived units (see Sec. 3), are those generally accepted and are the same as those given in ANSI/IEEE Std 268-1992. SI derived units are uniquely defined only in terms of SI base units; for example, 1 V = 1 m 2 kg s 3 A 1. A.2Meter (17th CGPM, 1983)The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. A.3Kilogram (3d CGPM, 1901)The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. A.4Second (13th CGPM, 1967)The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium- 133 atom. A.5Ampere (9th CGPM, 1948)The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 10 7 newton per meter of length. A.6Kelvin (13th CGPM, 1967)The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. A.7Mole (14th CGPM, 1971)1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. 2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. In the definition of the mole, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to. Note that this definition specifies at the same time the nature of the quantity whose unit is the mole. A.8Candela (16th CGPM, 1979)The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 10 12 hertz and that has a radiant intensity in that direction of ( 1/ 683) watt per steradian. A.9RadianThe radian is the plane angle between two radii of a circle that cut off on the circumference an arc equal in length to the radius. A.10SteradianThe steradian is the solid angle that, having its vertex in the center of a sphere, cuts off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere. 36. CONVERSION FACTORS The following table gives conversion factors from various units of measure to SI units. It is reproduced from NIST Special Publication 811, Guide for the Use of the International System of Units (SI). The table gives the factor by which a quantity expressed in a non-SI unit should be multiplied in order to calculate its value in the SI. The SI values are expressed in terms of the base, supplementary, and derived units of SI in order to provide a coherent presentation of the conversion factors and facilitate computations (see the table International System of Units in this Section). If desired, powers of ten can be avoided by using SI Prefixes and shifting the decimal point if necessary. Conversion from a non-SI unit to a different non-SI unit may be carried out by using this table in two stages, e.g., 1 calth = 4.184 J 1 BtuIT = 1.055056 E+03 J Thus, 1 BtuIT = (1.055056 E+03 4.184) calth = 252.164 calth Conversion factors are presented for ready adaptation to computer readout and electronic data transmission. The factors are written as a number equal to or greater than one and less than ten with six or fewer decimal places. This number is followed by the letter E (for exponent), a plus or a minus sign, and two digits which indicate the power of 10 by which the number must be multiplied to obtain the correct value. For example: 3.523 907 E-02 is 3.523 907 10-2 or 0.035 239 07 Similarly: 3.386 389 E+03 is 3.386 389 103 or 3 386.389 A factor in boldface is exact; i.e., all subsequent digits are zero. All other conversion factors have been rounded to the figures given in accordance with accepted practice. Where less than six digits after the decimal point are shown, more precision is not warranted. It is often desirable to round a number obtained from a conversion of units in order to retain information on the precision of the value. The following rounding rules may be followed: (1) If the digits to be discarded begin with a digit less than 5, the digit preceding the first discarded digit is not changed. Example: 6.974 951 5 rounded to 3 digits is 6.97 (2) If the digits to be discarded begin with a digit greater than 5, the digit preceding the first discarded digit is increased by one. Example: 6.974 951 5 rounded to 4 digits is 6.975 (3) If the digits to be discarded begin with a 5 and at least one of the following digits is greater than 0, the digit preceding the 5 is increased by 1. Example: 6.974 851 rounded to 5 digits is 6.974 9 (4) If the digits to be discarded begin with a 5 and all of the following digits are 0, the digit preceding the 5 is unchanged if it is even and increased by one if it is odd. (Note that this means that the final digit is always even.) Examples: 6.974 951 5 rounded to 7 digits is 6.974 952 6.974 950 5 rounded to 7 digits is 6.974 950REFERENCE Taylor, B. N., Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 1995 Edition, Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402, 1995. 2000 by CRC PRESS LLC 37. Factors in boldface are exact To convert fromtoMultiply byabampere. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ampere (A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 abcoulomb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0E+01 E+01abfarad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . farad (F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 abhenry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . henry (H) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 abmho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . siemens (S) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0E+09 E09 E+09abohm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ohm () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 abvolt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . volt (V) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.0 acceleration of free fall, standard (g n ). . . . . . . . . . . . . . . meter per second squared (m/s 2 ) . . . . . . . . . . . . . . 9.806 65 acre (based on U.S. survey foot)9 . . . . . . . . . . . . . . . . . . . square meter (m2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.046 873E09 E08acre foot (based on U.S. survey foot)9 . . . . . . . . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.233 489 ampere hour (A h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulomb (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6E+03 E+03ngstrom () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ngstrom () . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . nanometer (nm). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . are (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . astronomical unit (AU). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . meter (m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . atmosphere, standard (atm). . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . atmosphere, standard (atm). . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . atmosphere, technical (at) 10 . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .E10 E01 E+02 E+11 E+05 E+021.0 1.0 1.0 1.495 979 1.013 25 1.013 259.806 65 atmosphere, technical (at) 10 . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.806 65bar (bar). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pascal (Pa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . bar (bar). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kilopascal (kPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . barn (b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . square meter (m2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . barrel [for petroleum, 42 gallons (U.S.)](bbl) . . . . . . . cubic meter (m3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . barrel [for petroleum, 42 gallons (U.S.)](bbl) . . . . . . . liter (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . biot (Bi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ampere (A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . British thermal unit IT (BtuIT )11 . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . British thermal unit th (Btuth )11 . . . . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . British thermal unit (mean) (Btu) . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . British thermal unit (39 F) (Btu) . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . British thermal unit (59 F) (Btu) . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . British thermal unit (60 F) (Btu) . . . . . . . . . . . . . . . . . . . joule (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . British thermal unitIT foot per hour square foot degree Fahrenheit [BtuIT ft/(h ft2 F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m K)]. . . . . . . . . . . . . British thermal unitth foot per hour square foot degree Fahrenheit [Btuth ft/(h ft2 F)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m K)]. . . . . . . . . . . . .E+03E+04 E+011.0 1.0 1.0 1.589 873 1.589 873 1.0 1.055 056E+05 E+02 E28 E01 E+02 E+01 E+031.054 350 1.055 87 1.059 67 1.054 80 1.054 68E+03 E+03 E+03 E+03 E+031.730 735E+001.729 577E+00British thermal unitIT inch per hour square foot degree Fahrenheit [BtuIT in/(h ft2 F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m K)]. . . . . . . . . . . . . 1.442 279 British thermal unitth inch per hour square foot degree Fahrenheit [Btuth in/(h ft2 F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m K)]. . . . . . . . . . . . . 1.441 314 British thermal unitIT inch per second square foot degree Fahrenheit [BtuIT in/(s ft2 F)] . . . . . . . . . . . . . . . . . . . . . . . . . . . watt per meter kelvin [W/(m K)]. . . . . . . . . . . . . 5.192 2049E+00E01 E01 E+02The U.S. survey foot equals (1200/3937) m. 1 international foot = 0.999998 survey foot. One technical atmosphere equals one kilogram-force per square centimeter (1 at = 1 kgf/cm 2 ). 11 The Fifth International Conference on the Properties of Steam (London, July 1956) defined the International Table calorie as 4.1868 J. Therefore the exact conversion