SIST EN ISO 80000-10:2019
(Main)Quantities and units - Part 10: Atomic and nuclear physics (ISO 80000-10:2019)
Quantities and units - Part 10: Atomic and nuclear physics (ISO 80000-10:2019)
This document gives names, symbols, definitions and units for quantities used in atomic and nuclear
physics. Where appropriate, conversion factors are also given.
Größen und Einheiten - Teil 10: Atom- und Kernphysik (ISO 80000-10:2019)
Dieses Dokument enthält Benennungen, Formelzeichen, Definitionen und Einheiten für Größen, die in der Atom- und Kernphysik verwendet werden. Wo benötigt, sind auch Umrechnungsfaktoren aufgeführt.
Grandeurs et unités - Partie 10: Physique atomique et nucléaire (ISO 80000-10:2019)
Le présent document donne les noms, les symboles, les définitions et les unités des grandeurs utilisées en physique atomique et nucléaire. Des facteurs de conversion sont également indiqués, s'il y a lieu.
Veličine in enote - 10. del: Atomska in jedrska fizika (ISO 80000-10:2019)
Ta dokument podaja imena, simbole, definicije in enote za veličine, ki se uporabljajo v atomski in jedrski fiziki. Kadar je primerno, so navedeni tudi pretvorniki (pretvorni dejavniki).
General Information
Relations
Related Packages
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN ISO 80000-10:2019
01-december-2019
Nadomešča:
SIST EN ISO 80000-10:2013
Veličine in enote - 10. del: Atomska in jedrska fizika (ISO 80000-10:2019)
Quantities and units - Part 10: Atomic and nuclear physics (ISO 80000-10:2019)
Größen und Einheiten - Teil 10: Atom- und Kernphysik (ISO 80000-10:2019)
Grandeurs et unités - Partie 10: Physique atomique et nucléaire (ISO 80000-10:2019)
Ta slovenski standard je istoveten z: EN ISO 80000-10:2019
ICS:
01.060 Veličine in enote Quantities and units
07.030 Fizika. Kemija Physics. Chemistry
SIST EN ISO 80000-10:2019 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
---------------------- Page: 1 ----------------------
SIST EN ISO 80000-10:2019
---------------------- Page: 2 ----------------------
SIST EN ISO 80000-10:2019
EN ISO 80000-10
EUROPEAN STANDARD
NORME EUROPÉENNE
October 2019
EUROPÄISCHE NORM
ICS 01.060 Supersedes EN ISO 80000-10:2013
English Version
Quantities and units - Part 10: Atomic and nuclear physics
(ISO 80000-10:2019)
Grandeurs et unités - Partie 10: Physique atomique et Größen und Einheiten - Teil 10: Atom- und Kernphysik
nucléaire (ISO 80000-10:2019) (ISO 80000-10:2019)
This European Standard was approved by CEN on 5 May 2019.
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, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2019 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 80000-10:2019 E
worldwide for CEN national Members.
---------------------- Page: 3 ----------------------
SIST EN ISO 80000-10:2019
EN ISO 80000-10:2019 (E)
Contents Page
European foreword . 3
2
---------------------- Page: 4 ----------------------
SIST EN ISO 80000-10:2019
EN ISO 80000-10:2019 (E)
European foreword
This document (EN ISO 80000-10:2019) has been prepared by Technical Committee ISO/TC 12
"Quantities and units" in collaboration with Technical Committee CEN/SS F02 “Units and symbols” the
secretariat of which is held by CCMC.
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 April 2020, and conflicting national standards shall be
withdrawn at the latest by April 2020.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 80000-10:2013.
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, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the
United Kingdom.
Endorsement notice
The text of ISO 80000-10:2019 has been approved by CEN as EN ISO 80000-10:2019 without any
modification.
3
---------------------- Page: 5 ----------------------
SIST EN ISO 80000-10:2019
---------------------- Page: 6 ----------------------
SIST EN ISO 80000-10:2019
INTERNATIONAL ISO
STANDARD 80000-10
Second edition
2019-08
Quantities and units —
Part 10:
Atomic and nuclear physics
Grandeurs et unités —
Partie 10: Physique atomique et nucléaire
Reference number
ISO 80000-10:2019(E)
©
ISO 2019
---------------------- Page: 7 ----------------------
SIST EN ISO 80000-10:2019
ISO 80000-10:2019(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2019
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting
on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address
below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Fax: +41 22 749 09 47
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2019 – All rights reserved
---------------------- Page: 8 ----------------------
SIST EN ISO 80000-10:2019
ISO 80000-10:2019(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
Bibliography .41
Alphabetical index .42
© ISO 2019 – All rights reserved iii
---------------------- Page: 9 ----------------------
SIST EN ISO 80000-10:2019
ISO 80000-10:2019(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 which 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.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www. iso. org/directives).
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www. iso.o rg/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www. iso
.org/iso/foreword. html.
This document was prepared by Technical Committee ISO/TC 12, Quantities and units, in collaboration
with Technical Committee IEC/TC 25, Quantities and units.
This second edition cancels and replaces the first edition (ISO 80000-10:2009), which has been
technically revised.
The main changes compared to the previous edition are as follows:
— the table giving the quantities and units has been simplified;
— some definitions and the remarks have been stated physically more precisely;
— definitions in this document have been brought in line with their equivalent ones in ICRU 85a.
A list of all parts in the ISO 80000 and IEC 80000 series can be found on the ISO and IEC websites.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www. iso. org/members. html.
iv © ISO 2019 – All rights reserved
---------------------- Page: 10 ----------------------
SIST EN ISO 80000-10:2019
ISO 80000-10:2019(E)
Introduction
0 Special remarks
0.1 Quantities
Numerical values of physical constants in this document are quoted in the consistent values of the
fundamental physical constants published in CODATA recommended values. The indicated values are
the last known before publication. The user is advised to refer to the CODATA website for the latest
values, https: //physics .nist .gov/cuu/Constants/index .html.
h
The symbol is the reduced Planck constant, it is equal to , where h is the Planck constant.
2π
0.2 Special units
1 eV is the energy acquired by an electron in passing a potential difference of 1 V in vacuum.
0.3 Stochastic and non-stochastic quantities
Differences between results from repeated observations are common in physics. These can arise
from imperfect measurement systems, or from the fact that many physical phenomena are subject to
inherent fluctuations. Quantum-mechanical issues aside, one often needs to distinguish between a
stochastic quantity, the values of which follow a probability distribution, and a non-stochastic quantity
with its unique, expected value (expectation) of such distributions. In many instances the distinction
is not significant because the probability distribution is very narrow. For example, the measurement
of an electric current commonly involves so many electrons that fluctuations contribute negligibly to
inaccuracy in the measurement. However, as the limit of zero electric current is approached, fluctuations
can become manifest. This case, of course, requires a more careful measurement procedure, but perhaps
more importantly illustrates that the significance of stochastic variations of a quantity can depend on
the magnitude of the quantity. Similar considerations apply to ionizing radiation; fluctuations can play
a significant role, and in some cases need to be considered explicitly. Stochastic quantities, such as
the energy imparted and the specific energy imparted (item 10-81.2) but also the number of particle
traversals across microscopic target regions and their probability distributions, have been introduced
as they describe the discontinuous nature of the ionizing radiations as a determinant of radiochemical
and radiobiological effects. In radiation applications involving large numbers of ionizing particles, e.g. in
medicine, radiation protection and materials testing and processing, these fluctuations are adequately
represented by the expected values of the probability distributions. “Non-stochastic quantities” such
as particle fluence (item 10-43), absorbed dose (item 10-81.1) and kerma (item 10-86.1) are based on
these expected values.
This document contains definitions based on a differential quotient of the type dA/dB in which the
quantity A is of a stochastic nature, a situation common in ionizing radiation metrology. In these cases,
quantity A is understood as the expected or mean value whose element ΔA falls into element ΔB. The
differential quotient dA/dB is the limit value of the difference quotient ΔA/ΔB for ΔB → 0. In the remarks
of the definitions falling in this category, a reference to this paragraph is made.
© ISO 2019 – All rights reserved v
---------------------- Page: 11 ----------------------
SIST EN ISO 80000-10:2019
---------------------- Page: 12 ----------------------
SIST EN ISO 80000-10:2019
INTERNATIONAL STANDARD ISO 80000-10:2019(E)
Quantities and units —
Part 10:
Atomic and nuclear physics
1 Scope
This document gives names, symbols, definitions and units for quantities used in atomic and nuclear
physics. Where appropriate, conversion factors are also given.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
The names, symbols, and definitions for quantities and units used in atomic and nuclear physics are
given in Table 1.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https: //www .iso .org/obp
— IEC Electropedia: available at http: //www .electropedia .org/
© ISO 2019 – All rights reserved 1
---------------------- Page: 13 ----------------------
SIST EN ISO 80000-10:2019
ISO 80000-10:2019(E)
2 © ISO 2019 – All rights reserved
Table 1 — Quantities and units used in atomic and nuclear physics
Item No. Quantity Unit Remarks
Name Symbol Definition
10-1.1 atomic number, Z number of protons in an atomic nucleus 1 A nuclide is a species of atom with speci-
fied numbers of protons and neutrons.
proton number
Nuclides with the same value of Z but
different values of N are called isotopes
of an element.
The ordinal number of an element in
the periodic table is equal to the atom-
ic number.
The atomic number equals the quo-
tient of the charge (IEC 80000-6) of
the nucleus and the elementary charge
(ISO 80000-1).
10-1.2 neutron number N number of neutrons in an atomic nucleus 1 Nuclides with the same value of N but
different values of Z are called isotones.
N – Z is called the neutron excess number.
10-1.3 nucleon number, A number of nucleons in an atomic nucleus 1 A = Z + N
mass number Nuclides with the same value of A are
called isobars.
10-2 rest mass, m(X) for particle X, mass (ISO 80000-4) of that particle at rest in kg EXAMPLE
an inertial frame
proper mass m u m(H O) for a water molecule, m for an
X 2 e
electron.
Da
Rest mass is often denoted m .
0
1 u is equal to 1/12 times the mass of a
free carbon 12 atom, at rest and in its
ground state.
1 Da = 1 u
10-3 rest energy E energy E (ISO 80000-5) of a particle at rest: J
0 0
N m
2
Em= c
00 0
2 −2
kg m s
where
m is the rest mass (item 10-2) of that particle, and
0
c is speed of light in vacuum (ISO 80000-1)
0
---------------------- Page: 14 ----------------------
SIST EN ISO 80000-10:2019
ISO 80000-10:2019(E)
© ISO 2019 – All rights reserved 3
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-4.1 atomic mass m(X) rest mass (item 10-2) of an atom X in the ground state kg
m(X)
is called the relative atomic mass.
m u
X
m
u
Da
1 u is equal to 1/12 times the mass of a
free carbon 12 atom, at rest and in its
ground state.
1 Da = 1 u
10-4.2 nuclidic mass m(X) rest mass (item 10-2) of a nuclide X in the ground state kg 1 u is equal to 1/12 times the mass of a
free carbon 12 atom, at rest and in its
m u
X
ground state.
Da
1 Da = 1 u
10-4.3 unified atomic mass m 1/12 of the mass (ISO 80000-4) of an atom of the nuclide kg 1 u is equal to 1/12 times the mass of a
u
12
constant C in the ground state at rest free carbon 12 atom, at rest and in its
u
ground state.
Da
1 Da = 1 u
10-5.1 elementary charge e one of the fundamental constants in the SI system C
(ISO 80000-1), equal to the charge of the proton and oppo-
s A
site to the charge of the electron
10-5.2 charge number, c for a particle, quotient of the electric charge (IEC 80000-6) 1 A particle is said to be electrically neu-
and the elementary charge (ISO 80000-1) tral if its charge number is equal to zero.
ionization number
The charge number of a particle can be
positive, negative, or zero.
The state of charge of a particle may be
presented as a superscript to the symbol
of that particle, e.g.
+ ++ 3+ - -- 3-
H , He , Al , Cl , S , N .
---------------------- Page: 15 ----------------------
SIST EN ISO 80000-10:2019
ISO 80000-10:2019(E)
4 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-6 Bohr radius a radius (ISO 80000-3) of the electron orbital in the hydro- m The radius of the electron orbital in the
0
gen atom in its ground state in the Bohr model of the atom: H atom in its ground state is a in the
0
Å
Bohr model of the atom.
2
4πε
−10
0
ångström (Å), 1 Å: = 10 m
a =
0
2
me
e
where
ε is the electric constant (IEC 80000-6),
0
is the reduced Planck constant (ISO 80000-1),
m is the rest mass (item 10-2) of electron, and
e
e is the elementary charge (ISO 80000-1)
−1
10-7 Rydberg constant R spectroscopic constant that determines the wave numbers m The quantity R = R hc is called the
∞ y ∞ 0
of the lines in the spectrum of hydrogen: Rydberg energy.
2
e
R =
∞
8πε ahc
00 0
where
e is the elementary charge (ISO 80000-1),
ε is the electric constant (IEC 80000-6),
0
a is the Bohr radius (item 10-6),
0
h is the Planck constant (ISO 80000-1), and
c is the speed of light in vacuum (ISO 80000-1)
0
---------------------- Page: 16 ----------------------
SIST EN ISO 80000-10:2019
ISO 80000-10:2019(E)
© ISO 2019 – All rights reserved 5
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-8 Hartree energy E energy (ISO 80000-5) of the electron in a hydrogen atom eV The energy of the electron in an H atom
H
in its ground state: J in its ground state is E .
H
E
h 2 −2
kg m s
2
e
E =
H
4πε a
00
where
e is the elementary charge (ISO 80000-1),
ε is the electric constant (IEC 80000-6), and
0
a is the Bohr radius (item 10-6)
0
2
10-9.1 magnetic dipole μ for a particle, vector (ISO 80000-2) quantity causing a m A For an atom or nucleus, this energy is
moment change to its energy (ISO 80000-5) ΔW in an external mag- quantized and can be written as:
netic field of field flux density B (IEC 80000-6):
W = g μ M B
x
ΔW = −μ · B
where
g is the appropriate g factor (item 10-
14.1 or item 10-14.2), μ is mostly the
x
Bohr magneton or nuclear magneton
(item 10-9.2 or item 10-9.3), M is mag-
netic quantum number (item 10-13.4),
and B is magnitude of the magnetic flux
density.
See also IEC 80000-6.
2
10-9.2 Bohr magneton μ magnitude of the magnetic moment of an electron in a m A
B
state with orbital angular momentum quantum number
l=1 (item 10-13.3) due to its orbital motion:
e
μ =
B
2m
e
where
e is the elementary charge (ISO 80000-1),
is the reduced Planck constant (ISO 80000-1), and
m is the rest mass (item 10-2) of electron
e
---------------------- Page: 17 ----------------------
SIST EN ISO 80000-10:2019
ISO 80000-10:2019(E)
6 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
2
10-9.3 nuclear magneton μ absolute value of the magnetic moment of a nucleus: m A Subscript N stands for nucleus. For the
N
neutron magnetic moment, subscript
e
n is used. The magnetic moments of
μ =
N
protons and neutrons differ from this
2m
p
quantity by their specific g factors (item
where
10-14.2).
e is the elementary charge (ISO 80000-1),
is the reduced Planck constant (ISO 80000-1), and
m is the rest mass (item 10-2) of proton
p
2 −1
10-10 spin s vector (ISO 80000-2) quantity expressing the internal kg m s Spin is an additive vector quantity.
angular momentum (ISO 80000-4) of a particle or a par-
ticle system
10-11 total angular J vector (ISO 80000-2) quantity in a quantum system J s In atomic and nuclear physics, orbital
momentum composed of the vectorial sum of angular momentum L eV s angular momentum is usually denoted
(ISO 80000-4) and spin s (item 10-10) by l or L.
2 −1
kg m s
The magnitude of J is quantized so that:
22
J =+ jj()1
where j is the total angular momentum
quantum number (item 10-13.6).
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 .
---------------------- Page: 18 ----------------------
SIST EN ISO 80000-10:2019
ISO 80000-10:2019(E)
© ISO 2019 – All rights reserved 7
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
2 −1 −1 2 −1 −1
10-12.1 gyromagnetic ratio, γ proportionality constant between the magnetic dipole A m J s 1 A·m /(J·s) = 1 A·s/kg = 1 T ·s
moment and the angular momentum:
magnetogyric ratio, A s/kg The systematic name is “gyromagnetic
μ = γ J coefficient”, but “gyromagnetic ratio” is
−1
gyromagnetic coef- kg s A
more usual.
ficient where
The gyromagnetic ratio of the proton is
μ is the magnetic dipole moment (item 10-9.1), and
denoted by γ .
p
J is the total angular momentum (item 10-11)
The gyromagnetic ratio of the neutron is
denoted by γ .
n
2 −1 −1 2 −1 −1
10-12.2 gyromagnetic ratio γ proportionality constant between the magnetic dipole A m J s 1 A·m /(J·s) = 1 A·s/kg = 1 T ·s
e
of the electron, moment and the angular momentum of the electron
A s/kg
magnetogyric ratio μ = γ J
e −1
kg s A
of the electron,
where
gyromagnetic coeffi-
μ is the magnetic dipole moment (item 10-9.1), and
cient of the electron
J is the total angular momentum (item 10-11)
---------------------- Page: 19 ----------------------
SIST EN ISO 80000-10:2019
ISO 80000-10:2019(E)
8 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-13.1 quantum number N number describing a particular state of a quantum system 1 Electron states determine the binding
L energy E = E(n,l,m,j,s,f ) in an atom.
M
Upper case letters N, L, M, J, S, F are usu-
j
ally used for the whole system.
s
F
The spatial probability distribution of an
2
electron is given by │Ψ│ , where Ψ is its
wave function. For an electron in an H
atom in a non-relativistic approximation,
the wave function can be presented as:
m
ψ (rR,,ϑφ)(=⋅rY)(ϑφ,)
nl l
where
r ,,ϑφ are spherical coordinates
(ISO 80000-2) with respect to the
nucleus and to a given (quantization)
axis, Rr() is the radial distribution
nl
m
function, and Y (,ϑφ) are spherical
l
harmonics.
In the Bohr model of one-electron atoms,
n, l, and m define the possible orbits of
an electron about the nucleus.
10-13.2 principal quantum n atomic quantum number related to the number n−1 of 1 In the Bohr model, n = 1,2,…,∞ is related
number radial nodes of one-electron wave functions to the binding energy of an electron and
the radius of spherical orbits (principal
axis of the elliptic orbits).
For an electron in an H atom, the
semi-classical radius of its orbit is
2
r = a n and its binding energy is
n 0
2
E = E /n .
n H
---------------------- Page: 20 ----------------------
SIST EN ISO 80000-10:2019
ISO 80000-10:2019(E)
© ISO 2019 – All rights reserved 9
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-13.3 orbital angular l atomic quantum number related to the orbital angular 1
2
2
momentum quantum momentum l of a one-electron state l =− ll()1 , ln=−01,,, 1
l
i
number
where
L
l is the orbital angular momentum and
is the reduced Planck constant
(ISO 80000-1).
If reference is made to a specific particle
i, the symbol l is used instead of l;
i
if reference is made to the whole system,
the symbol L is used instead of l.
An electron in an H atom for l = 0 appears
as a spherical cloud. In the Bohr model, it
is related to the form of the orbit.
10-13.4 magnetic quantum m atomic quantum number related to the z component l , j or 1
z z
lm= , jm= , and sm= , with the
zl zj zs
number s , of the orbital, total, or spin angular momentum
z
m
i
ranges from −l to l, from −j to j, and ±1/2,
M
respectively.
m refers to a specific particle i. M is used
i
for the whole system.
Subscripts l, s, j, etc., as appropriate, in-
dicate the angular momentum involved.
is the reduced Planck constant
(ISO 80000-1).
10-13.5 spin quantum s characteristic quantum number s of a particle, related to 1 Spin quantum numbers of fermions are
number its spin (item 10-10), s: odd multiples of 1/2, and those of bos-
ons are integers.
22
s =+ ss()1
where is the reduced Planck constant (ISO 80000-1)
---------------------- Page: 21 ----------------------
SIST EN ISO 80000-10:2019
ISO 80000-10:2019(E)
10 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-13.6 total angular j quantum number in an atom describing the magnitude of 1 j refers to a specific particle i; J is used
i
momentum quantum total angular momentum J (item 10-11) for the whole system.
j
i
number
The quantum number J and the magni-
J
tude of total angular momentum J (item
10-11) are different quantities.
The two values of j are l±1/2. (See item
10-13.3.)
10-13.7 nuclear spin I quantum number related to the total angular momentum 1 Nuclear spin is composed of spins of the
quantum number (item 10-11), J, of a nucleus in any specified state, normally nucleons (protons and neutrons) and
called nuclear spin: their (orbital) motions.
In principle there is no upper limit for
22
J =+ II()1
the nuclear spin quantum number. It has
possible values I = 0,1,2,… for even A and
where is the reduced Planck constant (ISO 80000-1)
1 3
I= ,, for odd A.
2 2
In nuclear and particle physics, J is
often used.
10-13.8 hyperfine structure F quantum number of an atom describing the inclination of 1 The interval of F is │I−J│, │I−J│+1, ., I−J.
quantum number the nuclear spin with respect to a quantization axis given
This is related to the hyperfine splitting
by the magnetic field produced by the orbital electrons
of the atomic energy levels due to the
interaction between the electron and
nuclear magnetic moments.
10-14.1 Landé factor, g quotient of the magnetic dipole moment of an atom, and 1 These quantities are also called g values.
the product of the total angular momentum quantum num-
g factor of atom The Landé factor can be calculated from
ber and the Bohr magneton:
the expression:
μ
g= gL(),,SJ =+11()g −
e
J⋅μ
B
JJ+11++SS −+LL 1
() () ()
where ×
21JJ()+
μ is magnitude of magnetic dipole moment (item 10-9.1),
where g is the g factor of the electron.
e
J is total angular momentum quantum number (item
10-13.6), and
μ is the Bohr magneton (item 10-9.2)
B
---------------------- Page: 22 ----------------------
SIST EN ISO 80000-10:2019
ISO 80000-10:2019(E)
© ISO 2019 – All rights reserved 11
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
10-14.2 g factor of nucleus or g quotient of the magnetic dipole moment of an atom, and 1 The g factors for nuclei or nucleons are
nuclear particle the product of the nuclear spin quantum number and the known from measurements.
nuclear magneton:
μ
g=
I⋅μ
N
where
μ is magnitude of magnetic dipole moment (item 10-9.1),
I is nuclear spin quantum number (item 10-13.7), and
μ is the nuclear magneton (item 10-9.3)
N
−1
10-15.1 Larmor angular ω angular frequency (ISO 80000-3) of the electron angular rad s
L
frequency momentum (ISO 80000-4) vector precession about the
−1
s
axis of an external magnetic field:
e
ω = B
L
2m
e
where
e is the elementary charge (ISO 80000-1),
m is the rest mass (item 10-2) of electron, and
e
B is magnetic flux density (IEC 80000-6)
−1
10-15.2 Larmor frequency ν quotient of Larmor angular frequency (ISO 80000-3) and 2π s
L
−1
10-15.3 nuclear precession ω frequency (ISO 80000-3) by which the nucleus angular rad s
N
angular frequency momentum vector (ISO 80000-4) precesses about the axis
−1
s
of an external magnetic field:
ω = γ B
N
where
γ is the gyromagnetic ratio (item 10-12.1), and
B is magnetic flux density (IEC 80000-6)
---------------------- Page: 23 ----------------------
SIST EN ISO 80000-10:2019
ISO 80000-10:2019(E)
12 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
−1
10-16 cyclotron angular ω quotient o
...
SLOVENSKI STANDARD
oSIST prEN ISO 80000-10:2016
01-oktober-2016
9HOLþLQHLQHQRWHGHO $WRPVNDLQMHGUVNDIL]LND ,62',6
Quantities and units - Part 10: Atomic and nuclear physics (ISO/DIS 80000-10:2016)
Größen und Einheiten - Teil 10: Atom- und Kernphysik (ISO/DIS 80000-10:2016)
Grandeurs et unités - Partie 10: Physique atomique et nucléaire (ISO/DIS 80000-
10:2016)
Ta slovenski standard je istoveten z: prEN ISO 80000-10
ICS:
01.060 9HOLþLQHLQHQRWH Quantities and units
07.030 Fizika. Kemija Physics. Chemistry
oSIST prEN ISO 80000-10:2016 en,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
---------------------- Page: 1 ----------------------
oSIST prEN ISO 80000-10:2016
---------------------- Page: 2 ----------------------
oSIST prEN ISO 80000-10:2016
DRAFT INTERNATIONAL STANDARD
ISO/DIS 80000-10
ISO/TC 12 Secretariat: SIS
Voting begins Voting terminates on:
on: 2016-07-25 2016-10-17
Quantities and units —
Part 10:
Atomic and nuclear physics
Grandeurs et unités —
Partie 10: Physique atomique et nucléaire
ICS: 01.060
ISO/CEN PARALLEL PROCESSING
This draft has been developed within the International Organization for
Standardization (ISO), and processed under the ISO lead mode of collaboration
as defined in the Vienna Agreement.
This draft is hereby submitted to the ISO member bodies and to the CEN member
bodies for a parallel five month enquiry.
THIS DOCUMENT IS A DRAFT CIRCULATED
FOR COMMENT AND APPROVAL. IT IS
THEREFORE SUBJECT TO CHANGE AND MAY
To expedite distribution, this document is circulated as received from the
NOT BE REFERRED TO AS AN INTERNATIONAL
committee secretariat. ISO Central Secretariat work of editing and text
STANDARD UNTIL PUBLISHED AS SUCH.
composition will be undertaken at publication stage.
IN ADDITION TO THEIR EVALUATION AS
BEING ACCEPTABLE FOR INDUSTRIAL,
TECHNOLOGICAL, COMMERCIAL AND
USER PURPOSES, DRAFT INTERNATIONAL This draft is submitted to a parallel vote in ISO and in IEC.
STANDARDS MAY ON OCCASION HAVE TO
BE CONSIDERED IN THE LIGHT OF THEIR
POTENTIAL TO BECOME STANDARDS TO
WHICH REFERENCE MAY BE MADE IN
Reference number
NATIONAL REGULATIONS.
ISO/DIS 80000-10:2016(E)
RECIPIENTS OF THIS DRAFT ARE INVITED
TO SUBMIT, WITH THEIR COMMENTS,
NOTIFICATION OF ANY RELEVANT PATENT
RIGHTS OF WHICH THEY ARE AWARE AND TO
©
PROVIDE SUPPORTING DOCUMENTATION. ISO 2016
---------------------- Page: 3 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2016, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. +41 22 749 01 11
Fax +41 22 749 09 47
copyright@iso.org
www.iso.org
ii © ISO 2016 – All rights reserved
---------------------- Page: 4 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
Contents Page
Foreword . iv
Introduction . vi
0 Special remarks . vi
0.1 Quantities . vi
0.2 Special units . vi
0.3 Stochastic and non-stochastic quantities . vi
1 Scope .1
2 Normative references .1
3 Quantities, units and definitions .1
Annex A (informative) Non-SI units used in atomic and nuclear physics .1
Bibliography .2
© ISO 2016 – All rights reserved
---------------------- Page: 5 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(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 which 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.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the meaning of ISO specific terms and expressions related to conformity
assessment, as well as information about ISO's adherence to the WTO principles in the Technical
Barriers to Trade (TBT) see the following URL: Foreword - Supplementary information
The committee responsible for this document is ISO/TC 12, Quantities and units.
This second edition cancels and replaces the first edition of ISO 80000-10:2009.
ISO 80000 consists of the following parts, under the general title Quantities and units:
Part 1: General
Part 2: Mathematics
Part 3: Space and time
Part 4: Mechanics
Part 5: Thermodynamics
Part 7: Light and Radiation
Part 8: Acoustics
Part 9: Physical chemistry and molecular physics
Part 10: Atomic and nuclear physics
Part 11: Characteristic numbers
Part 12: Condensed matter physics
© ISO 2016 – All rights reserved
---------------------- Page: 6 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
IEC 80000 consists of the following parts (in collaboration with IEC/TC 25), under the general title
Quantities and units:
Part 6: Electromagnetism
Part 13: Information science and technology
Part 14: Telebiometrics related to human physiology
© ISO 2016 – All rights reserved
---------------------- Page: 7 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
Introduction
0 Special remarks
0.1 Quantities
Numerical values of physical constants in ISO 80000-10 are quoted in the consistent values of the
fundamental physical constants published in CODATA recommended values. The indicated values are
the last known before publication. The user is advised to refer to the CODATA website for the latest
values, http://physics.nist.gov/cuu/Constants/index.html
0.2 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 that are relevant for atomic and nuclear physics
are listed in Annex A.
0.3 Stochastic and non-stochastic quantities
Differences between results from repeated observations are common in physics. These can arise from
imperfect measurement systems, or from the fact that many physical phenomena are subject to
inherent fluctuations. Quantum-mechanical issues aside one often needs to distinguish between a
stochastic quantity, the values of which follow a probability distribution, and a non-stochastic quantity
with its unique values, the expected values (expectation) of such distributions. In many instances, the
distinction is not significant because the probability distribution is very narrow. For example, the
measurement of an electric current commonly involves so many electrons that fluctuations contribute
negligibly to inaccuracy in the measurement. However, as the limit of zero electric current is
approached, fluctuations can become manifest. This case of course requires a more careful
measurement procedure, but perhaps more importantly illustrates that the significance of stochastic
variations of a quantity can depend on the magnitude of the quantity. Similar considerations apply to
ionizing radiation; fluctuations can play a significant role, and in some cases need to be considered
explicitly. Stochastic quantities such as the energy imparted and the specific energy imparted (item 10-
80.2) but also the number of particle traversals across microscopic target regions and their probability
distributions have been introduced as they describe the discontinuous nature of the ionizing radiations
as a determinant of radiochemical and radiobiological effects. In radiation applications involving large
numbers of ionizing particles, e.g. in medicine, radiation protection and materials testing and
processing, these fluctuations are adequately represented by the expected values of the probability
distributions. “Non-stochastic quantities” such as the particle fluence (item10-42), the absorbed dose
(item 10-80.1) and the kerma (item10-85) are based on these expected values.
© ISO 2016 – All rights reserved
---------------------- Page: 8 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(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.
Radiation with quantum energies up to an including 10 eV is covered in ISO 80000-7. Radiation with
quantum energies above this value is covered in this Standard. In some applications, like e.g. in far-
ultraviolet lithography, radiation with energies above 10 eV is applied without intentionally making use
of the ionizing property of this radiation. For these cases ISO 80000-7 is applicable.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. 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 and radiation
ISO 80000-9:2009, Quantities and units — Part 9: Physical chemistry and molecular physics
© ISO 2016 – All rights reserved
---------------------- Page: 9 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
© ISO 2016 – All rights reserved
---------------------- Page: 10 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
3 Quantities, units and definitions
The names, symbols, and definitions for quantities and units used in atomic and nuclear physics are given on the following pages.
Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
Z
10-1.1 atomic number, number of protons in an atomic nucleus 1 A nuclide is a species of atom with
specified numbers of protons and
proton number
neutrons.
Nuclides with the same value of Z but
different values of N are called 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 divided by the elementary
charge (item 10-5.1).
10-1.2 neutron number N number of neutrons in an atomic nucleus Nuclides with the same value of N but
different values of Z are called isotones.
N – Z is called the neutron excess
number.
A
10-1.3 nucleon number, number of nucleons in an atomic nucleus A = Z + N
mass number Nuclides with the same value of A are
called isobars.
© ISO 2016 – All rights reserved
---------------------- Page: 11 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
10-2 rest mass, m(X),m for particle X, mass (ISO 80000-4:2006, item 4-1) of that kg Specifically, for an electron:
X
particle at rest
-31
proper mass u
m = 9,109 382 91(40)⋅10 kg
e
Da
Rest mass is often denoted m .
0
1 dalton is equal to 1/12 times the mass
of a free carbon 12 atom, at rest and in
its ground state
1 Da = 1 u
10-3 rest energy J
E energy E of a particle at rest
0 0
N m
2
, where
E = m c
0 0 0
2 −2
m kg s
m is the rest mass (item 10-2) of that particle, and
0
c is the speed of light in vacuum (ISO 80000-7:2008, item
0
7-4.1)
10-4.1 atomic mass, m(X),m rest mass (ISO 80000-4:2006, item 4-1) of an atom or a kg
m
a
a
is called the relative atomic mass.
nuclide X in the ground state
nuclidic mass u
m
u
Da
For a nuclide X, the rest mass may be
denoted m(X).
1 u is equal to 1/12 times the mass of a
m
10-4.2 unified atomic mass 1/12 of the mass (ISO 80000-4:2006, item 4-1) of an atom
u
free carbon 12 atom, at rest and in its
12
constant of the nuclide C in the ground state at rest
ground state
1 Da = 1 u
© ISO 2016 – All rights reserved
---------------------- Page: 12 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
e
10-5.1 elementary charge quantum of electric charge, equal to the charge of the C
proton and opposite to the charge of the electron (IEV-113-
s A
05-17)
c
10-5.2 charge number, for a particle, the electric charge (IEC 80000-6:2008, item 1 A particle is said to be electrically
6-2) divided by the elementary charge (item 10-5.1) neutral if its charge number is equal to
ionization number
zero.
The charge number of a particle can be
positive, negative, or zero.
The state of charge of a particle may be
presented as a superscript to the symbol
of that particle, e.g.,
+ ++ 3+ − − − 3−
H ,He , Al ,Cl ,S ,N
a
10-6 Bohr radius radius of the electron orbital in the hydrogen atom in its m The radius of the electron orbital in the
0
ground state in the Bohr model of the atom H atom in its ground state is a in the
Å 0
Bohr model of the atom.
2
4πε
0
, where
a =
−10
0
ångström (Å), 1 Å ∶= 10 m
2
m e
e
ε is the electric constant (IEC 80000-6:2008, item 6-14.1),
0
is the reduced Planck constant (ISO 80000-1, item ??),
is the rest mass of electron (item 10-2), and
m
e
e is the elementary charge (item 10-5.1)
−1
10-7 Rydberg constant R spectroscopic constant that determines the wave numbers The quantity is called the
m R = R ⋅ hc
∞
y ∞ 0
of the lines in the spectrum of hydrogen
Rydberg energy.
2
e
, where
R =
∞
8πε a hc
0 0 0
© ISO 2016 – All rights reserved
---------------------- Page: 13 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
e is the elementary charge (item 10-5.1),
is the electric constant (IEC 80000-6:2008, item 6-14.1),
ε
0
a is the Bohr radius (item 10-6),
0
h is the Planck constant (ISO 80000-1, item ??), and
c is the speed of light in vacuum (ISO 80000-7:2008, item
0
7-4.1)
quantity related to the energy of the electron in a hydrogen
10-8 Hartree energy E , E eV The energy of the electron in an H atom
H h
atom in its ground state
J in its ground state is E .
H
2 −2
m kg s
E = 2R ⋅ hc
2 H ∞ 0
e
, where
E =
H
4πε a
0 0
e is the elementary charge (item 10-5.1),
ε is the electric constant (IEC 80000-6:2008, item 6-14.1),
0
and is the Bohr radius (item 10-6)
a
0
μ
2
10-9.1 magnetic dipole for a particle or nucleus, a vector quantity causing a change m A For an atom or nucleus, this energy is
moment to its energy (ISO 80000-5:2007, item 5-20.1) in an quantized and can be written as
ΔW
external magnetic of field flux density B (IEC 80000-
, where
W= g⋅µ ⋅M⋅B
x
6:2008, item 6-21)
𝑔 is the appropriate 𝑔 factor (item 10-
ΔW=−μ⋅ B
14.1 or item 10-14.2), is mostly the
µ
x
Bohr magneton or nuclear magneton
(item 10-9.2 or item 10-9.3), M is the
magnetic quantum number (item 10-
13.4), and B is the magnitude of the
magnetic flux density.
See also IEC 80000-6:2008, item 6-23.
© ISO 2016 – All rights reserved
---------------------- Page: 14 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
absolute value of the magnetic moment of an electron in a
10-9.2 Bohr magneton µ is the absolute value of the magnetic
µ
B B
state with orbital quantum number l= 1 (item 10-13.3)
moment of an electron in a state with
due to its orbital motion
orbital quantum number l= 1 (item 10-
13.3) due to its orbital motion.
e
, where
µ =
B
2m
e
e is the elementary charge (item 10-5.1), and
is the reduced Planck constant (ISO 80000-1, item ??),
and m is the rest mass of electron (item 10-2)
e
absolute value of the magnetic moment of a nucleus
10-9.3 nuclear magneton µ Subscript N stands for nucleus. For the
N
neutron magnetic moment, subscript n
e
is used. The magnetic moments of
µ = , where
N
2m
protons and neutrons differ from this
p
quantity by their specific g factors (item
e is the elementary charge (item 10-5.1),
10-14.2).
is the reduced Planck constant (ISO 80000-1, item ??),
and m is the rest mass of proton (item 10-2)
p
2 −1
s
10-10 spin internal angular momentum (ISO 80000-4:2006, item m kg s Spin is an additive vector quantity.
4-12) of a particle or a particle system
10-11 total angular J vector quantity in a quantum microsystem composed of the J s In atomic and nuclear physics, orbital
momentum vectorial sum of angular momentum Λ (ISO 80000-4:2006, eV s angular momentum is usually denoted
item 4-12) and spin s (item 10-10) by l or L instead of Λ .
2 −1
m kg s
The magnitude of J is quantized so that
2 2
J = j(j+ 1), where j is the total
angular momentum quantum number
(item 10-13.6).
Total angular momentum and magnetic
© ISO 2016 – All rights reserved
---------------------- Page: 15 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
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 .
γ quotient of the magnetic dipole moment by the angular 2 −1 −1 −1 −1
2
10-12.1 gyromagnetic ratio, A m J s 1 A·m /(J·s) = 1 A·s/kg = 1 T ·s
momentum
−1
magnetogyric ratio, The systematic name is “gyromagnetic
kg s A
coefficient”, but “gyromagnetic ratio” is
gyromagnetic
, where
μ=γ⋅ J
more usual.
coefficient
μ is the magnetic dipole moment (item 10-9.1), and
The gyromagnetic ratio of the proton is
J is the total angular momentum (item 10-11)
denoted by γ .
p
The gyromagnetic ratio of the neutron is
denoted by γ .
n
10-12.2 gyromagnetic ratio of γ quotient of the electron magnetic dipole moment by the
e
the electron, angular momentum
magnetogyric ratio of
μ=γ ⋅ J , where
e
the electron,
μ is the magnetic dipole moment (item 10-9.1), and
gyromagnetic
is the total angular momentum (item 10-11)
J
coefficient of the
electron
10-13.1 quantum number n, l, m, j, number describing a particular state of a quantum 1 Electron states determine the binding
s, F microsystem energy in an atom.
E= E(n,m, j,s)
Capitals L, M, J, S are usually used for the
whole system.
The spatial probability distribution of an
© ISO 2016 – All rights reserved
---------------------- Page: 16 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
2
electron is given by ψ , where ψ is its
wave function. For an electron in an H
atom in a non-relativistic approxima-
tion, the wave function can be presented
as
m
ψ (r,ϑ,ϕ)= R (r)⋅Y (ϑ,ϕ) , where
nl l
are spherical coordinates (ISO
r,ϑ,ϕ
80000-2:2009, item 2-16.3) with respect
to the nucleus and to a given
(quantization) axis, R (r) is the radial
nl
m
distribution function, and Y (ϑ,ϕ) are
l
spherical harmonics.
In the Bohr model of one-electron
atoms, n, l, and m define the possible
orbits of an electron about the nucleus.
n
10-13.2 principal quantum atomic quantum number related to the number n− 1 of In the Bohr model, n= 1,2,,∞ is
number radial nodes of one-electron wave functions
related to the binding energy of an
electron and the radius of spherical
orbits (principal axis of the elliptic
orbits).
For an electron in an H atom, the semi-
2
classical radius of its orbit is r = a n
n 0
2
and its binding energy is E = E n .
n H
© ISO 2016 – All rights reserved
---------------------- Page: 17 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
2
10-13.3 orbital angular atomic quantum number related to the orbital angular 2
l,l ,L
i
l = l(l−1) , l= 0,1,,n− 1 . where
momentum quantum momentum l of a one-electron state
is the orbital angular momentum.
l
number
refers to a specific particle i;
l
i
L is used for the whole system.
An electron in an H atom for l= 0
appears as a spherical cloud. In the Bohr
model, it is related to the form of the
orbit.
10-13.4 magnetic quantum atomic quantum numbers related to the z component l , j
m,m ,M l = m , j = m, and s = m, with
i z z
z l z j z s
number or s , of the orbital, total, or spin angular momentum
z
the ranges from −l to l, from −j to j, and
± 1 2 , respectively.
refers to a specific particle 𝑖; M is
m
i
used for the whole system.
Subscripts l, s, j, etc., as appropriate,
indicate the angular momentum
involved.
s
10-13.5 spin quantum number characteristic quantum number of a particle, related to its Fermions have s= 1 2 or s= 3 2. Bosons
spin angular momentum s :
have s= 0 or s= 1. The total spin
2 2
quantum number S of an atom is related
s = s(s+ 1)
to the total spin (angular momentum),
which is the sum of the spins of the
electrons.
It has the possible values S= 0,1,2. for
© ISO 2016 – All rights reserved
---------------------- Page: 18 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
1 3
even Z and S= , , for odd Z.
2 2
10-13.6 total angular j, j , J quantum number in an atom describing the magnitude of j refers to a specific particle 𝑖; J is used
i i
momentum quantum total angular momentum J (item 10-11) for the whole system.
number
Care has to be taken, as quantum
number J is not the magnitude of total
angular momentum J (item 10-11).
The two values of j are l± 1/ 2. (See item
10-13.3.)
Here, “total” does not mean “complete”.
I quantum number related to the total angular momentum
10-13.7 nuclear spin quantum J Nuclear spin is composed of spins of the
number nucleons (protons and neutrons) and
of a nucleus in any specified state, normally called nuclear
their (orbital) motions.
spin:
In principle there is no upper limit for
2 2
J = I(I+1)
the nuclear spin quantum number. It has
possible values I= 0,1,2, for even A
1 3
and for odd A.
I= , ,
2 2
In nuclear and particle physics, is
J
often used.
F
10-13.8 hyperfine structure quantum number of an atom describing the inclination of
The interval of F is I− J , I− J+1, .,
quantum number the nuclear spin with respect to a quantization axis given
I+ J .
by the magnetic field produced by the orbital electrons
This is related to the hyperfine splitting
of the atomic energy levels due to the
interaction between the electron and
© ISO 2016 – All rights reserved
---------------------- Page: 19 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
nuclear magnetic moments.
g quotient of the magnetic dipole moment of an atom by the
10-14.1 Landé factor, 1 These quantities are also called g values.
product of the total angular momentum and the Bohr
g factor of atom The Landé factor can be calculated from
magneton
the expression
µ
g(L, S , J)=
g= , where
J⋅µ
B J(J+ 1)+ S(S+ 1)− L(L+ 1)
1+(g − 1)⋅
e
is magnitude of magnetic dipole moment (item 10-9.1), 2J(J+ 1)
µ
where g is the g factor of the electron.
𝐽 is total angular momentum quantum number (item 10-
e
13.6), and
𝜇 is the Bohr magneton (item 10-9.2)
B
g quotient of the magnetic dipole moment of an atom by the
10-14.2 g factor of nucleus or The g factors for nuclei or nucleons are
product of the total angular momentum and the Bohr
nuclear particle known from measurements
magneton
µ
g= , where
I⋅µ
N
µ is magnitude of magnetic dipole moment (item 10-9.1),
I is nuclear angular momentum quantum number (item 10-
13.7), and
µ is the nuclear magneton (item 10-9.2)
N
frequency that the electron angular momentum vector
−1
10-15.1 Larmor angular The quantity is called the
ω rad s ν =ω 2π
L L
L
precesses about the axis of an external magnetic field
frequency
−1
Larmor frequency.
s
e
, where
ω = B
L
2m
e
e is the elementary charge (item 10-5.1),
© ISO 2016 – All rights reserved
---------------------- Page: 20 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
m is the rest mass of electron (item 10-2), and
e
B is magnetic flux density (IEC 80000-6:2008, item 6-21)
the frequency that the nucleus angular momentum vector
10-15.2 nuclear precession
ω
N
precesses about the axis of an external magnetic field
angular frequency
ω =γ⋅ B , where
N
γ is the gyromagnetic ratio (item 10-12.1), and
B is magnetic flux density (IEC 80000-6:2008, item 6-21)
quotient of the product of the electric charge of a particle
−1
10-16.1 cyclotron angular The quantity is called the
rad s v =ω 2π
ω
c c
c
and the magnetic field, by the particle mass
frequency
−1
cyclotron frequency.
s
q
ω = B , where
c
m
q is electric charge (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)
m
10-16.2 gyroradius, r , radius of circular movement of a particle with mass (ISO
r
g L
80000-4:2006, item 4-1), velocity v (ISO 80000-3:2006,
Larmor radius
q
item 3-8.1), and electric charge (IEC 80000-6:2008, item
6-2), moving in a magnetic field with magnetic flux density
B (IEC 80000-6:2008, item 6-21):
m v× B
r =
g
2
qB
© ISO 2016 – All rights reserved
---------------------- Page: 21 ----------------------
oSIST prEN ISO 80000-10:2016
ISO/DIS 80000-10:2016(E)
Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
2
10-17 nuclear quadrupole 𝑄 m The electric nuclear quadrupole moment
z component of the diagonalized tensor of nuclear
moment is e Q.
quadrupole moment
2 2
This value is equal to the z component of
1
Q=( ) (3z − r )ρ(x, y,z)dV
∫
e
the diagonalized tensor of quadrupole
in the quantum state with the nuclear spin in the field
moment.
direction (z), where
ρ(x, y,z) is the nuclear electric charge density
(IEC 80000-6:2008, item 6-3),
𝑒 is the elementary charge (item 10-5.1),
2 2 2 2
r = x + y + z
, and
dV is the volume element dx dy dz
10-18 nuclear radius 𝑅 conventional radius of sphere in which the nuclear matter m This quantity is not exactly defined. It is
is included given approximately for nuclei in their
ground state by
1⁄3
𝑅 =𝑟𝐴
0
−15
where r ≈ 1.2×10 m, and 𝐴 is the
0
nucleon number.
Nuclear radius is usually expressed in
–15
femtometres. 1 fm = 10 m.
10-19 electron radius 𝑟 radius of a sphere such that the relativistic electron energy m This quantity corresponds to the
e
is distributed uniformly electrostatic energy 𝐸 of a charge
2
distributed inside a sphere of radius 𝑟
e
𝑒
𝑟
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.