Baixe o app para aproveitar ainda mais
Esta é uma pré-visualização de arquivo. Entre para ver o arquivo original
TeamLRNTeamLRN 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 TeamLRN 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. TeamLRN 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 TeamLRN 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 � �� � � � ����� ����� ����������������� � ����� ����������������������� � �������������� ����� ������������� �������������������� � ����������� ���������������������� ���������������������������������������������������� � �������������������������������������������� �������� � !����������������� ����"����������������� ������������ ���� ���������������##$ ��� � ����"������������%����������&��������������������������������������������##$���%�����������'� ������������������ ������� �� � �� ��'��� (������� ����##$)������ ���������������������%�������)�����(������� �������)������ ��������������������'���%�������"� �����������������'������������ ������������������������������������������� � ����&�*��������+��������� ����������"�������� ��������������& *��������, +"��� ����)�-��������. �������������/�0���� ��1*� � ���+�������)1�-�� �� ."�2"������)���������������)�2��&'� �-����������� ���������!)�3���������������� ������� 4"�+�%��)�/������ �5���� ����-������������6����)�6����� �"�*"�4������ ���)��"�-"�5���� ��� � �2�������2��������-�������������5���� ���)�2�������+���������� -"�7�������)���� �����3�� ���������������� ��������*8�� ����3�� ������)��'����� 9"� "�5������)� "�+"�-�����:������ ��������� �-��������)�2�������+���������� ;"�5����������)�6������;� ������*������3�� �����<�)�*������� :"�6"�5���)�/������ �-�������������������������������� ���)�3���������������� ������� +"�/�0)�7� ���������4��� ����9����� )�+������ 9"�;"�:�� ��)�/������ �:������ �7� �������)�3������4������� �"�6"�=����)�9������-����������� �����:��������5������� 9"�/"���� ��)�/������ �-�������������������������������� ���)�3���������������� ������� ;"�;8���)�:����&� ����������������9���������� �)�*������� 9"�5"�;���)�/������ �2�������������� )�������� >"�>����)�/������ �-������������5���� ���)��������:��� �?��2��� �����!� � � � � �� � 5���)�:�����6")�������� ��)�9�����/")�����,@@�������"����"�� @���������"� TeamLRN � �� � � � ����� ����� ��������������������������� ! � � ����� � �� ��� ��� � ��� �� � ������ ���� �� � ���� � �� � ������ � �� ���� �� � �� ������� ��� �� ��� � ��� � �� � ���� ����� � � � �� �� � �� !���� � "����� #�� ���� ���� $�� ��� � �� �� � �� ��%� �� ������ �� �� �&& '&� ()* � � �� + ,�� - ��%� �� ���� �� �� (π� .��� # ��� / .��)00 1'� 0.(��� � .��� # ��� + ,�� - � � �� ���� �� .2��� � �� *�*)( .*' *.'��� � .� ��� 3 ��� + ,�� - # 4 ����� ���� �� �� % ��� � ��� � 0�0'(�+.�- � .���� �� 5%�� ��� .�) � .��� 6����5 ���� �� � 0�0�0 �0&1+..- � .���� 7 � .�' � .��� ���π 8� .��)( )'. 0*+.*- � .���� 7 � .�'� .��� � � � � � ��� % .�0�� .'0 )1+.(- � .���� � *�)� .��� ��%� �� 9�, :��� �� �2� �� ���0' *11 '�+.*- � .� �� ;� *�)� .��� ������ ��� :��� �� � ��� �� '�'(* �&. '11+�0- � .� � " 1�1� .��� � � �� ���� &�.�& 1*�0+.0- � .� ��� 5% .�'� .��� � � �� ���� � .�0'� 0�. '.+�&- � .� ��� 5% .�'� .��� � � ��< � � �� ���� � �� �2 .*10�.)� 0'� 0.+*)- (�0� .� ��� =� <� �� � ���� �� ��(π��8�� � '��&' 1)� )0*+�(- � .��� 1�1� .��� ��� � =� <� �� � ���� �� ��� .1'��1) &&& ..+(0- 1�1� .��� ��� % ���� �� �� ���� �� .� &'1 '1.�)0* )�)+'1- � �� 0�0� .���� ���%�� � ���� �� �� � 0���� .(.)+.�- � .� �� ����� .�'� .��� 3� ���� ���� �� � � &0 (*)�11*1+*1- � ��� �� *�0� .��� ���� %�� ���� �� � *�1.( ('�+.)- 7 ����� >�� .�'� .�� ��� ?���� ���� �� �2 � � .�1*� 0)�)+�(- � .� ��� 7 >�� .�*� .�� " ���<��� ?���� ���� �� +π�20�-���8���� � )�0'� (��+(�- � .��� ; ��� >�� '��� .�� #��<"� ��� � ��� � � �� �� 4� � � "� � � �� ��� @ + 2�- 7 A .�0�� .'0 )1+.(- � .���� 7 *�)� .��� +���= �- � ���� ���� ��� . � / � / � �� +���- � .�00� )1* *0+�*- � .���� 5% .�' � .��� / .��� 5% ������ � � �� � ( � ����� ����� ��������������������������� ! ����� ��� ��� ���� �� �������� ������ �� ��� ����������� ��� ������ �� ����� � ��� �������� ����� �� ��� ���� �� �������! "������� ���! #������� $����� %����� �� ����� &��� �� ���! �� &%�'�"$�� ����� �� ��(�� �� �� ��� �� �� �)) *)� +,- � � �� .�/� �0 ��(���� ������� �� +π� 1��� % ��� 2 1��,33 4*� 31+��� � 1��� % ��� .�/� �0 ��� ��� ������� 15��� � �� -�-,+ 1-* -1*��� � 1� ��� 6 ��� .�/� �0 ���� ������� ������� � �� �� ��� � ����� 2 ��� �� 4*3�*4� 414 +31��� 7 .�/� �0 %�8������ ������� �� (���������� � 3�3*+�.1�0 � 1���� �� 9(�� ��� 1�, � 1��� ��: � 3�*�-*.1�0 � 1���� .;�'���0�� 1�, � 1��� <��� 9 ������� 3�3�3 �3)4.110 � 1���� = � 1�* � 1��� �� �' � +�14, 33* +4.4,0 � 1���� �' � -�, � 1�� ��π : 1��,+ ,*1 3-.1-0 � 1���� = � 1�*� 1��� �� �' � 3�,-� 11) 1,.,30� 1��� �' � -�,� 1�� : � �� >�� �� 1)*�4�3 )3-.1*0 >�' �� -�,� 1�� <��� 9 ���� .: ���0��� � ��1*3 +,.130 � 1� � 9( *�,� 1��� <��� 9 ����������� .: ����0����� �� 1�+13 *).110 � 1� �� ? *�,� 1��� <��� 9 ���(�� : � �� 2 .: ��� �0��� � 1�313 �+.1�0 � 1� ��� � *�,� 1��� <��� 9 ���� ��� 2 .: ��� �0��� �� ,�4)1 �1.+�0 � 1� ��� � *�,� 1��� ��� �" >�;%��� ���������� ���(� � 1�3�� 1*3 ,4.1+0� 1���� -�,� 1�� �� ��+1* )-) +�.�10� 1��� � =�� -�,� 1�� ��(���� @�/ A������ ��� �� ���3* -44 *�.1-0� 1� ��� B� -�,� 1�� ���� ��� � A������ ���� �� *�*+- �)1 *44.�30 � 1� �� $ 4�4� 1��� ������� �� ���� ��� � A������ ���� 1� )�3�+�4 *�,.+40 7 4�4� 1� �� =�������� �������� ��� �� +-4 ,)*�-*).+10 � 1� � CD '�� -�,� 1�� ��� ?���D��( �������� ��� 2 ������ � �, -1��-�* ++).-30 7 4�4� 1� �� ���� ��(����� �: �� � �� )�*�+�� )+).-�0 � 1� �� = ��� -�3� 1�� �� �' ��� ,�*-- 4-1 -�+.4)0 � 1��� �' ��� 3�*� 1��� ��� 14�))3 �+,-.1�0 � 1� � CD ��� -�3� 1�� ��� � +3�3-3 +,�*.+�0 � �� ��� -�3� 1�� ���� ��3*1 *141.1�0 ? � �� 1�-� 1�� �� ���� ��(����� �: �� � �� ,��,� *-4 +4.+40� 1� ��� = ��� -�3� 1�� �� �' ��� 4�1,� +,1 �,).�10 � 1�� �' ��� 3�*� 1��� ��� *�3�� ,)4 *1.3,0 >CD � �� -�3� 1�� ��� � ��,+� 3�4 ,-.��0 � 1� �� ��� ��� -�3� 1�� ���� 4�3,- �34*.3+0 � 1� �� ? ��� 1�-� 1�� �� >� �%� %& ���" ;������ E������� ���� ������� ���+π��: � � *��)* 4,� ,3-.�+0 � 1��� 4�4 � 1��� ������� E������� ���� ������� ��� 14*��4, ))) 11.+30 4�4 � 1��� � ��� ��� �������� ��� � � ��� ��� ��� ��� ������ � ��� ������ ������ ���� ��� ��� �� ������ ����� ��� ���� �� ��� ��� � ��� ��� �� ��� �� ������ � ��� ��� �������� ��� � � ��� ��� ��� ��� ������ � ��� ������ ������ ���� ��� ��� �� ������ ����� ��� ���� �� ��� ��� � ��� ��� �� ���� � �� ������ TeamLRN � �� � A � ����� ����� ��������������������������� ! ����� ��� �� �� ���� �������� ���� � � ���� ���� � � ������� ��� � � �� ����� �� ������ � ��� � ������!� �� "# $%& %&"�'() '!'�%&� � �� (�(� "#��� ��� &�!)$ )*" $(# &(#�!!� � "# �� +, (�( � "#��� ���� !�"%$ )%! #$�&%�� "# ��� - "�%� "#�� ���� � �. "&�(#' ($!&�"!� �. )�'� "# �� � /� ���� � ��*π�� 0 *π��1����� � � #�'!$ "%% !"#)�")� � "#��� � &�&� "#�� +������ � �� � ��*π�� � 0 !���� 0 ����� � � *�&'$ %** "%�%'� � "# ��� - "�% � "#�� � �. !%�!"" &)*'�!&� �. )�' � "#�� 2 � � � 3 ���� ���� ��!�� &�(&( $*% ''#�!*� � "# � �� ��� (�% � "#�� ���� %�!%& )$' "#"�*)� � "# � �� ��� (�% � "#�� ������ 4��5 6���� � 7�� � ��� �� ����1��� � "�"(( &$�"�� "#�� 8�.�� )�( � "#� 4��5 ��9� � �� � � :�/��� ��/���� �� � � 0 � � � � "� ������� � �� � � #�!!! "'�%(� &�* � "# �� ������ ; �� ������ ���� �� $�"#$ &)!(�"(� � "# ��� 5 "�% � "#�� � ; �� 0 ����� ������� �������� �� ��� ���� ����� � '�*)' %$$ #$*'�!*� � "#� *�* � "#��� � �� � �2 ����� � ��� � )�")% "#*%�"*� � "#�� - "�% � "#�� � <�. #�'"# $$) $")�**� <�. )�( � "#�� ������ :� ���� ���� ����µ *�)&( &&" (%�"&�� "# �� !�(� "#�� ������ :�� ���� ���� ����τ !�)%' (*�*%� � "# � "�(� "#� ������ :7� � ���� ���� ����� '�**( "%# !"%&�!'� � "# � *�(� "#��� ������ : � �� ���� ���� ����� '�*&) (%& **)"�&)� � "# � %�#� "#��� ������ :�� ��� ���� ���� ����� !�%!* *&% "#$'�"&� � "# � *�)� "#��� ������ � ��7/� 7������� ���� ���� ����α "�&%# $&& ''' %'�("� � "# � *�*� "#��� ������ �/�� � � ���� 2 ��� � � ��� �"�%') )!# "!�"'� � "# �� � 5 �� )�(� "#�� ������ � ��� ���� ���� ������� '�*)' %$$ #$*'�!*� � "# �� 5 � ��� *�*� "#��� � �7� 4����� �/ ����� �� !�*!( &"# !&)�"(� � "# ��� � (�%� "#�� ���!π 0 � � 0 ���*π�� �� &)(�"'$ !(%)�!(� � "#��� � (�% � "#�� ��������� ������ ���� � �� � �� !�)"% $*# &!'�!)� � "# ��� � "�# � "#�� �/ �� �� �� ����� �)π�&���� �� #�((' !*' )%&�"&� � "#��� �� !�#� "#�� ������ �� ���� � �� � �� �$!)�*%( *"!�)#�� "# �� - ��� )�( � "#�� � � /� �� �� ���� ����� �"�##" "'$ ('! ")'$�&)� &�)� "# ��� � ����� �� �� ���� ����� �")&)�!)" $%" #%�)'� *�(� "# ��� ������ �� ���� � �� � � ���� ������� � " � "�"'$ ('! ")'$�&)� � "# �� &�!� "#�� ������ �:3��� � �!�" = �� �� �!�##! &"$ &#* &%")�%'� &�)� "# ��� ������ :� �� ���� � �� � ���� ����µ !#(�%(( $)$*�'*� !�(� "# �� ������ :7� � �� ���� � �� � ���� ����� �(')�!"# ()(!�((� "�#� "# �� ������ � �/������ 7� � �� ���� � �� � ���� ���� � � �(')�!!% '$'(�%"� "�"� "# �� �+�>; �7/���; !' Æ�� � ����� ������� � �� �� ��� ���� �� � ����� ��������� �� ���� ������ ���� � �� �� �� �� �� ������ �� �� � ! ���� � ����� ������� � �� �� ��� ���� �� � ����� ��������� �� ���� ������ "�� #���� ��� �� ��� ��� ������� � ����� �� ���� � � ��� ������ #���� �� �� �� �$� �� ���� ��� ��� �� ���� ������� �� �� �%������ & ���'( �)��)�� � �� � B � ����� ����� ��������������������������� ! ����� ��� �� �� ���� �������� ���� � � ���� ���� � � ������� ��� � � �� ����� �� ������ � �� ��! ���� � �� � ���� ����� "#$�"%$ &$�%'� %�(� )$ �� ������ �� ��� ��! ���� � �� � ���� ����� �% )('�"%' ("'�%'� )�)� )$ �� ������ � �*������ *��� � ��! ���� � �� � ���� ���� � � +#(�$&+ %&&�)$� )�%� )$ �� �!��, �-*���, %& Æ�� ������ !�� ��! ���� ���� %�����.� �� )�/#$ +&" /(�)&�� )$ �� ��� ��� +�#� )$�� ���%π %+ $%(�"&'%�%(� 012 ��� +�# � )$�� 0 , µ� � ���� �µ )�++' &') ($�''�� )$ � � 3! )�/� )$�� � , �µ 4 ���µ� �� �������� �� ��� ���� ����� � $�))' (%+ "%#(�'$� %�# � )$�� � ��!� �5 ����� � �µ� )�#"% +'' #$�%"� � )$��� 6 )�/ � )$�� � 0�7 )$&�#&+ '#"%�"(� 0�7 +�" � )$�� � ������ ���� ���� �µ��� %$#�/#+ %+'+�&(� %�# � )$ �� � �� ���� ���� �µ��� &�"(& "%�"/� � )$ � )�# � )$� � -� � ���� ���� �µ��� $�))% #$" &%#"�%"� %�# � )$ �� � � �� ���� ���� �µ��� $�))% (&( &)/&�%"� %�# � )$ �� � � ��� ���� ��µ �µ�� µ $�))' (%+ "%#(�'$� � )$� 3! � ��� %�#� )$�� � � �-� 8����� !�* ���µ� ���µ ))�/'( (() $&�'$�� )$ ��� � %�&� )$�� ���µ�% ���µ )�+#/ &"( %"+�(/� � )$ ��� � %�&� )$�� � ��! ���� � �� � �µ �(�("$ ((/ ""�($� � )$ � � 6 ��� +�"� )$�� � � *� ��! �� ���� �µ��� �(�+() "/$ (&�)'� � )$ � %�# � )$�� � ����� ��! �� ���� �µ��� �+�+"$ &"# "+�%'� %�# � )$ �� � ��! ���� � �� � � ���� ��µ����.��%�µ�� ) �µ )�)#& ")" +)�#%�� )$ � &�'� )$�� � � 9��� � �%�) : �µ� �µ �%�$$% '') +'"#�)%� #�%� )$ ��� � -� � ��! ���� � �� � ���� �µ��� �'�)+' '(& ))+�+"� %�+ � )$ �� �� , τ� �� ����� �τ '�)#/ //�&%� � )$ � � 3! )�#� )$� � , �τ 4 ���τ� ��� �������� �� ��� ���� ����� � )�"$/ #+�')� )�#� )$� � ��!� �5 ����� � �τ� %�+(/ $&�(#� � )$��� 6 )�# � )$� � 0�7 )//#�""�%"� 0�7 )�# � )$� �� ������ ���� ���� �τ��� '(//�(+�&/� )�# � )$ � �� � ���� ���� �τ��µ )#�+)+'�%/� )�#� )$ � �� -� � ���� ���� �τ��� )�+"' "$�')� )�# � )$ � �� � �� ���� ���� �τ��� )�+") %"�')� )�# � )$ � �� � ��� ���� ��τ �τ�� τ )�"$/ #+�')� � )$� 3! � ��� )�#� )$� �� � �-� 8����� !�* ���τ� ���τ $�#"/ /%�))� � )$ ��� � )�#� )$� ���τ�% ���τ $�))) $(#�)+� � )$ ��� � )�#� )$� � ��� ������� � ��� �� �� ��� � ��� � �� ��� �� ��� � � ���� ��� ��� ����� ��� �� ��������� �τ ��� ����� �� ��� ��� � �� �τ� �� ��� ���� ����� � ��� �������� ���� ��� � ��������� �� ���� � �!� � � ���� � �������� ��������� �� ��" ��� ������ ���� ��� # ���� ��������� �� � ��$ ���� % ��" ���� TeamLRN � �� � C � ����� ����� ��������������������������� ! ����� ��� �� �� ���� �������� ���� � � ���� ���� � � ������� ��� � � �� ����� �� � � ! " "� � ���� �� #�$%& $&# %#�&'�� #( ��� )* #�% � #(�� � ! �� + ���"� �"� � �������� �� ��� ���� ����� � #�((% &%$ ,$$ --�#.� #�. � #(��� � ��*� �/ ����� � ��� � #�0(. &%% ,.�&$�� #(��� 1 #�% � #(�� � 2�3 '.-�&%& (&'�-(� 2�3 -�$ � #(�� "� � 4������ ���� ���� ����� #-.$�#0& $%& $#�-0� ,�$ � #( ��� "� � 4� ���� ���� ����µ -�--( &,. ..�&.� &�$� #( �� "� � 4�� ���� ���� ����τ (�0&- (#&�-$� #�$� #( �� "� � 4 � �� ���� ���� ���� (�''- $&. ,%- %&�0-� 0�-� #( ��� "� � �5��*� � ���� / ��� � ���� '�0%- -.. %$�-&�� #( � � )*�� -�$� #(�� "� � � ��� ���� � �� ��"�! �� #�((% &%$ ,$$ --�#.� � #( �� )* � ��� #�.� #(��� "� � � �"� 6����� *�5 ���� ��� #�.&# ,(' -000�--� � #( �� � $�%� #(�� ����&π ��� (�&#( .(- '#(,�#,� � #(�� � $�% � #(�� "� � ��� �5��*� ���� � �� (�-%0(�$-� � #( �� � %�- � #(�� "� � ��* ���� � �� � �� #�,#( $($ %#�#&� � #( ��� 1 ��� -�% � #(�� � � 5� ��* �� ���� ����� #�0&# (.& &($�#0� � #( �� #�( � #(�� � ����� ��* �� ���� ����� &�%'& -,% .0#�&-� #�( � #( �� "� � 47��� � &����� � 0�0-0 $', %(#�0$� #�( � #( �� "� � 4 � �� ��* ���� � �� � ���� ���� �#�,0' -'- (0�.,� &�, � #( �� �5������ "� � ��* ���� � �� � ��� #�,#( 0%( ,%�#&� � #( ��� 1 ��� -�% � #(�� �8�9! �"5���! &0 Æ�� � � 5� ��* �� ���� ������ #�0&( ''. #.&�#$� � #( �� #�# � #(�� � ����� ��* �� ���� ������ &�%'& %%0 $(,�.(� #�# � #( �� "� � ��* ���� �5����� * � ������ #� ������ � � � &0�$-'�#0� � #( �� 0�% � #(�� �8�9! �"5���! &0 Æ�� "� � *�� ��* ���� ���� &���: �� &�$%0 &&& (0�&.� � #( � ��� ��� -�$ � #(�� ���&π ,&�0%% ,-#.�.%� 28; ��� -�$ � #(�� �5������ "� � *�� ��* ���� ���� &����: � � � &�$%0 #0. ..�&.�� #( � ��� ��� -�$ � #(�� �8�9! �"5���! &0 Æ�� ����&π ,&�0%$ .-%0�.%� 28; ��� -�$ � #(�� �� �� ! � �� ���� � #�$%, '&% &-�&'�� #( ��� )* #�% � #(�� � ! � + ��� � � � �� �������� �� ��� ���� ����� � #�((- $$, '#0 $(�00� 0�0 � #(��� � ��*� �/ ����� � � � � #�0(0 .,' 0%�&$�� #(��� 1 #�% � #(�� � 2�3 '.'�0$0 .$(�-#� 2�3 -�$ � #(�� � �� 4������ ���� ���� � ��� #-.-�$-. $0'-�#.� %�( � #( ��� � �� 4� ���� ���� � ��µ -�-'& ,-, (&�&.� &�$� #( �� � �� 4�� ���� ���� � ��τ (�0&- %,(�-$� #�$� #( �� � �� 4"� � ���� ���� � ��� #�((# .%- ,#- %(�0-� 0�-� #( ��� � �� � ��� ���� � � �� ��� #�((- $$, '#0 $(�00� � #( �� )* � ��� 0�0� #(��� � �� � �"� 6����� *�5 �� � �� #�.#' 0'( '($%�--� � #( �� � $�%� #(�� �� �&π �� (�&#( (#' ,#0%�#,� � #(�� � $�% � #(�� � �� ��* ���� � �� � � �(�'$$ &.$ ,0�&,�� #( ��� 1 ��� &�0 � #(�� � � 5� ��* �� ���� � ��� �#�(,# -%0 $.�&0�� #( �� &�, � #(�� � ����� ��* �� ���� � ��� �#�'#. (,& %.�,0� &�, � #( �� � �� 47��� � &� ��� �.�-&$ (-0 ,$�'(� &�, � #( �� � �� � D � ����� ����� ��������������������������� ! ����� ��� �� �� ���� �������� ���� � � ���� ���� � � ������� ��� � � �� ����� �� � �� ������ ��! ���� � �� � ���� ����� "�#$# %%& &'�'(�� "# �� '�$� "#�� � �� )� � ��! ���� � �� � ���� ����� �#�%&$ *+* ,$�"%� '�$� "# �� � �� � �-������ )� � ��! ���� � �� � ���� ���� � � �#�%&$ **% *$�"%� '�$� "# �� �.�/0 �)-���0 '( Æ�� � �� !�� ��! ���� ���� '�����1� �� "�&,' $+" &,�$%�� "# � ��� ��� '�( � "#�� ���'π '*�"%$ %*(#�+,� 2.3 ��� '�( � "#�� 4� ��� 0 � �� ��� ���� � ,�,$, (&, ,(�(+�� "# ��� 5! "�+ � "#�� � 0 � 6 ����� ��� ��� �������� �� ��� ���� ����� � '�#", ((, '"' +#�,(� "�+ � "#�� � ��!� �7 ����� � � � � ,�##( #%' &(�("�� "#�� 8 "�+ � "#�� � 2�9 "&+(�%"' &'�"%� 2�9 &�% � "#�� �� ��� ������ ���� ���� � ��� ,%+#�$&' *%('�"&� $�& � "# �� �� ��� )� � ���� ���� � ��� "�*** ##+ (## &'�$"� '�# � "# �� �� ��� � ��� ���� �� ���� '�#", ((, '"' +#�,(� � "# �� 5! � ��� "�+ � "#�� �� ��� ��� �-��!� ���� � � '�",*$�'&� � "# ��� � "�, � "#�� �� ��� ��! ���� � �� � � #�$,, #+, $&'�,&� � "# �� 8 ��� &�+ � "#�� � � -� ��! �� ���� � ��� #�$%% *+( $(%+�(#� � "# �� "�" � "#�� � ����� ��! �� ���� � ��� #�&(+ $,& ','*�*'� "�" � "# �� �� ��� ������ ��! ���� � �� � ���� � ��� �$�%%$ ,$( ($&�(#� � "# �� "�" � "#�� �� ��� )� � ��! ���� � �� � ���� � ��� #�,#+ #"' '#&$�$(� "�( � "# �� �� ��� � �� ��! ���� � �� � ���� � ��� �#�$$& '#% ('�""� '�$ � "# �� .��� 0 - -��� ����� �� (�##% $"' "$�&%�� "# ��� 5! "�+ � "#�� � 0 �� 6 ���-� �-��� �������� �� ��� ���� ����� � ,�#"$ *,' '$,$�(&� "�* � "#�� � ��!� �7 ����� � ��� � $�$** (,& &$�++�� "#�� 8 "�+ � "#�� � 2�9 '&#&�,*" $'�'$� 2�9 &�% � "#�� -��� ������ ���� ���� ����� ($*(�&&( '%*�""� '�# � "# �� -��� )� � ���� ���� ����� '�**, "(' %%+"�(&� "�* � "# �� -��� � ��� ���� ��� �-�� � ,�#"$ *,' '$,$�(&� � "# �� 5! � ��� "�* � "#�� �-������ -��� ��! ���� � �� � ��� �"�#+$ ((, #'$�*,� � "# �� 8 ��� &�+ � "#�� �!��0 �)-���0 '( Æ�� � � -� ��! �� ���� ������ �"�"(& %+" $+$�"$� � "# �� "�' � "#�� � ����� ��! �� ���� ������ �'�"'+ $*+ +',�'(� "�' � "# �� �-������ -��� � )� � ��! ���� � �� � ���� ������ �#�+%" +%% (%'�"'� "�( � "# �� �!��0 �)-���0 '( Æ�� �-������ -��� � �-������ )� � ��! ���� � �� � ���� ����� � � �#�+%" +&% ",",�,,� $�, � "# �� �!��:.�/0 �)-����0 '( Æ�� �-������ -��� !�� ��! ���� ���� '������1� � � � '�#,+ &*$ +#�"&�� "# � ��� ��� &�+ � "#�� �!��0 �)-���0 '( Æ�� ����'π ,'�$,$ "#"(�'&� 2.3 ��� &�+ � "#�� TeamLRN � �� � $ � ����� ����� ��������������������������� ! ����� ��� �� �� ���� �������� ���� � � ���� ���� � � ������� ��� � � �� ����� �� �� !� �������" α �� !� ������� ���� �α #�#$$ #%#%�&&� � &' ��� () &�*� &'�� � " �α + ���α� ��� !� ������� �������� �� ��� ���� ����� � $�''& %'# &*, &$,�%#� &�$ � &'��� � ��)� �- ����� � �α� � %�,*& ,&,$�&'� � &'��� . &�* � &'�� � /�0 1*2*�1*, &*�12� /�0 3�# � &'�� �� !� ������� � ������ ���� ���� �α��� *2,$�2,, %1#1�12� $�$ � &' ��� �� !� ������� � � � ���� ���� �α��� 1�,*2 %,, #3, '*�%2� &�1 � &' ��� �� !� ������� � ��� ���� ���α ��α���α $�''& %'# &*, &$,�%#� � &'� () � ��� &�$� &'��� 456���78�5�/���� �� )��� � ��� � ��� #�'22 &$&%�&'� � &' � � ��� &�*� &'�� �� ��� ���� � ��� � � + � �� ������ + & � &�##' %13 3#�23�� &' ��� () &�*� &'�� + &'� () � ������ � ��)� �- ����� � � � � &�$,2 $&* ,'�2#�� &'��� . &�*� &'�� � /�0 ,1&�$,$ '$1�3'� /�0 3�#� &'�� 9������ � ��� �� �� � ,# $3%�1131�31� � � � �� 3�#� &'�� � ��� 4�� �( � ��� � ��� 1�,,' 1&2 *&#�2*� � &' ��� . � � ��� #�*� &'�� ���� '�&&, #2# %#% *2�3'� . � � � �� #�*� &'�� � ��� )�� � ��� � 3�1&$ $*2�&%� . � ��� :�� &�*� &'�� � ��;�� � ��� � ��� � &�13' #%'%�2$� � &' �� . :�� &�3� &'�� � �0 :�� 3�#&* 1$1�&%� � &'� �0 :�� &�3� &'�� ��� 2�'31 ##$$�1#� � &'�� 5; :�� &�*� &'�� ���� #,�%'1 %#�&2� ��� :�� &�*� &'�� � ��� � � �� < ����� )�� ��� � + 2*1�&% :� � + &'&�12% (4� �� 22�$&1 ,,#�1,�� &' � � � ��� &�*� &'�� � ��!���� � ��� � ����� �� 2�#3# ***1�$*� � &' � �� &�3� &'�� � + 2*1�&% :� � + &'' (4� �� 22�*&' ,3&�$'� � &' � � � ��� &�*� &'�� ���( �8���� �� � ��� � ���� � �� � �� � � ��� ��� � = � >�2π� ������� ��������? �� + & :� �� + &'' (4� ��� �&�&%& *'$*�$$� 1�3 � &' �� �� + & :� �� + &'&�12% (4� �&�&#$ 3#**�$$� 1�3 � &' �� ���<� 8� ��;�� � ��� � �π��#'����@� �� � %�#*' $''�$'� � &'�� A ��� :�� *�' � &'�� B��� ������� � ��� � 2π��� �� 1�*$& **& 13�#$�� &'��� A �� &�*� &'�� B��� ������� � ��� � < � � ������ ����� �� 2��� ��� &�&,& '$2 32�2'�� &' ��� A �� ���� &�*� &'�� ��� � ������� � ��� � ���� �� &�$13 **%2�2%� � &' �� � : &�*� &'�� A�� ��� ������ � ��C � ��� � � + ����� + ���$�,#% &&$ 21&��� � 2�3,* *#3%�%&� � &' � � : &�*� &'�� � ��� ������� � �� � � �� �� ���� �� ��� ������� ������ �� ��������� �� �� ����������� ���� � ����� ���� ��� �� �� �� ������� �� �� ����� �� ����� � �� ������ ����� � ��� �� � �� ��� � ��� �� ��� !��� ���� �� "� ���� # �$���� �� ��� ������ ���� % �� ��� ���������� � ��� � ��� !��� ���� �� ��� & ��'��( ����� ��� ����� �� ����� (���� �� ��� )*�� ��� � ���+ � � �, � ��� ����� % � � ��� ���� ����� ( � � �� ���� ����� � �� �� �� (���� �% � - �� . � � ��� � � ������� . � � ����&�� � �� � # � ����� ����� ��������������������������� ! ����� ���� ��� ���� ����� �� �� � ���� � � �� � �� �������� �� � ����� ���� �������� ���� � ��� ���� ���� ���� ��� �� �� � �� ���� � �� �!�� " #$� #%�� &' � ��� ! (���" � �� ���� � ������� �!�� ")#$ �� #� #% �� &' � ��� ! (���" � �� ��� ��� ���� � * � �+� � � ������� ����� ,-. /01�0 234 5 �� ! (���" � �� ��� ��� ���� � � � 6���4��' � ������� ����� $/ -#$�-%1 7 ! (���" ������ � ��� ��+ #%# .$/ 8� ! (���" ������ � ��� � ��� � � ' ����� � 0�-%9 9/ � � �� ! (���" TeamLRN � �� � �� � ����� ����� ��������������������������� ! ����� �� ��� ��� �� ��� ������ ���� ���� ���� �� ���� ��� ��� ���� � � ��� � ���� � �� � �� � �� � �� �� ��� ���� �� ��� �!� ����� �� ��� ��� �� ��� "�� � �� # $ �� � % ��& '� $ � � �� � � �� �%���& � $��� (� ������ �� �� �� � ����� � � ���� � � ��� ) ����� ������ %� �����&* +��� �� ���� ' (� ��� ), $ ' %$ '& � %$ '&-�� � %$ '&-�� � %$ '&-� � $ ' $ $$� ./� �/.� $���� (� / �01 $$2 ��%3.& � $��� ��� $ /�4 $4� 02%�.& � $��� ), $ (� %$ (�&�� � %$ (�& � %$ (�&��� � %$ (�&���� � 3 432 //$ 232 � $�� ' $ (� 1 /�1 103 4$%22& � $��� ��� $ 0/. 04� ..%�0& � $� � ), $ ��� %$ ���&�� � %$ ���&��� � %$ ���& � %$ ���&� � $ 43. 11/ .$%01&� $��� ' � �$� �$3 3$%03& � $���� (� $ ��� �44 24� 1/3 ), $ ), %$ ),&� � %$ ),&���� � %$ ),&-� � %$ ),& � . .�. �.40%$$& � $���� ' 2 02� 14.1%$0& � $�� � (� 0 00/ .1� 4/� � $��� ��� $ ), $ 5 %$ 5&� � %$ 5&���� � %$ 5&���� � %$ 5&��� � $ 03� ./�/%�1& � $���� ' $ /0. $3�3%�2& � $���� (� .4 /�0 /.%$�& ��� � �30 ..11%0.& � $��� ), $ �� %$ ��& � %$ ��&��� � %$ ��&��� � %$ ��&�� � $ .�� $2. /0%$1&� $���� ' $ 23� ..$ 3$%$/& � $��� (� 3 �./ /11 1/%.4& � $� ��� � 1$2 434 1�%�$& � $��� ), $ � %$ �&�� � %$ �& � %$ �&��� � %$ �&���� � $ 14� 1$2 4�%�.&� $���� ' $ ..� /03 3.%�3& � $���� (� 2 /$0 ��. .�3%/�& � $��� ��� � �/� 01� 2$3%$/& � $��� ), $ �� %$ ��& � %$ ��&�� � � %$ ��&��� � %$ ��&�� � 1 0/4 211 $2%2/& � $��� ' 1 3/� 3.4 .�%30& � $��� (� � $41 21. 0$0 2�/%$/& � $�� ��� . /24 .30 4�� 2�$%11& � $�� ), � �� � �� � ����� ����� ��������������������������� ! ����� � ��� � ��� � � �� ������ ����� ���� ������� �� � ��� �� �� �� � � ��� � ���� � �� � �� � �� � ��� � ��� ���� ������ � ������� � ��� � ��� � ��� ! ��� ���" # �� � $ ��% &� # � � �� � � �� �$���% � #��� '� � ��� �� �� �� � ����� � � ���� � �� ��� ( ����� ������ $� �����%) *� �� �� ���� + �� � �� # & $# &%,� � $# &% � $# &%,�� � $# &% � - �.� /01$#1% � #��� + 0 �.# 2�/ .-$21% � #��� �� 0 -�� 210#$##% � #�� � � �/1 -#� 2-$1/% � #�� �� # '� $# '�%���� � $# '�%�� � $# '�% � $# '�%�� � 0 2�/ 02�$##% � #��� + 2 0�/ 233 /0$.3% � #�� �� 0 ��� #.#2$#�% � #��� � � �0# .30 �2$12% � #��� �� # ��� $# ���%���� � $# ���%�� � $# ���%��� � $# ���%�� � # .13 --2�$�2% � #��� + # �1/ 3.# /#$##% � #��� �� # 11# ��2 �2�0$3/% � #��� � . 220 112 �2� -0�$1�% � #��� �� # (4 $# (4%��� � $# (4%� � $# (4%���� � $# (4%� � . -// �1-.$3.% � #���� + . #12 00- .1$12% � #��� �� . .1/ 3�# 00-$1�% � #���� � # 2#/ 3�/ 3.0 ��0$#�% � #���� �� # + $# +% � $# +%� � $# +%���� � $# +%� � # + 3 0#- 1.1$#2% � #�� �� / �2# �/3$#0% � #���� � 1 #00 3#21$22% � #��� �� # �� $# ��%,� � $# ��% � $# ��%��� � $# ��% � # #0� .2�2$��% � #�� + # �� # �-1 2.. #-#$/�% � #��� � 1 0-. /1� .2$1#% � #��� �� # � $# �%���� � $# �%�� � $# �% � $# �%�� � # �3� /2�-$#/% � #��� + /1# ./. �.1$3�% � #�� �� # � 1 .�1 #-- 030$�1% � #� �� # �� $# ��%�� � $# ��% � $# ��%�� � � $# ��% � 1 #2- -.02$22% � #� + �- �## 13.2$�1% �� � /�# �0� 1�1$#/% � #��� � # �� TeamLRN 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 TeamLRN 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 TeamLRN 1-18 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). TeamLRN 1-26 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.) TeamLRN 1-28 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
Compartilhar