EN ISO 80000-10:2013

SLOVENSKI STANDARD
01-junij-2013
1DGRPHãþD
SIST ISO 31-10:1995/Amd. 1:2001
SIST ISO 31-10+A1:2008
SIST ISO 31-9:1995/Amd. 1:2001
SIST ISO 31-9+A1:2008
9HOLþLQHLQHQRWHGHO$WRPVNDLQMHGUVNDIL]LND,62
Quantities and units - Part 10: Atomic and nuclear physics (ISO 80000-10:2009)
Größen und Einheiten - Teil 10: Atom- und Kernphysik (ISO 80000-10:2009)
Grandeurs et unités - Partie 10: Physique atomique et nucléaire (ISO 80000-10:2009)
Ta slovenski standard je istoveten z: EN ISO 80000-10:2013
ICS:
01.060 9HOLþLQHLQHQRWH Quantities and units
07.030 Fizika. Kemija Physics. Chemistry
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 80000-10
NORME EUROPÉENNE
EUROPÄISCHE NORM
April 2013
ICS 01.060
English Version
Quantities and units - Part 10: Atomic and nuclear physics (ISO
80000-10:2009)
Grandeurs et unités - Partie 10: Physique atomique et Größen und Einheiten - Teil 10: Atom- und Kernphysik (ISO
nucléaire (ISO 80000-10:2009) 80000-10:2009)
This European Standard was approved by CEN on 14 March 2013.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN member.

This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same
status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United
Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2013 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 80000-10:2013: E
worldwide for CEN national Members.

Contents Page
Foreword . 3

Foreword
The text of ISO 80000-10:2009 has been prepared by Technical Committee ISO/TC 12 “Quantities and units”
of the International Organization for Standardization (ISO) and has been taken over as EN ISO 80000-
10:2013.
This European Standard shall be given the status of a national standard, either by publication of an identical
text or by endorsement, at the latest by October 2013, and conflicting national standards shall be withdrawn at
the latest by October 2013.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech
Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece,
Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,
Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom.
Endorsement notice
The text of ISO 80000-10:2009 has been approved by CEN as EN ISO 80000-10:2013 without any
modification.
INTERNATIONAL ISO
STANDARD 80000-10
First edition
2009-12-01
Quantities and units —
Part 10:
Atomic and nuclear physics
Grandeurs et unités —
Partie 10: Physique atomique et nucléaire

Reference number
ISO 80000-10:2009(E)
©
ISO 2009
ISO 80000-10:2009(E)
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ii © ISO 2009 – All rights reserved

ISO 80000-10:2009(E)
Contents Page
Foreword .iv
Introduction.vi
1 Scope.1
2 Normative references.1
3 Names, symbols, and definitions .1
Annex A (informative) Non-SI units used in atomic and nuclear physics .66
Bibliography.67

ISO 80000-10:2009(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for whom a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
Draft International Standards adopted by the technical committees are circulated to the member bodies for
voting. Publication as an International Standard requires approval by at least 75 % of the member bodies
casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
International Standard ISO 80000-10 was prepared by Technical Committee ISO/TC 12, Quantities and units,
in co-operation with IEC/TC 25, Quantities and units.
This first edition of ISO 80000-10 cancels and replaces ISO 31-9:1992 and ISO 31-10:1992. It also
incorporates Amendments ISO 31-9:1992/Amd.1:1998 and ISO 31-10:1992/Amd.1:1998. The major technical
changes from the previous standards are the following:
⎯ Annex A and Annex B to ISO 31-9:1992 have been deleted (as they are covered by ISO 80000-9);
⎯ Annex C to ISO 31-9:1992 has become Annex A;
⎯ Annex D to ISO 31-9:1992 has been deleted;
⎯ the presentation of numerical statements has been changed;
⎯ the Normative references have been changed;
⎯ items 10-33 and 10-53 from ISO 31-10:1992 have been deleted;
⎯ new items have been added;
⎯ many definitions have been re-formulated;
⎯ newer values for fundamental constants have been used.
ISO 80000 consists of the following parts, under the general title Quantities and units:
⎯ Part 1: General
⎯ Part 2: Mathematical signs and symbols to be used in the natural sciences and technology
⎯ Part 3: Space and time
⎯ Part 4: Mechanics
iv © ISO 2009 – All rights reserved

ISO 80000-10:2009(E)
⎯ Part 5: Thermodynamics
⎯ Part 7: Light
⎯ Part 8: Acoustics
⎯ Part 9: Physical chemistry and molecular physics
⎯ Part 10: Atomic and nuclear physics
⎯ Part 11: Characteristic numbers
⎯ Part 12: Solid state physics
IEC 80000 consists of the following parts, under the general title Quantities and units:
⎯ Part 6: Electromagnetism
⎯ Part 13: Information science and technology
⎯ Part 14: Telebiometrics related to human physiology
ISO 80000-10:2009(E)
Introduction
0.1 Arrangements of the tables
The tables of quantities and units in this International Standard are arranged so that the quantities are
presented on the left-hand pages and the units on the corresponding right-hand pages.
All units between two full lines on the right-hand pages belong to the quantities between the corresponding full
lines on the left-hand pages.
Where the numbering of an item has been changed in the revision of a part of ISO 31, the number in the
preceding edition is shown in parenthesis on the left-hand page under the new number for the quantity; a dash
is used to indicate that the item in question did not appear in the preceding edition.
0.2 Tables of quantities
The names in English and in French of the most important quantities within the field of this International
Standard are given together with their symbols and, in most cases, their definitions. These names and
symbols are recommendations. The definitions are given for identification of the quantities in the International
System of Quantities (ISQ), listed on the left hand pages of the table; they are not intended to be complete.
The scalar, vector or tensor character of quantities is pointed out, especially when this is needed for the
definitions.
In most cases only one name and only one symbol for the quantity are given; where two or more names or
two or more symbols are given for one quantity and no special distinction is made, they are on an equal
footing. When two types of italic letters exist (for example as with ϑ and θ; φ and φ ; a and a; g and g), only one
of these is given. This does not mean that the other is not equally acceptable. It is recommended that such
variants not be given different meanings. A symbol within parentheses implies that it is a reserve symbol, to
be used when, in a particular context, the main symbol is in use with a different meaning.
In this English edition, the quantity names in French are printed in an italic font, and are preceded by fr. The
gender of the French name is indicated by (m) for masculine and (f) for feminine, immediately after the noun in
the French name.
0.3 Tables of units
0.3.1 General
The names of units for the corresponding quantities are given together with the international symbols and the
definitions. These unit names are language-dependent, but the symbols are international and the same in all
th
languages. For further information, see the SI Brochure (8 edition, 2006) from BIPM and ISO 80000-1.
The units are arranged in the following way:
a) The coherent SI units are given first. The SI units have been adopted by the General Conference on
Weights and Measures (Conférence Générale des Poids et Mesures, CGPM). The coherent SI units and
their decimal multiples and submultiples formed with the SI prefixes are recommended, although the
decimal multiples and submultiples are not explicitly mentioned.
vi © ISO 2009 – All rights reserved

ISO 80000-10:2009(E)
b) Some non-SI units are then given, namely those accepted by the International Committee for Weights
and Measures (Comité International des Poids et Mesures, CIPM), or by the International Organization of
Legal Metrology (Organisation Internationale de Métrologie Légale, OIML), or by ISO and IEC, for use
with the SI.
Such units are separated from the SI units in the item by use of a broken line between the SI units and
the other units.
c) Non-SI units currently accepted by the CIPM for use with the SI are given in small print (smaller than the
text size) in the “Conversion factors and remarks” column.
d) Non-SI units that are not recommended are given only in annexes in some parts of this International
Standard. These annexes are informative, in the first place for the conversion factors, and are not integral
parts of the standard. These deprecated units are arranged in two groups:
1) units in the CGS system with special names;
2) units based on the foot, pound, second, and some other related units.
e) Other non-SI units given for information, especially regarding the conversion factors, are given in
informative annexes in some parts of this International Standard.
0.3.2 Remark on units for quantities of dimension one, or dimensionless quantities
The coherent unit for any quantity of dimension one, also called a dimensionless quantity, is the number one,
symbol 1. When the value of such a quantity is expressed, the unit symbol 1 is generally not written out
explicitly.
EXAMPLE 1 Refractive index n = 1,53 × 1 = 1,53
Prefixes shall not be used to form multiples or submultiples of this unit. Instead of prefixes, powers of 10 are
recommended.
EXAMPLE 2 Reynolds number Re = 1,32 × 10
Considering that the plane angle is generally expressed as the ratio of two lengths and the solid angle as the
ratio of two areas, in 1995 the CGPM specified that, in the SI, the radian, symbol rad, and steradian, symbol sr,
are dimensionless derived units. This implies that the quantities plane angle and solid angle are considered as
derived quantities of dimension one. The units radian and steradian are thus equal to one; they may either be
omitted, or they may be used in expressions for derived units to facilitate distinction between quantities of
different kind but having the same dimension.
0.4 Numerical statements in this International Standard
The sign = is used to denote “is exactly equal to”, the sign ≈ is used to denote “is approximately equal to”, and
the sign := is used to denote “is by definition equal to”.
Numerical values of physical quantities that have been experimentally determined always have an associated
measurement uncertainty. This uncertainty should always be specified. In this International Standard, the
magnitude of the uncertainty is represented as in the following example.
EXAMPLE l = 2,347 82(32) m
In this example, l = a(b) m, the numerical value of the uncertainty b indicated in parentheses is assumed to
apply to the last (and least significant) digits of the numerical value a of the length l. This notation is used
when b represents the standard uncertainty (estimated standard deviation) in the last digits of a. The
numerical example given above may be interpreted to mean that the best estimate of the numerical value of
the length l, when l is expressed in the unit metre is 2,347 82, and that the unknown value of l is believed to
ISO 80000-10:2009(E)
lie between (2,347 82 − 0,000 32) m and (2,347 82 + 0,000 32) m with a probability determined by the
standard uncertainty 0,000 32 m and the probability distribution of the values of l.
0.5 Special remarks
0.5.1 Quantities
The fundamental physical constants given in ISO 80000-10 are quoted in the consistent values of the
fundamental physical constants published in “2006 CODATA recommended values”. See the CODATA
website: http://physics.nist.gov/cuu/constants/index.html.
0.5.2 Special units
Individual scientists should have the freedom to use non-SI units when they see a particular scientific
advantage in their work. For this reason, non-SI units which are relevant for atomic and nuclear physics are
listed in Annex A.
viii © ISO 2009 – All rights reserved

INTERNATIONAL STANDARD ISO 80000-10:2009(E)

Quantities and units —
Part 10:
Atomic and nuclear physics
1 Scope
ISO 80000-10 gives the names, symbols, and definitions for quantities and units used in atomic and nuclear
physics. Where appropriate, conversion factors are also given.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 80000-3:2006, Quantities and units — Part 3: Space and time
ISO 80000-4:2006, Quantities and units — Part 4: Mechanics
ISO 80000-5:2007, Quantities and units — Part 5: Thermodynamics
IEC 80000-6:2008, Quantities and units — Part 6: Electromagnetism
ISO 80000-7:2008, Quantities and units — Part 7: Light
ISO 80000-9:2009, Quantities and units — Part 9: Physical chemistry and molecular physics
3 Names, symbols, and definitions
The names, symbols, and definitions for quantities and units used in atomic and nuclear physics are given on
the following pages.
ISO 80000-10:2009(E)
ATOMIC AND NUCLEAR PHYSICS QUANTITIES
Item No. Name Symbol Definition Remarks
10-1.1 atomic number, number of protons in an A nuclide is a species of atom with
Z
(9-1)
proton number atomic nucleus specified numbers of protons and
neutrons.
fr numéro (m)
atomique,
Nuclides with the same value of Z
nombre (m) de
but different values of N are called
protons
isotopes of an element.
The ordinal number of an element in
the periodic table is equal to the
atomic number.
The atomic number equals the charge
of the nucleus in units of the
elementary charge (item 10-5.1).
10-1.2 neutron number N number of neutrons in an Nuclides with the same value of N
(9-2) atomic nucleus
but different values of Z are called
fr nombre (m) de
isotones.
neutrons
NZ− is called the neutron excess
number.
10-1.3 nucleon number, number of nucleons in an
A AZ=+N
(9-3)
mass number atomic nucleus
Nuclides with the same value of A are
fr nombre (m) de
called isobars.
nucléons,
nombre (m) de
masse
10-2 rest mass, m()X , for particle X, mass Specifically,
(9-5.1)  proper mass (ISO 80000-4:2006, item
m
for an electron:
X
(9-5.2) 4-1) of that particle at rest
−31
fr masse (f) au
m=×9,109 382 15(45) 10 kg;
(9-5.3)
e
repos,
for a proton:
masse (f)
−27
propre
m=×1,672 621 637(83) 10 kg;
p
for a neutron:
−27
m=×1,674 927 211(84) 10 kg
n
[2006 CODATA recommended
values].
Rest mass is often denoted m .
10-3 rest energy
for a particle,
E
(—)
fr énergie (f) au E =mc
repos
where m is the rest mass
(item 10-2) of that particle,
and c is the speed of
light in vacuum
(ISO 80000-7:2008, item
7-4.1)
2 © ISO 2009 – All rights reserved

ISO 80000-10:2009(E)
UNITS ATOMIC AND NUCLEAR PHYSICS
Item No. Name Symbol Definition Conversion factors and remarks
10-1.a one 1 See the Introduction, 0.3.2.
10-2.a kilogram kg
10-2.b dalton, Da 1 dalton is equal to 1/12 times
1 Da = 1 u =
–27
unified atomic the mass of a free carbon 12
1,660 538 782(83) × 10 kg
u
mass unit atom, at rest and in its ground
[2006 CODATA recommended
state
values].
10-3.a joule J
(continued)
ISO 80000-10:2009(E)
ATOMIC AND NUCLEAR PHYSICS QUANTITIES
Item No. Name Symbol Definition Remarks
10-4.1 atomic mass, rest mass
m()X , m
a
is called the relative atomic
(9-4.1)
nuclidic mass (ISO 80000-4:2006, item
m
m
u
a
4-1) of a neutral atom or a
fr masse (f)
mass.
nuclide X in the ground
atomique,
state
masse (f)
nucléidique
–27
10-4.2 unified atomic 1/12 of the mass
m m = 1,660 538 782(83) × 10 kg
u u
(9-4.2)  mass constant (ISO 80000-4:2006, item
[2006 CODATA recommended
4-1) of a neutral atom of
values].
fr constante (f)
the nuclide C in the
unifiée de
ground state at rest
masse
atomique
–19
e
10-5.1 elementary negative of electric charge
e = 1,602 176 487(40) × 10 C
(9-6)
charge (IEC 80000-6:2008,
[2006 CODATA recommended
item 6-2) of the electron
values].
fr charge (f)
élémentaire
c
10-5.2 charge number, for a particle, the electric A particle is said to be electrically
(—)  ionization charge neutral if its charge number is equal
number (IEC 80000-6:2008, item to zero.
6-2) divided by the The charge number of a particle can
fr nombre (m) de
elementary charge (item be positive, negative, or zero.
charge,
10-5.1) The state of charge of a particle may
charge (f)
be presented as a superscript to the
ionique
symbol of that particle, e.g.
+++3=+ − 3−
H , He , Al , Cl , S , N
–34
10-6.1 Planck constant elementary quantum of
h h = 6,626 068 96(33) × 10 J s
(9-7) action (ISO 80000-4:2006,
[2006 CODATA recommended
fr constante (f)
item 4-37)
values].
de Planck
Energy E of harmonic vibration of
frequency f can change for
multiples of ∆=Ehf=�ω only.
–34
10-6.2 reduced Planck �
h � = 1,054 571 628(53) × 10 J s
�=
(—)  constant
[2006 CODATA recommended
2π
values].
fr constante (f)
where h is the Planck
de Planck
� is sometimes known as hbar or the
constant (item 10-6.1)
réduite
Dirac constant.
4 © ISO 2009 – All rights reserved

ISO 80000-10:2009(E)
UNITS ATOMIC AND NUCLEAR PHYSICS
Item No. Name Symbol Definition Conversion factors and remarks
10-4.a kilogram kg
10-4.b dalton, Da, u 1 dalton is equal to 1/12 times
1 Da = 1 u =
–27
unified atomic the mass of a free carbon 12
1,660 538 782(83) × 10 kg
mass unit atom, at rest and in its ground
[2006 CODATA recommended
state
values].
10-5.a coulomb C
10-6.a joule second J · s
(continued)
ISO 80000-10:2009(E)
ATOMIC AND NUCLEAR PHYSICS QUANTITIES
Item No. Name Symbol Definition Remarks
2 –10
10-7 Bohr radius
a a = 0,529 177 208 59(36) × 10 m
4πε �
0 0
(9-8)
a =
fr rayon (m) de 2 [2006 CODATA recommended
me
e
values].
Bohr
where ε is the electric
The radius of the electron orbital in
constant
the H-atom in its ground state is a in
(IEC 80000-6:2008, item
the Bohr model of the atom.
6-14.1),
� is the reduced Planck
constant (item 10-6.2),
m is the rest mass of
e
electron (item 10-2), and
e is the elementary
charge (item 10-5.1)
10-8 Rydberg constant 2
R R =
∞ e ∞
(9-9) R =
∞ –1
fr constante (f) 10 973 731,568 527(73) m
8πε ahc
00 0
[2006 CODATA recommended
de Rydberg
where e is the elementary
values]
charge (item 10-5.1),
R=⋅R hc
The quantity is called
y ∞ 0
ε is the electric constant
Rydberg energy.
(IEC 80000-6:2008, item
6-14.1),
a is the Bohr radius (item
10-7),
h is the Planck constant
(item 10-6.1), and
c is the speed of light in
vacuum
(ISO 80000-7:2008, item
7-4.1)
–18
10-9 Hartree energy
E , E E = 4,359 743 94(22) × 10 J
H h e H
(9-10) E =
H
[2006 CODATA recommended
fr énergie (f) de
4πε a
values].
Hartree
where e is the elementary
The energy of the electron in
charge (item 10-5.1),
H-atom in its ground state is −E .
H
ε is the electric constant
(IEC 80000-6:2008, item
E=⋅2Rhc .
H0∞
6-14.1), and
a is the Bohr radius (item
10-7)
6 © ISO 2009 – All rights reserved

ISO 80000-10:2009(E)
UNITS ATOMIC AND NUCLEAR PHYSICS
Item No. Name Symbol Definition Conversion factors and remarks
–10
10-7.a metre m ångström (Å), 1 Å := 10 m
–1
10-8.a metre to the
m
power minus
one
10-9.a joule J
(continued)
ISO 80000-10:2009(E)
ATOMIC AND NUCLEAR PHYSICS QUANTITIES
Item No. Name Symbol Definition Remarks
µ
10-10.1 magnetic dipole for a particle or nucleus, For an atom or nucleus, this energy is
(9-11.1)
moment vector quantity causing an quantized and may be written as
increment
Wg= µMB
X
fr moment (m)
∆=W - µB⋅
magnétique
where g is the appropriate g-factor
to its energy W
(item 10-15.1 or item 10-15.2),
(ISO 80000-5:2007, item
is mostly the Bohr magneton or
µ
5-20.1) in an external X
nuclear magneton (item 10-10.2 or
magnetic field with
item 10-10.3), M is the magnetic
magnetic flux density B
(IEC 80000-6:2008, item
quantum number (item 10-14.4), and
6-21)
B is the magnitude of the magnetic
flux density.
See also IEC 80000-6:2008, item
6-23.
–26 –1
10-10.2
Bohr magneton
µ e� µ = 927,400 915(23) × 10 J T
B
B
µ =
(9-11.2) B
[2006 CODATA recommended
fr magnéton (m) 2m
e
values].
de Bohr
where e is the elementary
µ is magnetic moment of an
B
charge (item 10-5.1), and
electron in a state with orbital
m is the rest mass of
e
quantum number l = 1 (item 10-14.3)
electron (item 10-2)
due to its orbital motion.
–27 –1
10-10.3 nuclear magneton
µ µ = 5,050 783 24(13) × 10 J T
e�
Ν Ν
µ =
(9-11.3)
N
[2006 CODATA recommended
fr magnéton (m) 2m
p
values].
nucléaire
where e is the elementary
Subscript N stands for nucleus. For
charge (item 10-5.1), and
the neutron magnetic moment,
m is the rest mass of
p subscript n is used. The magnetic
proton (item 10-2)
moments of protons or neutrons differ
from this quantity by their specific
g-factors (item 10-15.2).
s
10-11 spin internal angular Spin is an additive vector quantity.
(—) momentum
fr spin (m)
(ISO 80000-4:2006, item
4-12) of a particle or a
particle system
8 © ISO 2009 – All rights reserved

ISO 80000-10:2009(E)
UNITS ATOMIC AND NUCLEAR PHYSICS
Item No. Name Symbol Definition Conversion factors and remarks
10-10.a ampere square
A · m
metre
2 –1
10-11.a kilogram metre
kg · m · s
squared per
second
(continued)
ISO 80000-10:2009(E)
ATOMIC AND NUCLEAR PHYSICS QUANTITIES
Item No. Name Symbol Definition Remarks
10-12 total angular vector quantity in a In atomic and nuclear physics, orbital
J
(—)  momentum quantum microsystem angular momentum is usually
composed of angular
denoted by l or L instead of Λ.
fr moment (m)
momentum Λ
cinétique
The magnitude of J is quantized so
(ISO 80000-4:2006, item
total 22
that Jj=+�j 1 , where j is the
()
4-12) and spin s (item
total angular momentum quantum
10-11)
number (item 10-14.6).
Total angular momentum and
magnetic dipole moment have the
same direction.
j is not the magnitude of the total
angular momentum J but its
projection onto the quantization axis,
divided by �.
10-13.1 gyromagnetic
γ µ = γ J
e e
(9-12)  ratio for electron,
magnetogyric
where µ is the magnetic
ratio for electron,
dipole moment (item
gyromagnetic
10-10.1), and
coefficient for
J is the total angular
electron
momentum (item 10-12)
fr coefficient (m)
gyro-
magnétique
de l'électron
γ
10-13.2 gyromagnetic The systematic name is
µ = γ J
(9-12)  ratio, “gyromagnetic coefficient”, but
where µ is the magnetic
magnetogyric “gyromagnetic ratio” is more usual.
ratio,
dipole moment (item
The gyromagnetic ratio of the proton
gyromagnetic
10-10.1), and
is denoted by γ .
coefficient p
J is the total angular
8 –1 –1
momentum (item 10-12)
γ = 2,675 222 099(70) × 10 s T
fr coefficient (m)
p
gyro-
[2006 CODATA recommended
magnétique
values].
10 © ISO 2009 – All rights reserved

ISO 80000-10:2009(E)
UNITS ATOMIC AND NUCLEAR PHYSICS
Item No. Name Symbol Definition Conversion factors and remarks
10-12.a joule second J · s
2 2 –1 –1
10-13.a ampere square
A · m /(J · s) 1 A · m /(J · s) = 1 A · s/kg = 1 T · s
metre per
joule second
(continued)
ISO 80000-10:2009(E)
ATOMIC AND NUCLEAR PHYSICS QUANTITIES
Item No. Name Symbol Definition Remarks
10-14.1 quantum number number describing Electron states determine the binding
n, l, m,
(—) particular state of a energy E =Enm(, , ,j s) in an atom.
j, s, F
fr nombre (m)
quantum microsystem
Capitals L, M, J, S are usually
quantique
used for the whole system.
The spatial probability distribution of
ψ
an electron is given by where ψ
is its wave function. For an electron in
an H-atom in a non-relativistic
approximation, it can be presented as
m
ψ(rR, ϑ, ϕ)=⋅()Yr (ϑ,ϕ)
nl l
where
r,,ϑ ϕ are spherical coordinates
(ISO 80000-2:2009, item 2-16.3) with
respect to the nucleus and to a given
(quantization) axis,
R ()r
is the radial distribution
nl
m
function and Y(ϑ,ϕ) are spherical
l
harmonics.
In the Bohr model of one-electron
atoms, n , l and m define the
possible orbits of an electron around
the nucleus.
n
10-14.2 principal quantum atomic quantum number
In the Bohr model, n=∞1, 2,,… is
(9-23)  number
related to the number n −1
related to the binding energy of an
of radial nodes of one-
electron and the radius of spherical
fr nombre (m)
electron wave functions orbits (principal axis of the elliptic
quantique
orbits).
principal
For an electron in an H-atom, the
semi-classical radius of its orbit is
ra= n and its binding energy is
n 0
E =En/ .
n H
10-14.3 orbital angular atomic quantum number 22
ll,,L
i ll=+�()l 1 , ln=−01,,…, 1.
(9-18)  momentum related to the orbital
quantum
angular momentum l of a
l refers to a specific particle i;
i
number
one-electron state
L is used for the whole system.
fr nombre (m)
An electron in an H-atom for l = 0
quantique du
appears as a spherical cloud. In the
moment
Bohr model, it is related to the form of
cinétique
the orbit.
orbital,
nombre (m)
quantique
orbital
12 © ISO 2009 – All rights reserved

ISO 80000-10:2009(E)
UNITS ATOMIC AND NUCLEAR PHYSICS
Item No. Name Symbol Definition Conversion factors and remarks
10-14.a one 1 See the Introduction, 0.3.2.
(continued)
ISO 80000-10:2009(E)
ATOMIC AND NUCLEAR PHYSICS QUANTITIES
Item No. Name Symbol Definition Remarks
10-14.4 magnetic
atomic quantum numbers lm= �, jm= �, s = m� with the
mm,,M
z l z j z s
i
(9-24)  quantum
related to the the z- ranges from −l to l, from − j to j,
number
component l , j or s and ±1/2, respectively.
z z z
fr nombre (m) of the orbital, total or spin
m refers to a specific particle i;
i
quantique
angular momentum
M is used for the whole system.
magnétique
Subscripts l, s, j, etc., as
appropriate, indicate the angular
momentum involved.
s
10-14.5 spin quantum characteristic quantum
Fermions have s =1/ 2 or s =3/ 2.
(9-19)  number number of a particle,
Observed bosons have s = 0 or s = 1.
related to its spin angular
The total spin quantum number S of
fr nombre (m)
momentum s:
an atom is related to the total spin
quantique
s=�ss()+1
(angular momentum), which is the
du spin
sum of the spins of the electrons.
It has the possible values
S = 0,1, 2,… for even Z and
1 3
S = ,,… for odd Z.
10-14.6 total angular quantum number in an
j
jj,,J refers to a specific particle i;
i i
(9-20)  momentum atom describing
J is used for the whole system.
quantum magnitude of total
Care has to be taken, as quantum
number
angular momentum J
number J is not the magnitude of
(item 10-12)
fr nombre (m)
total angular momentum J (item
quantique du
10-12).
moment
cinétique
The two values of j are l ±1/ 2.
total
(See item 10-14.3.)
Here, “total” does not mean
“complete”.
10-14.7 nuclear spin quantum number related
I Nuclear spin is composed of spins of
(9-21)  quantum to the total angular
the nucleons (protons and neutrons)
number
momentum J of a
and their (orbital) motions.
nucleus in any specified
fr nombre (m) In principle there is no upper limit for
state, normally called
quantique
the nuclear spin quantum number. It
nuclear spin:
de spin
has possible values I = 0,1, 2… for
nucléaire II=+�(1I ) 1 35
even A and I = ,, ,… for odd A.
22 2
In nuclear and particle physics, J is
often used.
14 © ISO 2009 – All rights reserved

ISO 80000-10:2009(E)
UNITS ATOMIC AND NUCLEAR PHYSICS
Item No. Name Symbol Definition Conversion factors and remarks
10-14.a one 1 See the Introduction, 0.3.2.
(continued)
ISO 80000-10:2009(E)
ATOMIC AND NUCLEAR PHYSICS QUANTITIES
Item No. Name Symbol Definition Remarks
10-14.8 hyperfine quantum number of an
F
The interval of F is I − J , IJ−+1, .,
(9-22)  structure atom describing
I + J.
quantum inclination of the nuclear
number spin with respect to a
This is related to the hyperfine splitting of
quantization axis given
the atomic energy levels due to the
fr nombre (m)
by the magnetic field
interaction between the electron and
quantique de
produced by the orbital
nuclear magnetic moments.
structure
electrons
hyperfine
g
10-15.1 Landé factor of These quantities are also called g-values.
µ
g =
(9-13.1)  atom or electron,
Jµ
The Landé factor can be calculated from
B
g-factor of atom
the expression
or electron
where µ is magnitude of
gL(, ,S J) =
magnetic dipole moment
fr facteur (m)
JJ( ++1)(S S+1)−L(1L+)
(item 10-10.1),
de Landé
1(+−g 1)⋅
e
J is total angular
d'un atome
2(JJ +1)
ou d'un
momentum quantum
where
électron,
number (item 10-14.6),
g = −2,002 319 304 362 2(15)
facteur (m)
e
and µ is the Bohr
B
g d'un atome
is the g-factor of the electron
magneton (item 10-10.2)
ou d'un
[2006 CODATA recommended values].
électron
g
10-15.2 g-factor of The g-factors for nuclei or nucleons are
µ
g =
(9-13.2)
nucleus or known from measurements; e.g. the
Iµ
B
nuclear particle
g-factor of the proton is
where µ is magnitude of
g = 5,585 694 713(46)
fr facteur (m) p
magnetic dipole moment
g d'un noyau [2006 CODATA recommended values].
(item 10-10.1),
ou d'une
I is nuclear angular
particule
nucléaire momentum quantum
number (item 10-14.7),
and µ is the Bohr
B
magneton (item 10-10.2)
16 © ISO 2009 – All rights reserved

ISO 80000-10:2009(E)
UNITS ATOMIC AND NUCLEAR PHYSICS
Item No. Name Symbol Definition Conversion factors and remarks
10-14.a one 1 See the Introduction, 0.3.2.
10-15.a one 1 See the Introduction, 0.3.2.
(continued)
ISO 80000-10:2009(E)
ATOMIC AND NUCLEAR PHYSICS QUANTITIES
Item No. Name Symbol Definition Remarks
10-16.1 Larmor angular e The quantity
ω
L
ω = B
L
(9-14.1)
frequency
νω= / 2π
2m
LL
e
fr pulsation (f) de
is called the Larmor frequency.
where e is the elementary
Larmor
charge (item 10-5.1),
m is the rest mass of electron
e
(item 10-2), and
B is magnetic flux density
(IEC 80000-6:2008, item
6-21)
10-16.2 nuclear
ω ω = γ B
N N
(9-14.2)  precession
where γ is the gyromagnetic
angular
frequency
coefficient (item 10-13.2),
and B is magnetic flux density
fr pulsation (f) de
(IEC 80000-6:2008, item 6-21)
précession
nucléaire de
Larmor
10-17 cyclotron angular The quantity
ω q
c
(9-15)  frequency ω = B
νω= / 2π
c
cc
m
fr puIsation (f)
is called the cyclotron frequency.
where q is electric charge
cycIotron
(IEC 80000-6:2008, item 6-2) of
the particle, m is its mass
(ISO 80000-4:2006, item 4-1),
and B is the magnitude of the
magnetic flux density
(IEC 80000-6:2008, item 6-21)
10-18 nuclear 22 The electric nuclear quadrupole
Q
Qe=−()1/ (3z r)ρ(xy,,z)dV
∫
(9-16)  quadrupole
moment is eQ.
moment in the quantum state with the
This value is equal to the
nuclear spin in the field
fr moment (m)
z-component of the diagonalized
direction ()z , where ρ(,xy,z)
quadripolaire
tensor of quadrupole moment.
is the nuclear electric charge
nucléaire
density (IEC 80000-6:2008,
item 6-3), e is the elementary
charge (item 10-5.1),
22 2 2
rx=+y+z , and
dV is the volume element
ddx yzd
18 © ISO 2009 – All rights reserved

ISO 80000-10:2009(E)
UNITS ATOMIC AND NUCLEAR PHYSICS
Item No. Name Symbol Definition Conversion factors and remarks
10-16.a radian per rad/s See the Introduction, 0.3.2.
second
–1
10-16.b second to the
s
power minus
one
10-17.a radian per rad/s
second
–1
10-17.b second to the
s
power minus
one
10-18.a metre squared
m
(continued)
ISO 80000-10:2009(E)
ATOMIC AND NUCLEAR PHYSICS QUANTITIES
Item No. Name Symbol Definition Remarks
10-19 nuclear radius conventional radius of This quantity is not exactly defined. It
R
(9-17)
sphere in which the is given approximately for nuclei in
fr rayon (m)
nuclear matter is included their ground state only by
nucléaire
1/ 3
Rr= A
−15
where r ≈ 1,2 × 10 m and A is
the nucleon number.
α
10-20 fine-structure 2 α = 1/137,035 999 679(94)
e
(9-25)  constant
α =
[2006 CODATA recommended
4πε�c
00 values].
fr constante (f)
de structure
where e is the elementary This is a factor historically related to
fine
the change and splitting of atomic
charge (item 10-5.1),
energy levels due to relativistic
ε is the electric constant
effects.
(IEC 80000-6:2008, item
6-14.1), � is the reduced
Planck constant (item
10-6.2), and c is the
speed of light in vacuum
(ISO 80000-7:2008, item
7-4.1)
10-21 electron radius 2
This quantity corresponds to the
r
e e
(9-26)
r =
electrostatic energy E of a charge
e
fr rayon (m) de 2
4πε mc
0e0
distributed inside a sphere of radius
l'électron
r as if all the rest energy (item 10-3)
where e is the elementary
e
of the electron were attributed to the
charge (item 10-5.1),
energy of electromagnetic origin,
ε is the electric constant
using the relation E =mc .
(IEC 80000-6:2008, item
e0
6-14.1), m is the rest
e –19
r = 2,817 940 289 4(58) × 10 m
e
mass of electron (item
[2006 CODATA recommended
10-2), and c is the speed
values].
of light in vacuum
(ISO 80000-7:2008, item
7-4.1)
10-22 Compton
The wavelength of electromagnetic
λ h
C
λ =
(9-27)  wavelength
C
radiation scattered from free electrons
mc
(Compton scattering) is larger than
fr longueur (f)
where h is the Planck
d'onde de that of the incident radiation by a
constant (item 10-6.1),
Compton
maximum of 2λ .
C
m is the rest mass (item
10-2) of a particle, and
c is the speed of light in
vacuum
(ISO 80000-7:2008, item
7-4.1)
20 © ISO 2009 – All rights reserved

ISO 80000-10:2009(E)
UNITS ATOMIC AND NUCLEAR PHYSICS
Item No. Name Symbol Definition Conversion factors and remarks
10-19.a metre m Nuclear radius is usually expressed
–15
in femtometres. 1 fm = 10 m.
10-20.a one 1 See the Introduction, 0.3.2.
10-21.a metre m
10-22.a metre m
(continued)
ISO 80000-10:2009(E)
ATOMIC AND NUCLEAR PHYSICS QUANTITIES
Item No. Name Symbol Definition Remarks
10-23.1 mass excess
∆
∆=mA−m
au
(9-28.1)
fr excès (m) de
where m is the rest mass
a
masse
(item 10-2) of the atom,
A is its nucleon number
(item 10-1.3), and
m is the unified atomic
u
mass constant (item
10-4.2)
10-23.2 mass defect 1
B If the binding energy of the atomic
B=+Zm()H Nm− m
na
(9-28.2) 2
electrons is neglected, Bc is equal
fr défaut (m) de
where Z is the proton
to the binding energy of the nucleus.
masse
number (item 10-1.1) of
the atom, m()H is atomic
mass (item 10-4.1) of H,
N is neutron number
(item 10-1.2), m is the
n
rest mass (item 10-2) of
the neutron, and m is the
a
rest mass (item 10-2) of
the atom
10-24.1 relative mass
∆ ∆=∆ / m
r ru
(9-29.1)  excess
where ∆ is the mass
fr excès (m) de
excess (item 10-23.1) and
masse relatif
m is the unified atomic
u
mass constant (item
10-4.2)
10-24.2 relative mass
B B =Bm/
r ru
(9-29.2)  defect
where B is the mass
fr défaut (m) de
defect (item 10-23.2) and
masse relatif
m is the unified atomic
u
mass constant (item
10-4.2)
10-25.1 packing fraction
f
fA=∆ /
r
(9-30.1)
fr facteur (m) de
where ∆ is relative mass
r
tassement
excess (item 10-24.1) and
A is the nucleon number
(item 10-1.3)
10-25.2 binding fraction
b
bB= /A
r
...