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Handbook CRC Chemistry and Physics 84th edition

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CRC Handbook of Chemistry and Physics 
Editor-in-Chief 
 
David R. Lide 
Former Director, Standard Reference Data 
National Institute of Standards and Technology 
 
 
Editorial Advisory Board 
Grace Baysinger 
Swain Chemistry and Chemical Engineering Library 
Stanford University 
Stanford, CA 94305-5080 
 
Lev I. Berger 
California Institute of Electronics and Materials Science 
2115 Flame Tree Way 
Hemet, CA 92545 
 
Robert N. Goldberg 
Biotechnology Division 
National Institute of Standards and Technology 
Gaithersburg, MD 20899 
 
Henry V. Kehiaian 
ITODYS 
University of Paris VII 
1, rue Guy de la Brosse 
75005 Paris, France 
 
Kozo Kuchitsu 
Department of Chemistry 
Josai University, 
Sakado 350-0295, Japan 
 
Gerd Rosenblatt 
1177 Miller Avenue 
Berkeley, CA 94708 
 
Dana L. Roth 
Millikan Library / Caltech 1-32 
1200 E. California Blvd. 
Pasadena, CA 91125 
 
Daniel Zwillinger 
Mathematics Department 
Rensselaer Polytechnic Institute 
Troy, NY 12180 
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FOREWORD 
 
 My acquaintance with the CRC Handbook goes back sixty years, for when 
I was inducted into the wonders of chemistry by an uncle of mine (“Uncle 
Tungsten”)—I was ten—he lent me his copy of the 23rd (1939) edition. This was 
not pocket-sized, like the earlier editions he had on his shelf, and indeed 
contained over 2200 pages, but these were printed on thin India paper, and the 
whole book, with its soft red morocco cover, fitted easily in the hand. I fell in love 
with it straightaway—my uncle, seeing this, told me I might keep it—for its tables 
were so full of information that I thought of it as containing the whole universe 
between its covers. I was especially attracted to the Physical Constants of 
Inorganic Compounds, a hundred and fifty densely-packed pages which, through 
constant poring over, I got almost by heart. 
I think I owe the only original idea I had in my chemical boyhood to these 
tables—for, having been struck by the steadily rising melting points and densities 
of the transition metals in Groups IV-VI as one went from Period 3 to 6 (Ti, Zr, 
Hf; V, Nb, Ta; Cr, Mo, W), I was then taken aback to find that the Period 7 
analogues of these broke the series. Thorium had a lower melting point and 
density than hafnium; uranium lower ones than tungsten. Could it be, I wondered, 
that they were not in fact analogues of hafnium and tungsten, not transition metals 
at all, but belonged to an interpolated series which resembled the rare-earth 
metals? To my joy, after the War, I found that this naïf idea of mine, a possibly 
unjustified leap of the imagination, turned out to be true—but it was entirely due 
to poring over the tables of the CRC Handbook that I owed it. 
 Although my interests later turned more to biology and then medicine, the 
CRC Handbook has never lost its enchantment for me. I got the 30th (1947) and 
the 41st (1959-1960) editions—at this point the Handbook still had its smaller 
format, but had become almost cubical in shape (the 41st edition had nearly 3500 
pages); and then, of course, it morphed into its present, monumental format. 
While I keep the massive recent editions in my study, I keep my original one, the 
23rd edition, on my bedside table, for it is easy to handle (especially when one is 
reading in bed), and was my most cherished gift as a boy. Indeed, one way and 
another, whether reading in bed or in my study, I have always had a Handbook 
near me. While the CRC Handbook is monumental in its scope, a huge, always-
to-be-relied-upon mine of information, it is also a friendly book, a companion 
which has given me joy for the greater part of my life. 
 
Oliver Sacks 
New York 
October 2003 
PREFACE
Since the First Edition of the CRC Handbook of Chemistry and Physics appeared
in 1913, the size and scope have expanded in step with the growth of scientific knowledge.
It has not only served as a reference source for professionals and students, but has provided
inspiration to many young people as they developed their interest in science. The late
Linus Pauling, in his Foreword to the 74th Edition, wrote "I attribute much of my
knowledge about substances and their properties to my study of the information that the
Handbook provided." In the Foreword to the present edition Oliver Sacks, author of the
best seller Uncle Tungsten: Memories of a Chemical Boyhood, describes the strong
influence the Handbook had on him from the age of ten.
Throughout its history the overall philosophy of the Handbook has been to provide
broad coverage of all types of data commonly encountered by physical scientists and
engineers. While the Internet has spawned numerous large databases covering narrow
areas of science, we feel there is still a need for a concise reference source spanning the
full range of the physical sciences and focusing on key data that are frequently needed by
R&D professionals, engineers, and students. We hope this Internet version of the CRC
Handbook will be a step in continuing to serve these needs.
The 85th Edition includes updates and expansions of several tables, such as
Aqueous Solubility of Organic Compounds, Thermal Conductivity of Liquids, and Table
of the Isotopes. A new table on Azeotropic Data for Binary Mixtures has been added, as
well as tables on Index of Refraction of Inorganic Crystals and Critical Solution
Temperatures of Polymer Solutions. In response to user requests, several topics such as
Coefficient of Friction and Miscibility of Organic Solvents have been restored to the
Handbook. The latest recommended values of the Fundamental Physical Constants,
released in December 2003, are included in this edition. Finally, the Appendix on
Mathematical Tables has been revised by Dr. Daniel Zwillinger, editor of the CRC
Standard Mathematical Tables and Formulae; it includes new information on factorials,
Clebsch-Gordan coefficients, orthogonal polynomials, statistical formulas, and other
topics.
This new Internet edition has added 13 new subsections that can be accessed as
interactive tables. These include tables on atomic and molecular polarizabilities, diffusion
in gases and liquids, vapor pressure and density of mercury, ionic radii in crystals, surface
tension, and other topics. All material in the printed Handbook is accessible in the Internet
version as interactive tables and/or pdf displays.
The Editor appreciates suggestions on new topics for the Handbook and
notification of any errors. Input from users plays a key role in keeping the book up to date.
Address all comments to Editor-in-Chief, Handbook of Chemistry and Physics, CRC Press
LLC, 2000 N. W. Corporate Blvd., Boca Raton, FL 33431. Comments may also be sent by
electronic mail to drlide@post.harvard.edu.
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The Handbook of Chemistry and Physics is dependent on the efforts of many
contributors throughout the world. Valuable suggestions have been received from the
Editorial Advisory Board and from many users. The assistance and support of Dr. Fiona
Macdonald, Chemistry Publisher at CRC Press, is greatly appreciated. Finally, I want to
thank Susan Fox, James Miller, Helena Redshaw, James Yanchak, Robert Morris, and
Ronel Decius of the CRC Press staff for all their efforts.
David R. Lide
October 2004
How To Cite this Reference
The recommended form of citation is: David R. Lide, ed., CRC Handbook of Chemistry
and Physics, Internet Version 2005, <http://www.hbcpnetbase.com>, CRC Press, Boca
Raton, FL, 2005. If a specific table is cited, use the format: "Physical Constants of Organic
Compounds", in CRC Handbook of Chemistry and Physics, Internet Version 2005, David
R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.
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. Best efforts have been made to select and verify
the data on the basis of sound scientific judgment, 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 2005
Lev I. Berger
California Institute of Electronics
and Materials Science
2115 Flame Tree Way
Hemet, California 92545
A. K. Covington
Department of Chemistry
University of Newcastle
Newcastle upon Tyne NE1 7RU
England
K. Fischer
LTP GmbH
Oppelner Strasse 12
D-26135 Oldenburg, Germany
Jean-Claude Fontaine
ITODYS
CNRS, University of Paris VII
1 rue Guy de la Brosse
75005 Paris, France
H. P. R. Frederikse
9625 Dewmar Lane
Kensington, Maryland 20895
J.R. Fuhr
Atomic Physics Division
National Institute of Standards and
Technology
Gaithersburg, Maryland 20899
J. Gmehling
Universität Oldenburg
Fakultät V, Technische Chemie
D-26111 Oldenburg, Germany
Robert N. Goldberg
Biotechnology Division
National Institute of Standards and
Technology
Gaithersburg, Maryland 20899
C. R. Hammond
17 Greystone Rd.
West Hartford, Connecticut 06107
Norman E. Holden
National Nuclear Data Center
Brookhaven National Laboratory
Upton, New York 11973
H. Donald Brooke Jenkins
Department of Chemistry
University of Warwick
Coventry CV4 7AL England
Henry V. Kehiaian
ITODYS
University of Paris VII
1 rue Guy de la Brosse
75005 Paris, France
J. Alistair Kerr
School of Chemistry
University of Birmingham
Birmingham B15 2TT England
J. Krafczyk
DDBST GmbH
Industriestrasse 1
D-26121 Oldenburg, Germany
Frank J. Lovas
8616 Melwood Rd.
Bethesda, Maryland 20817
William C. Martin
Atomic Physics Division
National Institute of Standards and
Technology
Gaithersburg, Maryland 20899
J. Menke
DDBST GmbH
Industriestrasse 1
D-26121 Oldenburg, Germany
Thomas M. Miller
Air Force Research Laboratory/VSBP
29 Randolph Rd.
Hanscom AFB, Massachusetts
01731-3010
Peter J. Mohr
Physics Laboratory
National Institute of Standards and
Technology
Gaithersburg, Maryland 20899
Joseph Reader
Atomic Physics Division
National Institute of Standards and
Technology
Gaithersburg, Maryland 20899
Lewis E. Snyder
Astronomy Department
University of Illinois
Urbana, Illinois 61801
B. N. Taylor
Physics Laboratory
National Institute of Standards and
Technology
Gaithersburg, Maryland 20899
Thomas G. Trippe
Particle Data Group
Lawrence Berkeley Laboratory
1 Cyclotron Road
Berkeley, California 94720
Petr Vanýsek
Department of Chemistry
Northern Illinois University
DeKalb, Illinois 60115
Wolfgang L. Wiese
Atomic Physics Division
National Institute of Standards and
Technology
Gaithersburg, Maryland 20899
Christian Wohlfarth
Institut für Physikalische Chemie
Martin Luther University
D-06217 Merseburg
Germany
Daniel Zwillinger
Mathematics Department
Rensselaer Polytechnic Institute
Troy, New York 12180
CURRENT CONTRIBUTORS
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 Section 1: Basic Constants, Units, and Conversion Factors
 Fundamental Physical Constants
 Standard Atomic Weights (2001)
 Atomic Masses and Abundances
 Electron Configuration of Neutral Atoms in the Ground State
 International Temperature Scale of 1990 (ITS-90)
 Conversion of Temperatures from the 1948 and 1968 Scales to ITS-90
 International System of Units (SI)
 Units for Magnetic Properties
 Conversion Factors
 Conversion of Temperatures
 Conversion Factors for Energy Units
 Conversion Factors for Pressure Units
 Conversion Factors for Thermal Conductivity Units
 Conversion Factors for Electrical Resistivity Units
 Conversion Factors for Chemical Kinetics
 Conversion Factors for Ionizing Radiation
 Values of the Gas Constant in Different Unit Systems
 Periodic Table of the Elements
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1-12
STANDARD ATOMIC WEIGHTS (2001)
This table of atomic weights includes the changes made in 1999 and 2001 by 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 atomic weight entry in
brackets indicates that the element that has no stable isotopes; the value given is the atomic mass in u (or the mass number, if the mass is not
accurately known) for the isotope of longest half-life. Thorium, protactinium, and uranium have no stable isotopes, but the terrestrial isotopic
composition is sufficiently uniform to permit a standard atomic weight to be specified.
REFERENCES
1. Vocke, R. D., Pure Appl. Chem. 71, 1593, 1999.
2. Coplen, T. D., Pure Appl. Chem. 73, 667, 2001.
3. Coplen, T. D., J. Phys. Chem. Ref. Data, 30, 701, 2001.
4. Loss, R. D., Atomic Weights of the Elements 2001, Pure Appl. Chem., 75, 1107, 2003.
Name Symbol Atomic No. Atomic Weight Footnotes
Actinium Ac 89 [227.0277] a
Aluminum Al 13 26.981538(2)
Americium Am 95 [243.0614] a
Antimony Sb 51 121.760(1) g
Argon Ar 18 39.948(1) g r
Arsenic As 33 74.92160(2)
Astatine At 85 [209.9871] a
Barium Ba 56 137.327(7)
Berkelium Bk 97 [247.0703] a
Beryllium Be 4 9.012182(3)
Bismuth Bi 83 208.98038(2)
Bohrium Bh 107 [264.12] a
Boron B 5 10.811(7) g m r
Bromine Br 35 79.904(1)
Cadmium Cd 48 112.411(8) g
Calcium Ca 20 40.078(4) g
Californium Cf 98 [251.0796] a
Carbon C 6 12.0107(8) g r
Cerium Ce 58 140.116(1) g
Cesium Cs 55 132.90545(2)
Chlorine Cl 17 35.453(2) g m r
Chromium Cr 24 51.9961(6)
Cobalt Co 27 58.933200(9)
Copper Cu 29 63.546(3) r
Curium Cm 96 [247.0704] a
Darmstadtium Ds 110 [281] a
Dubnium Db 105 [262.1141] a
Dysprosium Dy 66 162.500(1) g
Einsteinium Es 99 [252.0830] a
Erbium Er 68 167.259(3) g
Europium Eu 63 151.964(1) g
Fermium Fm 100 [257.0951] a
Fluorine F 9 18.9984032(5)
Francium Fr 87 [223.0197] a
Gadolinium Gd 64 157.25(3) g
Gallium Ga 31 69.723(1)
Germanium Ge 32 72.64(1)
Gold Au 79 196.96655(2)
1-13
Hafnium Hf 72 178.49(2)
Hassium Hs 108 [277] a
Helium He 2 4.002602(2) g r
Holmium Ho 67 164.93032(2)
Hydrogen H 1 1.00794(7) g m r
Indium In 49 114.818(3)
Iodine I 53 126.90447(3)
Iridium Ir 77 192.217(3)
Iron Fe 26 55.845(2)
Krypton Kr 36 83.798(2) g m
Lanthanum La 57 138.9055(2) g
Lawrencium Lr 103 [262.1097] a
Lead Pb 82 207.2(1) g r
Lithium Li 3 6.941(2) b g m r
Lutetium Lu 71 174.967(1) g
Magnesium Mg 12 24.3050(6)
Manganese Mn 25 54.938049(9)
Meitnerium Mt 109 [268.1388] a
Mendelevium Md 101 [258.0984] a
Mercury Hg 80 200.59(2)
Molybdenum Mo 42 95.94(2) g
Neodymium Nd 60 144.24(3) g
Neon Ne 10 20.1797(6) g m
Neptunium Np 93 [237.0482] a
Nickel Ni 28 58.6934(2)
Niobium Nb 41 92.90638(2)
Nitrogen N 7 14.0067(2) g r
Nobelium No 102 [259.1010] a
Osmium Os 76 190.23(3) g
Oxygen O 8 15.9994(3) g r
Palladium Pd 46 106.42(1) g
Phosphorus P 15 30.973761(2)
Platinum Pt 78 195.078(2)
Plutonium Pu 94 [244.0642] a
Polonium Po 84 [208.9824] a
Potassium K 19 39.0983(1) g
Praseodymium Pr 59 140.90765(2)
Promethium Pm 61 [144.9127] a
Protactinium Pa 91 231.03588(2)
Radium Ra 88 [226.0254] a
Radon Rn 86 [222.0176] a
Rhenium Re 75 186.207(1)
Rhodium Rh 45 102.90550(2)
Rubidium Rb 37 85.4678(3) g
Ruthenium Ru 44 101.07(2) g
Rutherfordium Rf 104 [261.1088] a
Samarium Sm 62 150.36(3) g
Scandium Sc 21 44.955910(8)
Seaborgium Sg 106 [266.1219] a
Selenium Se 34 78.96(3) r
Silicon Si 14 28.0855(3) r
Silver Ag 47 107.8682(2) g
Sodium Na 11 22.989770(2)
Strontium Sr 38 87.62(1) g r
Sulfur S 16 32.065(5) g r
Tantalum Ta 73 180.9479(1)
Technetium Tc 43 [97.9072] a
Tellurium Te 52 127.60(3) g
STANDARD ATOMIC WEIGHTS (2001) (continued)
Name Symbol Atomic No. Atomic Weight Footnotes
TeamLRN
1-14
Terbium Tb 65 158.92534(2)
Thallium Tl 81 204.3833(2)
Thorium Th 90 232.0381(1) g
Thulium Tm 69 168.93421(2)
Tin Sn 50 118.710(7) g
Titanium Ti 22 47.867(1)
Tungsten W 74 183.84(1)
Ununbium Uub 112 [285] a
Ununhexium Uuh 116 [289] a
Ununquadium Uuq 114 [289] a
Unununium Uuu 111 [272.1535] a
Uranium U 92 238.02891(3) g m
Vanadium V 23 50.9415(1)
Xenon Xe 54 131.293(6) g m
Ytterbium
Yb 70 173.04(3) g
Yttrium Y 39 88.90585(2)
Zinc Zn 30 65.409(4)
Zirconium Zr 40 91.224(2) g
STANDARD ATOMIC WEIGHTS (2001) (continued)
Name Symbol Atomic No. Atomic Weight Footnotes
a No stable isotope exists. The atomic mass in u (or the mass number, if the mass is not accurately known) is given in brackets for the isotope of
longest half-life.
b Commercially available Li materials have atomic weights that range between 6.939 and 6.996; if a more accurate value is required, it must be
determined for the specific material.
g Geological specimens are known in which the element has an isotopic composition outside the limits for the 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.
m Modified isotopic compositions may be found in commercially available material because it has been subject to an undisclosed or inadvertent
isotopic fractionation. Substantial deviations in atomic weight of the element from that given in the table can occur.
r Range in isotopic composition of normal terrestrial material prevents a more precise atomic weight being given; the tabulated value should be
applicable to any normal material.
1-15
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.
1 1H 1.0078250321(4) 99.9850(70)
2D 2.0141017780(4) 0.0115(70)
3T 3.0160492675(11)
2 3He 3.0160293097(9) 0.000137(3)
4He 4.0026032497(10) 99.999863(3)
3 6Li 6.0151223(5) 7.59(4)
7Li 7.0160040(5) 92.41(4)
4 9Be 9.0121821(4) 100
5 10B 10.0129370(4) 19.9(7)
11B 11.0093055(5) 80.1(7)
6 12C 12.0000000(0) 98.93(8)
13C 13.0033548378(10) 1.07(8)
7 14N 14.0030740052(9) 99.632(7)
15N 15.0001088984(9) 0.368(7)
8 16O 15.9949146221(15) 99.757(16)
17O 16.99913150(22) 0.038(1)
18O 17.9991604(9) 0.205(14)
9 19F 18.99840320(7) 100
10 20Ne 19.9924401759(20) 90.48(3)
21Ne 20.99384674(4) 0.27(1)
22Ne 21.99138551(23) 9.25(3)
11 23Na 22.98976967(23) 100
12 24Mg 23.98504190(20) 78.99(4)
25Mg 24.98583702(20) 10.00(1)
26Mg 25.98259304(21) 11.01(3)
13 27Al 26.98153844(14) 100
14 28Si 27.9769265327(20) 92.2297(7)
29Si 28.97649472(3) 4.6832(5)
30Si 29.97377022(5) 3.0872(5)
15 31P 30.97376151(20) 100
16 32S 31.97207069(12) 94.93(31)
33S 32.97145850(12) 0.76(2)
34S 33.96786683(11) 4.29(28)
36S 35.96708088(25) 0.02(1)
17 35Cl 34.96885271(4) 75.78(4)
37Cl 36.96590260(5) 24.22(4)
18 36Ar 35.96754628(27) 0.3365(30)
38Ar 37.9627322(5) 0.0632(5)
40Ar 39.962383123(3) 99.6003(30)
19 39K 38.9637069(3) 93.2581(44)
40K 39.96399867(29) 0.0117(1)
41K 40.96182597(28) 6.7302(44)
20 40Ca 39.9625912(3) 96.941(156)
42Ca 41.9586183(4) 0.647(23)
43Ca 42.9587668(5) 0.135(10)
44Ca 43.9554811(9) 2.086(110)
46Ca 45.9536928(25) 0.004(3)
48Ca 47.952534(4) 0.187(21)
21 45Sc 44.9559102(12) 100
22 46Ti 45.9526295(12) 8.25(3)
47Ti 46.9517638(10) 7.44(2)
48Ti 47.9479471(10) 73.72(3)
49Ti 48.9478708(10) 5.41(2)
50Ti 49.9447921(11) 5.18(2)
23 50V 49.9471628(14) 0.250(4)
51V 50.9439637(14) 99.750(4)
24 50Cr 49.9460496(14) 4.345(13)
52Cr 51.9405119(15) 83.789(18)
53Cr 52.9406538(15) 9.501(17)
54Cr 53.9388849(15) 2.365(7)
25 55Mn 54.9380496(14) 100
26 54Fe 53.9396148(14) 5.845(35)
56Fe 55.9349421(15) 91.754(36)
57Fe 56.9353987(15) 2.119(10)
58Fe 57.9332805(15) 0.282(4)
27 59Co 58.9332002(15) 100
28 58Ni 57.9353479(15) 68.0769(89)
60Ni 59.9307906(15) 26.2231(77)
61Ni 60.9310604(15) 1.1399(6)
62Ni 61.9283488(15) 3.6345(17)
64Ni 63.9279696(16) 0.9256(9)
29 63Cu 62.9296011(15) 69.17(3)
65Cu 64.9277937(19) 30.83(3)
30 64Zn 63.9291466(18) 48.63(60)
66Zn 65.9260368(16) 27.90(27)
67Zn 66.9271309(17) 4.10(13)
Z Isotope Mass in u Abundance in % Z Isotope Mass in u Abundance in %
TeamLRN
1-16
106Pd 105.903483(5) 27.33(3)
108Pd 107.903894(4) 26.46(9)
110Pd 109.905152(12) 11.72(9)
47 107Ag 106.905093(6) 51.839(8)
109Ag 108.904756(3) 48.161(8)
48 106Cd 105.906458(6) 1.25(6)
108Cd 107.904183(6) 0.89(3)
110Cd 109.903006(3) 12.49(18)
111Cd 110.904182(3) 12.80(12)
112Cd 111.9027572(30) 24.13(21)
113Cd 112.9044009(30) 12.22(12)
114Cd 113.9033581(30) 28.73(42)
116Cd 115.904755(3) 7.49(18)
49 113In 112.904061(4) 4.29(5)
115In 114.903878(5) 95.71(5)
50 112Sn 111.904821(5) 0.97(1)
114Sn 113.902782(3) 0.66(1)
115Sn 114.903346(3) 0.34(1)
116Sn 115.901744(3) 14.54(9)
117Sn 116.902954(3) 7.68(7)
118Sn 117.901606(3) 24.22(9)
119Sn 118.903309(3) 8.59(4)
120Sn 119.9021966(27) 32.58(9)
122Sn 121.9034401(29) 4.63(3)
124Sn 123.9052746(15) 5.79(5)
51 121Sb 120.9038180(24) 57.21(5)
123Sb 122.9042157(22) 42.79(5)
52 120Te 119.904020(11) 0.09(1)
122Te 121.9030471(20) 2.55(12)
123Te 122.9042730(19) 0.89(3)
124Te 123.9028195(16) 4.74(14)
125Te 124.9044247(20) 7.07(15)
126Te 125.9033055(20) 18.84(25)
128Te 127.9044614(19) 31.74(8)
130Te 129.9062228(21) 34.08(62)
53 127I 126.904468(4) 100
54 124Xe 123.9058958(21) 0.09(1)
126Xe 125.904269(7) 0.09(1)
128Xe 127.9035304(15) 1.92(3)
129Xe 128.9047795(9) 26.44(24)
130Xe 129.9035079(10) 4.08(2)
131Xe 130.9050819(10) 21.18(3)
132Xe 131.9041545(12) 26.89(6)
134Xe 133.9053945(9) 10.44(10)
136Xe 135.907220(8) 8.87(16)
55 133Cs 132.905447(3) 100
56 130Ba 129.906310(7) 0.106(1)
132Ba 131.905056(3) 0.101(1)
134Ba 133.904503(3) 2.417(18)
135Ba 134.905683(3) 6.592(12)
136Ba 135.904570(3) 7.854(24)
137Ba 136.905821(3) 11.232(24)
138Ba 137.905241(3) 71.698(42)
57 138La 137.907107(4) 0.090(1)
139La 138.906348(3) 99.910(1)
58 136Ce 135.907140(50) 0.185(2)
138Ce 137.905986(11) 0.251(2)
140Ce 139.905434(3) 88.450(51)
68Zn 67.9248476(17) 18.75(51)
70Zn 69.925325(4) 0.62(3)
31 69Ga 68.925581(3) 60.108(9)
71Ga 70.9247050(19) 39.892(9)
32 70Ge 69.9242504(19) 20.84(87)
72Ge 71.9220762(16) 27.54(34)
73Ge 72.9234594(16) 7.73(5)
74Ge 73.9211782(16) 36.28(73)
76Ge 75.9214027(16) 7.61(38)
33 75As 74.9215964(18) 100
34 74Se 73.9224766(16) 0.89(4)
76Se 75.9192141(16) 9.37(29)
77Se 76.9199146(16) 7.63(16)
78Se 77.9173095(16) 23.77(28)
80Se 79.9165218(20) 49.61(41)
82Se 81.9167000(22) 8.73(22)
35 79Br 78.9183376(20) 50.69(7)
81Br 80.916291(3) 49.31(7)
36 78Kr 77.920386(7) 0.35(1)
80Kr 79.916378(4) 2.28(6)
82Kr 81.9134846(28) 11.58(14)
83Kr 82.914136(3) 11.49(6)
84Kr 83.911507(3) 57.00(4)
86Kr 85.9106103(12) 17.30(22)
37 85Rb 84.9117893(25) 72.17(2)
87Rb 86.9091835(27) 27.83(2)
38 84Sr 83.913425(4) 0.56(1)
86Sr 85.9092624(24) 9.86(1)
87Sr 86.9088793(24) 7.00(1)
88Sr 87.9056143(24) 82.58(1)
39 89Y 88.9058479(25)
100
40 90Zr 89.9047037(23) 51.45(40)
91Zr 90.9056450(23) 11.22(5)
92Zr 91.9050401(23) 17.15(8)
94Zr 93.9063158(25) 17.38(28)
96Zr 95.908276(3) 2.80(9)
41 93Nb 92.9063775(24) 100
42 92Mo 91.906810(4) 14.84(35)
94Mo 93.9050876(20) 9.25(12)
95Mo 94.9058415(20) 15.92(13)
96Mo 95.9046789(20) 16.68(2)
97Mo 96.9060210(20) 9.55(8)
98Mo 97.9054078(20) 24.13(31)
100Mo 99.907477(6) 9.63(23)
43 97Tc 96.906365(5)
98Tc 97.907216(4)
99Tc 98.9062546(21)
44 96Ru 95.907598(8) 5.54(14)
98Ru 97.905287(7) 1.87(3)
99Ru 98.9059393(21) 12.76(14)
100Ru 99.9042197(22) 12.60(7)
101Ru 100.9055822(22) 17.06(2)
102Ru 101.9043495(22) 31.55(14)
104Ru 103.905430(4) 18.62(27)
45 103Rh 102.905504(3) 100
46 102Pd 101.905608(3) 1.02(1)
104Pd 103.904035(5) 11.14(8)
105Pd 104.905084(5) 22.33(8)
ATOMIC MASSES AND ABUNDANCES (continued)
Z Isotope Mass in u Abundance in % Z Isotope Mass in u Abundance in %
1-17
142Ce 141.909240(4) 11.114(51)
59 141Pr 140.907648(3) 100
60 142Nd 141.907719(3) 27.2(5)
143Nd 142.909810(3) 12.2(2)
144Nd 143.910083(3) 23.8(3)
145Nd 144.912569(3) 8.3(1)
146Nd 145.913112(3) 17.2(3)
148Nd 147.916889(3) 5.7(1)
150Nd 149.920887(4) 5.6(2)
61 145Pm 144.912744(4)
147Pm 146.915134(3)
62 144Sm 143.911995(4) 3.07(7)
147Sm 146.914893(3) 14.99(18)
148Sm 147.914818(3) 11.24(10)
149Sm 148.917180(3) 13.82(7)
150Sm 149.917271(3) 7.38(1)
152Sm 151.919728(3) 26.75(16)
154Sm 153.922205(3) 22.75(29)
63 151Eu 150.919846(3) 47.81(3)
153Eu 152.921226(3) 52.19(3)
64 152Gd 151.919788(3) 0.20(1)
154Gd 153.920862(3) 2.18(3)
155Gd 154.922619(3) 14.80(12)
156Gd 155.922120(3) 20.47(9)
157Gd 156.923957(3) 15.65(2)
158Gd 157.924101(3) 24.84(7)
160Gd 159.927051(3) 21.86(19)
65 159Tb 158.925343(3) 100
66 156Dy 155.924278(7) 0.06(1)
158Dy 157.924405(4) 0.10(1)
160Dy 159.925194(3) 2.34(8)
161Dy 160.926930(3) 18.91(24)
162Dy 161.926795(3) 25.51(26)
163Dy 162.928728(3) 24.90(16)
164Dy 163.929171(3) 28.18(37)
67 165Ho 164.930319(3) 100
68 162Er 161.928775(4) 0.14(1)
164Er 163.929197(4) 1.61(3)
166Er 165.930290(3) 33.61(35)
167Er 166.932045(3) 22.93(17)
168Er 167.932368(3) 26.78(26)
170Er 169.935460(3) 14.93(27)
69 169Tm 168.934211(3) 100
70 168Yb 167.933894(5) 0.13(1)
170Yb 169.934759(3) 3.04(15)
171Yb 170.936322(3) 14.28(57)
172Yb 171.9363777(30) 21.83(67)
173Yb 172.9382068(30) 16.13(27)
174Yb 173.9388581(30) 31.83(92)
176Yb 175.942568(3) 12.76(41)
71 175Lu 174.9407679(28) 97.41(2)
176Lu 175.9426824(28) 2.59(2)
72 174Hf 173.940040(3) 0.16(1)
176Hf 175.9414018(29) 5.26(7)
177Hf 176.9432200(27) 18.60(9)
178Hf 177.9436977(27) 27.28(7)
179Hf 178.9458151(27) 13.62(2)
180Hf 179.9465488(27) 35.08(16)
73 180Ta 179.947466(3) 0.012(2)
181Ta 180.947996(3) 99.988(2)
74 180W 179.946706(5) 0.12(1)
182W 181.948206(3) 26.50(16)
183W 182.9502245(29) 14.31(4)
184W 183.9509326(29) 30.64(2)
186W 185.954362(3) 28.43(19)
75 185Re 184.9529557(30) 37.40(2)
187Re 186.9557508(30) 62.60(2)
76 184Os 183.952491(3) 0.02(1)
186Os 185.953838(3) 1.59(3)
187Os 186.9557479(30) 1.96(2)
188Os 187.9558360(30) 13.24(8)
189Os 188.9581449(30) 16.15(5)
190Os 189.958445(3) 26.26(2)
192Os 191.961479(4) 40.78(19)
77 191Ir 190.960591(3) 37.3(2)
193Ir 192.962924(3) 62.7(2)
78 190Pt 189.959930(7) 0.014(1)
192Pt 191.961035(4) 0.782(7)
194Pt 193.962664(3) 32.967(99)
195Pt 194.964774(3) 33.832(10)
196Pt 195.964935(3) 25.242(41)
198Pt 197.967876(4) 7.163(55)
79 197Au 196.966552(3) 100
80 196Hg 195.965815(4) 0.15(1)
198Hg 197.966752(3) 9.97(20)
199Hg 198.968262(3) 16.87(22)
200Hg 199.968309(3) 23.10(19)
201Hg 200.970285(3) 13.18(9)
202Hg 201.970626(3) 29.86(26)
204Hg 203.973476(3) 6.87(15)
81 203Tl 202.972329(3) 29.524(14)
205Tl 204.974412(3) 70.476(14)
82 204Pb 203.973029(3) 1.4(1)
206Pb 205.974449(3) 24.1(1)
207Pb 206.975881(3) 22.1(1)
208Pb 207.976636(3) 52.4(1)
83 209Bi 208.980383(3) 100
84 209Po 208.982416(3)
210Po 209.982857(3)
85 210At 209.987131(9)
211At 210.987481(4)
86 211Rn 210.990585(8)
220Rn 220.0113841(29)
222Rn 222.0175705(27)
87 223Fr 223.0197307(29)
88 223Ra 223.018497(3)
224Ra 224.0202020(29)
226Ra 226.0254026(27)
228Ra 228.0310641(27)
89 227Ac 227.0277470(29)
90 230Th 230.0331266(22)
232Th 232.0380504(22) 100
91 231Pa 231.0358789(28) 100
92 233U 233.039628(3)
234U 234.0409456(21) 0.0055(2)
235U 235.0439231(21) 0.7200(51)
ATOMIC MASSES AND ABUNDANCES (continued)
Z Isotope Mass in u Abundance in % Z Isotope Mass in u Abundance in %
TeamLRN
1-18
236U 236.0455619(21)
238U 238.0507826(21) 99.2745(106)
93 237Np 237.0481673(21)
239Np 239.0529314(23)
94 238Pu 238.0495534(21)
239Pu 239.0521565(21)
240Pu 240.0538075(21)
241Pu 241.0568453(21)
242Pu 242.0587368(21)
244Pu 244.064198(5)
95 241Am 241.0568229(21)
243Am 243.0613727(23)
96 243Cm 243.0613822(24)
244Cm 244.0627463(21)
245Cm 245.0654856(29)
246Cm 246.0672176(24)
247Cm 247.070347(5)
248Cm 248.072342(5)
97 247Bk 247.070299(6)
ATOMIC MASSES AND ABUNDANCES (continued)
Z Isotope Mass in u Abundance in % Z Isotope Mass in u Abundance in %
249Bk 249.074980(3)
98 249Cf 249.074847(3)
250Cf 250.0764000(24)
251Cf 251.079580(5)
252Cf 252.081620(5)
99 252Es 252.082970(50)
100 257Fm 257.095099(7)
101 256Md 256.094050(60)
258Md 258.098425(5)
102 259No 259.101020(110)*
103 262Lr 262.109690(320)*
104 261Rf 261.108750(110)*
105 262Db 262.114150(200)*
106 263Sg 263.118310(130)*
107 264Bh 264.124730(300)*
108 265Hs 265.130000(320)*
109 268Mt 268.138820(340)*
110 269Uun 269.145140(310)*
111 272Uuu 272.153480(360)*
*Mass values derived not purely from experimental data, but at least partly from systematic trends.
1-19
ELECTRON CONFIGURATION OF NEUTRAL ATOMS IN THE GROUND STATE
K L M N O P Q
Atomic n = 1 2 3 4 5 6 7
no. Element s s p s p d s p d f s p d f s p d s p
1 H 1
2 He 2
3 Li 2 1
4 Be 2 2
5 B 2 2 1
6 C 2 2 2
7 N 2 2 3
8 O 2 2 4
9 F 2 2 5
10 Ne 2 2 6
11 Na 2 2 6 1
12 Mg 2 2 6 2
13 Al 2 2 6 2 1
14 Si 2 2 6 2 2
15 P 2 2 6 2 3
16 S 2 2 6 2 4
17 Cl 2 2 6 2 5
18 Ar 2 2 6 2 6
19 K 2 2 6 2 6 1
20 Ca 2 2 6 2 6 2
21 Sc 2 2 6 2 6 1 2
22 Ti 2 2 6 2 6 2 2
23 V 2 2 6 2 6 3 2
24 Cr 2 2 6 2 6 5 1
25 Mn 2 2 6 2 6 5 2
26 Fe 2 2 6 2 6 6 2
27 Co 2 2 6 2 6 7 2
28 Ni 2 2 6 2 6 8 2
29 Cu 2 2 6 2 6 10 1
30 Zn 2 2 6 2 6 10 2
31 Ga 2 2 6 2 6 10 2 1
32 Ge 2 2 6 2 6 10 2 2
33 As 2 2 6 2 6 10 2 3
34 Se 2 2 6 2 6 10 2 4
35 Br 2 2 6 2 6 10 2 5
36 Kr 2 2 6 2 6 10 2 6
37 Rb 2 2 6 2 6 10 2 6 1
38 Sr 2 2 6 2 6 10 2 6 2
39 Y 2 2 6 2 6 10 2 6 1 2
40 Zr 2 2 6 2 6 10 2 6 2 2
41 Nb 2 2 6 2 6 10 2 6 4 1
42 Mo 2 2 6 2 6 10 2 6 5 1
43 Tc 2 2 6 2 6 10 2 6 5 2
44 Ru 2 2 6 2 6 10 2 6 7 1
45 Rh 2 2 6 2 6 10 2 6 8 1
46 Pd 2 2 6 2 6 10 2 6 10
47 Ag 2 2 6 2 6 10 2 6 10 1
48 Cd 2 2 6 2 6 10 2 6 10 2
49 In 2 2 6 2 6 10 2 6 10 2 1
50 Sn 2 2 6 2 6 10 2 6 10 2 2
51 Sb 2 2 6 2 6 10 2 6 10 2 3
52 Te 2 2 6 2 6 10 2 6 10 2 4
53 I 2 2 6 2 6 10 2 6 10 2 5
54 Xe 2 2 6 2 6 10 2 6 10 2 6
55 Cs 2 2 6 2 6 10 2 6 10 2 6 1
56 Ba 2 2 6 2 6 10 2 6 10 2 6 2
TeamLRN
1-20
ELECTRON CONFIGURATION OF NEUTRAL ATOMS IN THE GROUND STATE (continued)
K L M N O P Q
Atomic n = 1 2 3 4 5 6 7
no. Element s s p s p d s p d f s p d f s p d s p
REFERENCE
Martin, W. C., Musgrove, A., and Kotochigova, S., Ground Levels and Ionization Energies for Neutral Atoms, Web Version 1.2.2, http://
physics.nist.gov/IonEnergy, National Institute of Standards and Technology, Gaithersburg, MD, December 2002.
57 La 2 2 6 2 6 10 2 6 10 2 6 1 2
58 Ce 2 2 6 2 6 10 2 6 10 1 2 6 1 2
59 Pr 2 2 6 2 6 10 2 6 10 3 2 6 2
60 Nd 2 2 6 2 6 10 2 6 10 4 2 6 2
61 Pm 2 2 6 2 6 10 2 6 10 5 2 6 2
62 Sm 2 2 6 2 6 10 2 6 10 6 2 6 2
63 Eu 2 2 6 2 6 10 2 6 10 7 2 6 2
64 Gd 2 2 6 2 6 10 2 6 10 7 2 6 1 2
65 Tb 2 2 6 2 6 10 2 6 10 9 2 6 2
66 Dy 2 2 6 2 6 10 2 6 10 10 2 6 2
67 Ho 2 2 6 2 6 10 2 6 10 11 2 6 2
68 Er 2 2 6 2 6 10 2 6 10 12 2 6 2
69 Tm 2 2 6 2 6 10 2 6 10 13 2 6 2
70 Yb 2 2 6 2 6 10 2 6 10 14 2 6 2
71 Lu 2 2 6 2 6 10 2 6 10 14 2 6 1 2
72 Hf 2 2 6 2 6 10 2 6 10 14 2 6 2 2
73 Ta 2 2 6 2 6 10 2 6 10 14 2 6 3 2
74 W 2 2 6 2 6 10 2 6 10 14 2 6 4 2
75 Re 2 2 6 2 6 10 2 6 10 14 2 6 5 2
76 Os 2 2 6 2 6 10 2 6 10 14 2 6 6 2
77 Ir 2 2 6 2 6 10 2 6 10 14 2 6 7 2
78 Pt 2 2 6 2 6
10 2 6 10 14 2 6 9 1
79 Au 2 2 6 2 6 10 2 6 10 14 2 6 10 1
80 Hg 2 2 6 2 6 10 2 6 10 14 2 6 10 2
81 Tl 2 2 6 2 6 10 2 6 10 14 2 6 10 2 1
82 Pb 2 2 6 2 6 10 2 6 10 14 2 6 10 2 2
83 Bi 2 2 6 2 6 10 2 6 10 14 2 6 10 2 3
84 Po 2 2 6 2 6 10 2 6 10 14 2 6 10 2 4
85 At 2 2 6 2 6 10 2 6 10 14 2 6 10 2 5
86 Rn 2 2 6 2 6 10 2 6 10 14 2 6 10 2 6
87 Fr 2 2 6 2 6 10 2 6 10 14 2 6 10 2 6 1
88 Ra 2 2 6 2 6 10 2 6 10 14 2 6 10 2 6 2
89 Ac 2 2 6 2 6 10 2 6 10 14 2 6 10 2 6 1 2
90 Th 2 2 6 2 6 10 2 6 10 14 2 6 10 2 6 2 2
91 Pa 2 2 6 2 6 10 2 6 10 14 2 6 10 2 2 6 1 2
92 U 2 2 6 2 6 10 2 6 10 14 2 6 10 3 2 6 1 2
93 Np 2 2 6 2 6 10 2 6 10 14 2 6 10 4 2 6 1 2
94 Pu 2 2 6 2 6 10 2 6 10 14 2 6 10 6 2 6 2
95 Am 2 2 6 2 6 10 2 6 10 14 2 6 10 7 2 6 2
96 Cm 2 2 6 2 6 10 2 6 10 14 2 6 10 7 2 6 1 2
97 Bk 2 2 6 2 6 10 2 6 10 14 2 6 10 9 2 6 2
98 Cf 2 2 6 2 6 10 2 6 10 14 2 6 10 10 2 6 2
99 Es 2 2 6 2 6 10 2 6 10 14 2 6 10 11 2 6 2
100 Fm 2 2 6 2 6 10 2 6 10 14 2 6 10 12 2 6 2
101 Md 2 2 6 2 6 10 2 6 10 14 2 6 10 13 2 6 2
102 No 2 2 6 2 6 10 2 6 10 14 2 6 10 14 2 6 2
103 Lr 2 2 6 2 6 10 2 6 10 14 2 6 10 14 2 6 2 1
104 Rf 2 2 6 2 6 10 2 6 10 14 2 6 10 14 2 6 2 2
1-15
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 Comité International des
Poids et Mesures (CIPM), meeting 26—28 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 Comité Consultatif de Thermométrie (CCT), meeting
12—14 September 1989 at the BIPM in its 17th Session. The ITS-90 became the official international temperature scale on 1 January 1990. The ITS-
90 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 961.78°C 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 λ 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:
The 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 (–259.3467°C) and 1234.93 K (961.78°C), 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 Planck’s 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
Material a Equilibrium state b Temperature
T90 (K) t90 (°C)
He VP 3 to 5 –270.15 to –268.15
e-H2 TP 13.8033 –259.3467
e-H2 (or He) VP (or CVGT) ≈17 ≈ –256.15
e-H2 (or He) VP (or CVGT) ≈20.3 ≈ –252.85
Nec TP 24.5561 –248.5939
O2 TP 54.3584 –218.7916
Ar TP 83.8058 –189.3442
Hgc TP 234.3156 –38.8344
H2O TP 273.16 0.01
Gac MP 302.9146 29.7646
Inc FP 429.7485 156.5985
Sn FP 505.078 231.928
Zn FP 692.677 419.527
Al c FP 933.473 660.323
Ag FP 1234.93 961.78
Au FP 1337.33 1064.18
Cuc FP 1357.77 1084.62
T / A A p/ – B / C
i
90 0
1
9
K Pai
i
= + ( )( )[ ]
=
∑ ln
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1-16
INTERNATIONAL TEMPERATURE SCALE OF 1990 (ITS-90) (continued)
Defining Fixed Points of the ITS-90 (continued)
a e-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.
b 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.
c Previously, these were secondary fixed points.
Values of Coefficients in the Vapor Pressure Equations for Helium
Coef.or 3He 4He 4He
constant 0.65—3.2 K 1.25—2.1768 K 2.1768—5.0 K
A0 1.053 447 1.392 408 3.146 631
A1 0.980 106 0.527 153 1.357 655
A2 0.676 380 0.166 756 0.413 923
A3 0.372 692 0.050 988 0.091 159
A4 0.151 656 0.026 514 0.016 349
A5 –0.002 263 0.001 975 0.001 826
A6 0.006 596 –0.017 976 –0.004 325
A7 0.088 966 0.005 409 –0.004 973
A8 –0.004 770 0.013 259 0
A9 –0.054 943 0 0
B 7.3 5.6 10.3
C 4.3 2.9 1.9
1-17
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 4000°C from IPTS-68 or IPTS-48 to ITS-
90. Within the accuracy of the corrections, the temperature in the first column may be identified with either t
68
, t
48
, or t
90
. 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 1064°C 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/°C t
90
-t
68
t
90
-t
48
-180 0.008 0.020
-170 0.010 0.017
-160 0.012 0.007
-150 0.013 0.000
-140 0.014 0.001
-130 0.014 0.008
-120 0.014 0.017
-110 0.013 0.026
-100 0.013 0.035
-90 0.012 0.041
-80 0.012 0.045
-70 0.011 0.045
-60 0.010 0.042
-50 0.009 0.038
-40 0.008 0.032
-30 0.006 0.024
-20 0.004 0.016
-10 0.002 0.008
0 0.000 0.000
10 -0.002 -0.006
20 -0.005 -0.012
30 -0.007 -0.016
40 -0.010 -0.020
50 -0.013 -0.023
60 -0.016 -0.026
70 -0.018 -0.026
80 -0.021 -0.027
90 -0.024 -0.027
100 -0.026 -0.026
110 -0.028 -0.024
120 -0.030 -0.023
130 -0.032 -0.020
140 -0.034 -0.018
150 -0.036 -0.016
160 -0.037 -0.012
170 -0.038 -0.009
180 -0.039 -0.005
190 -0.039 -0.001
200 -0.040 0.003
210 -0.040 0.007
220 -0.040 0.011
230 -0.040 0.014
240 -0.040 0.018
250 -0.040 0.021
260 -0.040 0.024
270 -0.039 0.028
280 -0.039 0.030
290 -0.039 0.032
300 -0.039 0.034
310 -0.039 0.035
320 -0.039 0.036
330 -0.040 0.036
340 -0.040 0.037
350 -0.041 0.036
360 -0.042 0.035
370 -0.043 0.034
380 -0.045 0.032
390 -0.046 0.030
400 -0.048 0.028
410 -0.051 0.024
420 -0.053 0.022
430 -0.056 0.019
440 -0.059 0.015
450 -0.062 0.012
460 -0.065 0.009
470 -0.068 0.007
480 -0.072 0.004
490 -0.075 0.002
500 -0.079 0.000
510 -0.083 -0.001
520 -0.087 -0.002
530 -0.090 -0.001
540 -0.094 0.000
550 -0.098 0.002
560 -0.101 0.007
570 -0.105 0.011
580 -0.108 0.018
590 -0.112 0.025
600 -0.115 0.035
610 -0.118 0.047
620 -0.122 0.060
630 -0.125 0.075
640 -0.11 0.12
650 -0.10 0.15
660 -0.09 0.19
670 -0.07 0.24
680 -0.05 0.29
690 -0.04 0.32
700 -0.02 0.37
710 -0.01 0.41
720 0.00 0.45
730 0.02 0.49
740 0.03 0.53
750 0.03 0.56
760 0.04 0.60
770 0.05 0.63
780 0.05 0.66
790 0.05 0.69
800 0.05 0.72
810 0.05 0.75
820 0.04 0.76
830 0.04 0.79
840 0.03 0.81
850 0.02 0.83
860 0.01 0.85
870 0.00 0.87
880 -0.02 0.87
890 -0.03 0.89
900 -0.05 0.90
910 -0.06 0.92
920 -0.08 0.93
930 -0.10 0.94
940 -0.11 0.96
950 -0.13 0.97
960 -0.15 0.97
970 -0.16 0.99
980 -0.18 1.00
990 -0.19 1.02
1000 -0.20 1.04
1010 -0.22 1.05
1020 -0.23 1.07
1030 -0.23 1.10
1040 -0.24 1.12
1050 -0.25 1.14
1060 -0.25 1.17
1070 -0.25 1.19
1080 -0.26 1.20
1090 -0.26 1.20
1100 -0.26 1.2
1200 -0.30 1.4
1300 -0.35 1.5
1400 -0.39 1.6
1500 -0.44 1.8
1600 -0.49 1.9
1700 -0.54 2.1
t/°C t90-t68 t90-t48 t/°C t90-t68 t90-t48
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CONVERSION OF TEMPERATURES FROM THE 1948 AND 1968 SCALES TO ITS-90 (continued)
t/°C t90-t68 t90-t48
1800 -0.60 2.2
1900 -0.66 2.3
2000 -0.72 2.5
2100 -0.79 2.7
2200 -0.85 2.9
2300 -0.93 3.1
2400 -1.00 3.2
2500 -1.07 3.4
2600 -1.15 3.7
2700 -1.24 3.8
2800 -1.32 4.0
2900 -1.41 4.2
3000 -1.50 4.4
3100 -1.59 4.6
3200 -1.69 4.8
3300 -1.78 5.1
3400 -1.89 5.3
3500 -1.99 5.5
3600 -2.10 5.8
3700 -2.21 6.0
3800 -2.32 6.3
3900 -2.43 6.6
4000 -2.55 6.8
T/K T90-T76 T90-T68
5 -0.0001
6 -0.0002
7 -0.0003
8 -0.0004
9 -0.0005
10 -0.0006
11 -0.0007
12 -0.0008
13 -0.0010
14 -0.0011 -0.006
15 -0.0013 -0.003
16 -0.0014 -0.004
17 -0.0016 -0.006
18 -0.0018 -0.008
19 -0.0020 -0.009
20 -0.0022 -0.009
21 -0.0025 -0.008
22 -0.0027 -0.007
23 -0.0030 -0.007
24 -0.0032 -0.006
25 -0.0035 -0.005
26 -0.0038 -0.004
27 -0.0041 -0.004
T/K T90-T76 T90-T68 T/K T90-T76 T90-T68
28 -0.005
29 -0.006
30 -0.006
31 -0.007
32 -0.008
33 -0.008
34 -0.008
35 -0.007
36 -0.007
37 -0.007
38 -0.006
39 -0.006
40 -0.006
41 -0.006
42 -0.006
43 -0.006
44 -0.006
45 -0.007
46 -0.007
47 -0.007
48 -0.006
49 -0.006
50 -0.006
51 -0.005
52 -0.005
53 -0.004
54 -0.003
55 -0.002
56 -0.001
57 0.000
58 0.001
59 0.002
60 0.003
61 0.003
62 0.004
63 0.004
64 0.005
65 0.005
66 0.006
67 0.006
68 0.007
69 0.007
70 0.007
71 0.007
72 0.007
73 0.007
74 0.007
75 0.008
76 0.008
77 0.008
78 0.008
79 0.008
80 0.008
81 0.008
82 0.008
83 0.008
84 0.008
85 0.008
86 0.008
87 0.008
88 0.008
89 0.008
90 0.008
91 0.008
92 0.008
93 0.008
94 0.008
95 0.008
96 0.008
97 0.009
98 0.009
99 0.009
100 0.009
110 0.011
120 0.013
130 0.014
140 0.014
150 0.014
160 0.014
170 0.013
180 0.012
190 0.012
200 0.011
210 0.010
220 0.009
230 0.008
240 0.007
250 0.005
260 0.003
270 0.001
273.16 0.000
300 -0.006
400 -0.031
500 -0.040
600 -0.040
700 -0.055
800 -0.089
900 -0.124
 
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.
2 SI deriived units
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 sub-
stance) 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.
2.1 SI de rived units with special names and symbols
Certain 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.
Table 1. SI base units
SI base unit
Base quantity Name Symbol
length meter m
mass kilogram kg
time second s
electric current ampere A
thermodynamic temperature kelvin K
amount of substance mole mol
luminous intensity candela cd
Table 2. Examples of SI derived units expressed in terms of SI base units
SI derived unit
Derived quantity Name Symbol
area square meter m2
volume cubic meter m3
speed, velocity meter per second m/s
acceleration meter per second squared m/s2
wave number reciprocal meter m�1
mass density (density) kilogram per cubic meter kg/m3
specific volume cubic meter per kilogram m3/kg
current density ampere per square meter A/m2
magnetic field strength ampere per meter A/m
amount-of-substance concentration
(concentration) mole per cubic meter mol/m3
luminance candela per square meter cd/m2
1-25
 
INTERNATIONAL SYSTEM OF UNITS (SI) (continued)
Table 3a. SI derived units with special names and symbols, including the radian and steradian
SI derived unit
Expression Expression
Derived quantity Special name Special symbol in terms in terms
of other of SI base
SI units units
plane angle radian rad m � m�1 = 1
solid angle steradian sr m2 � m�2 = 1
frequency hertz Hz s�1
force newton N m � kg � s�2
pressure, stress pascal Pa N/m2 m�1 � kg � s�2
energy, work, quantity
of heat joule J N � m m2 � kg � s�2
power, radiant flux watt W J/s m2 � kg � s�3
electric charge,
quantity of electricity coulomb C s � A
electric potential,
potential difference,
electromotive force volt V W/A m2 � kg � s�3 � A�1
capacitance farad F C/V m�2 � kg�1 � s4 � A2
electric resistance ohm � V/A m2 � kg � s�3 � A�2
electric conductance siemens S A/V m�2 � kg�1 � s3 � A2
magnetic flux weber Wb V � s m2 � kg � s�2 � A�1
magnetic flux density tesla T Wb/m2 kg � s�2 � A�1
inductance henry H Wb/A m2 � kg � s�2 � A�2
Celsius temperature(a) degree Celsius �C K
luminous flux lumen lm cd � sr cd � sr(b)
illuminance lux lx lm/m2 m�2 � cd � sr(b)
(a) See Sec. 2.1.1.
(b) The steradian (sr) is not an SI base unit. However, in photometry the steradian (sr) is maintained in expressions
for units (see Sec. 3).
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 = T�T0 ,
where T0 = 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.) 
Table 3b. SI derived units with special names and symbols admitted for reasons of safeguarding human health(a)
SI derived unit
Derived quantity Special Special Expression in terms Expression in terms
name symbol of other SI units of SI base units
activity (of a
radionuclide) becquerel Bq s�1
absorbed dose,
specific energy
(imparted), kerma gray Gy J/kg m2 � s�2
dose equivalent, ambient dose
equivalent, directional dose
equivalent, personal dose
equivalent, equivalent dose sievert Sv J/kg m2 � s�2
(a) The 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).
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INTERNATIONAL
SYSTEM OF UNITS (SI) (continued)
2.2 Use of SI derived units with special names and symbols
Examples 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.
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, m2 � 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 quan-
tities 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).
Table 4. Examples of SI derived units expressed with the aid of SI derived units having special names and symbols
SI derived unit
Expression
Derived quantity Name Symbol in terms of
SI base units
angular velocity radian per second rad/s m � m�1 � s�1 = s�1
angular acceleration radian per second squared rad/s2 m � m�1 � s�2 = s�2
dynamic viscosity pascal second Pa � s m�1 � kg � s�1
moment of force newton meter N � m m2 � kg � s�2
surface tension newton per meter N/m kg � s�2
heat flux density,
irradiance watt per square meter W/m2 kg � s�3
radiant intensity watt per steradian W/sr m2 � kg � s�3 � sr�1 (a)
radiance watt per square
meter steradian W/(m2 � sr) kg � s�3 � sr�1 (a)
heat capacity, entropy joule per kelvin J/K m2 � kg � s�2 � K�1
specific heat capacity, joule per kilogram
specific entropy kelvin J/(kg � K) m2 � s�2 � K�1
specific energy joule per kilogram J/kg m2 � s�2
thermal conductivity watt per meter kelvin W/(m � K) m � kg � s�3 � K�1
energy density joule per cubic meter J/m3 m�1 � kg � s�2
electric field strength volt per meter V/m m � kg � s�3 � A�1
electric charge density coulomb per cubic meter C/m3 m�3 � s � A
electric flux density coulomb per square meter C/m2 m�2 � s � A
permittivity farad per meter F/m m�3 � kg�1 � s4 � A2
permeability henry per meter H/m m � kg � s�2 � A�2
molar energy joule per mole J/mol m2 � kg � s�2 � mol�1
molar entropy, molar
heat capacity joule per mole kelvin J/(mol � K) m2 � kg � s�2 � K�1 � mol�1
exposure (x and � rays) coulomb per kilogram C/kg kg�1 � s � A
absorbed dose rate gray per second Gy/s m2 � s�3
(a) The steradian (sr) is not an SI base unit. However, in radiometry the steradian (sr) is maintained in expressions
for units (see Sec. 3).
1-27
 
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 s�1, 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, Comité Consultatif des Unités) 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: Alternative definitions of the SI prefixes and their symbols are not permitted. For example,
it is unacceptable to use kilo (k) to represent 210 = 1024, mega (M) to represent
220 = 1 048 576, or giga (G) to represent 230 = 1 073 741 824.
3 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 supplemen-
tary 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 Reso-
lution 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.)
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INTERNATIONAL SYSTEM OF UNITS (SI) (continued)
5 Units Outside the SI
Units 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

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