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In [[chemistry]] and [[physics]], the '''atomic mass''' (formerly '''atomic weight''') is the [[mass]] of an atom expressed in [[unified atomic mass unit]]s (u). The atomic mass is equal in value to relative atomic mass, ''A''<sub>r</sub>(X), where X is an [[isotope]]. While atomic mass has the dimension u, relative atomic mass&mdash;the proportion of an atomic mass to one twelfth of the mass of <sup>12</sup>C&mdash;is dimensionless.  
In [[chemistry]] and [[physics]], '''atomic mass''' (formerly known as '''atomic weight''') is the [[mass]] of an atom expressed in [[unified atomic mass unit]]s (u).  


Different isotopes of an atom have different numbers of neutrons in the atomic nucleus, while, by definition, an atomic nucleus has a fixed number of protons. Different isotopes of the same atom have different masses, due to the differing number of neutrons. For instance, [[carbon]] (six protons) has two stable isotopes and one radioactive&mdash;but long-lived&mdash;isotope. Their respective  atomic masses are, <sup>12</sup>C: 12 u (six neutrons),  <sup>13</sup>C: 13.0033548378 u (seven neutrons), and <sup>14</sup>C: 14.003241988 u (eight neutrons). The relative atomic mass of <sup>12</sup>C is by definition the integral number 12. By the same definition the atomic mass is 12 u.
Atomic mass is numerically equal to '''relative atomic mass''', denoted by ''A''<sub>r</sub>( X), where X is the [[isotope]] of which the mass is indicated. The difference between atomic mass and relative atomic mass is that the former has a dimension (u), while the latter is dimensionless. The relative atomic mass is the ratio of atomic mass to one twelfth of the mass of the nuclide <sup>12</sup>C at rest in its nuclear and electronic ground state.  


In [[high resolution spectroscopy]] and [[mass spectrometry]] masses of different isotopes are observed in the spectra, and in these fields computations are usually done for [[molecule]]s consisting of well defined isotopes. In most of [[chemistry]] this is different. Chemicals used in the laboratory are in general isotopic mixtures: their molecules consist of different isotopes of one and the same element. The proportion of different isotopes in the molecule is determined by the ''natural abundance'' of the isotope.
Recall that different isotopes of an atom have different numbers of neutrons and the same number (the [[atomic number]] ''Z'') of protons. So, different isotopes of a given atom have the same charge but differ in mass.  
Take [[chlorine]] as an example. This element has two stable isotopes:&nbsp; <sup>35</sup>Cl (with a mass of 34.96885271 u) and <sup>37</sup>Cl (with a mass of  36.96590260 u). Of all the chlorine atoms occurring on earth  75.78 % is of the lighter kind, while  24.22 % is the heavier isotope.
The average mass of the Cl atom is thus (34.969&times;75.78 + 36.966&times;24.22)/100 = 35.453 u.


The atomic mass averaged over isotopic abundances is called the  '''standard atomic weight'''. (For historical reasons the term "weight" is  used here.)  
As an example we look at the [[carbon]] atom  (atomic number ''Z'' = 6, i.e., 6 protons). It has two stable isotopes and one radioactive&mdash;but long-lived&mdash;isotope. The respective  atomic masses are, <sup>12</sup>C: 12 u (six neutrons),  <sup>13</sup>C: 13.0033548378 u  (seven neutrons), and <sup>14</sup>C: 14.003241988 u (eight neutrons). The ''relative'' atomic mass of e.g. the isotope <sup>13</sup>C is the dimensionless number 13.0033548378.
 
In [[high resolution spectroscopy]] and [[mass spectrometry]] masses of different isotopes are observed in the spectra, and in these fields computations are usually done for isotopically pure substances.
 
In most of practical [[chemistry]] chemicals are used that are isotopic mixtures: different molecules contain different isotopes. The concentration of different isotopes is determined by the terrestrial ''natural abundance'' of the isotope.
 
Take the element [[chlorine]] as an example. It has two stable isotopes:&nbsp; <sup>35</sup>Cl (with a mass of 34.96885271 u) and <sup>37</sup>Cl (with a mass of  36.96590260 u). Of all the chlorine atoms occurring on earth  75.78 % is of the lighter kind, while  24.22 % is the heavier isotope. The average mass of the Cl atom is
: (34.969&times;75.78 + 36.966&times;24.22)/100 = 35.453 u.
 
The atomic mass averaged over isotopic abundances is called the  '''standard atomic weight'''. (For historical reasons the term "weight" is  still used here.)  


==Note on nomenclature==
==Note on nomenclature==
Although "relative atomic mass" is in principle a simple concept, unfortunately there is confusion about its definition. We followed the lead of [[NIST]], see the [http://physics.nist.gov/PhysRefData/Compositions/notes.html NIST web site], where clearly and unambiguously the ''relative mass'' is defined of an ''isotope''. The site states:
Although the concept "relative atomic mass" is in principle simple, yet there is some confusion about its definition. We followed [[NIST]], see the [http://physics.nist.gov/PhysRefData/Compositions/notes.html NIST web site], where clearly and unambiguously the ''relative mass'' is defined of an ''isotope''. The site states:
<blockquote>
<blockquote>
'''Relative Atomic Mass (of the isotope):''' ''A''<sub>r</sub>(X), where X is an isotope
'''Relative Atomic Mass (of the isotope):''' ''A''<sub>r</sub>(X), where X is an isotope
</blockquote>
</blockquote>
This usage is also followed by Mohr and Taylor<ref>P. J. Mohr and B. N. Taylor, Reviews of Modern Physics, vol. '''77''', p. 1  (2005)</ref>
This usage is followed by Mohr and Taylor<ref>P. J. Mohr and B. N. Taylor, Reviews of Modern Physics, vol. '''77''', p. 1  (2005)</ref>
who state that (they define ''m''<sub>u</sub> as a twelfth of the mass of <sup>12</sup>C):  
who state that (the [[atomic mass constant]] ''m''<sub>u</sub> is a twelfth of the mass of <sup>12</sup>C):  
<blockquote>
<blockquote>
The relative atomic mass ''A''<sub>r</sub>(X) of an elementary particle, atom, or more generally an entity X, is defined by ''A''<sub>r</sub>(X) = ''m''(X) /''m''<sub>u</sub>, where ''m''(X) is the mass of X. Thus ''A''<sub>r</sub>(X) is the numerical value of ''m''(X) when ''m''(X) is expressed
The relative atomic mass ''A''<sub>r</sub>(X) of an elementary particle, atom, or more generally an entity X, is defined by ''A''<sub>r</sub>(X) = ''m''(X) /''m''<sub>u</sub>, where ''m''(X) is the mass of X. Thus ''A''<sub>r</sub>(X) is the numerical value of ''m''(X) when ''m''(X) is expressed
in u, and evidently ''A''<sub>r</sub>(<sup>12</sup>C)=12.
in u, and evidently ''A''<sub>r</sub>(<sup>12</sup>C)=12.
</blockquote>
</blockquote>
However, the official [[IUPAC]]  publication, [http://www.iupac.org/goldbook/R05258.pdf IUPAC Goldbook], defines:
On the other hand, the official [[IUPAC]]  publication, [http://www.iupac.org/goldbook/R05258.pdf IUPAC Goldbook], defines:
<blockquote>
<blockquote>
'''relative atomic mass (atomic weight)''', ''A''<sub>r</sub> <br/>
'''relative atomic mass (atomic weight)''', ''A''<sub>r</sub> <br/>
The ratio of the average mass of the atom to the unified atomic mass unit  
The ratio of the average mass of the atom to the unified atomic mass unit  
</blockquote>
</blockquote>
Although it is not explicitly stated here what the average mass is, it is plausible that the averaging is over different isotopes weighted by terrestrial isotopic abundance. Hence, acccording to IUPAC's definition, the ''relative atomic mass'' is nearly synonymous with the ''standard atomic weight'' defined above. In IUPAC's definition, a standard atomic weight is a ''recommended'' relative atomic mass, which means that IUPAC's standard atomic weight will change over time (because recommendations change regularly), but that IUPAC's relative atomic mass is invariant in time.
Although it is not explicitly stated in the Goldbook what the average mass is, it is likely and plausible that the averaging is over different isotopes weighted by terrestrial isotopic abundance. Hence, acccording to IUPAC's definition, the ''relative atomic mass'' is almost synonymous with the ''standard atomic weight'' defined above.  
 
IUPAC also defines ''standard atomic weight'', but  adds ''recommended'' to its definition, that is, IUPAC defines standard atomic weight as  ''recommended relative atomic mass'', implying that the value may change in the future.


Ref. <ref> [http://www.iupac.org/publications/pac/1992/pdf/6410x1535.pdf Article about Atomic Weights] </ref> makes it clear that this&mdash;messy and unnecessary&mdash;confusion is created by too many international comittees addressing this, basically very simple, problem.
From reading Ref. <ref> [http://www.iupac.org/publications/pac/1992/pdf/6410x1535.pdf Article about Atomic Weights] </ref> it becomes clear that the confusion is created by too many international comittees addressing this, basically very simple, problem of definition.


==Standard Atomic Weights of the Elements==
==Standard Atomic Weights of the Elements==
A table <ref> The numbers in this table are taken from the web site of [[NIST]] on December 2, 2007.
The following table <ref>[http://physics.nist.gov/PhysRefData/Compositions/index.html Physical Reference Data]. The numbers in this table are taken from the web site of [[NIST]] on December 2, 2007. </ref> lists the standard atomic weights. The uncertainties in the last given decimal are in parentheses.  Square brackets [ ] indicate the mass number of the most stable isotope. CS stands for chemical symbol. ''Z'' is the [[atomic number]]. See [[element|this article]] for a list of the full names of the elements.
[http://physics.nist.gov/PhysRefData/Compositions/index.html Physical Reference Data].</ref> is given for the standard atomic weights. The uncertainties in the last given decimal are listed in parentheses.  Square brackets [ ] indicate the mass number of the most stable isotope. CS stands for chemical symbol. ''Z'' is the [[atomic number]]. See [[element|this article]] for a list of the full names of the elements.


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Revision as of 11:19, 20 January 2008

In chemistry and physics, atomic mass (formerly known as atomic weight) is the mass of an atom expressed in unified atomic mass units (u).

Atomic mass is numerically equal to relative atomic mass, denoted by Ar( X), where X is the isotope of which the mass is indicated. The difference between atomic mass and relative atomic mass is that the former has a dimension (u), while the latter is dimensionless. The relative atomic mass is the ratio of atomic mass to one twelfth of the mass of the nuclide 12C at rest in its nuclear and electronic ground state.

Recall that different isotopes of an atom have different numbers of neutrons and the same number (the atomic number Z) of protons. So, different isotopes of a given atom have the same charge but differ in mass.

As an example we look at the carbon atom (atomic number Z = 6, i.e., 6 protons). It has two stable isotopes and one radioactive—but long-lived—isotope. The respective atomic masses are, 12C: 12 u (six neutrons), 13C: 13.0033548378 u (seven neutrons), and 14C: 14.003241988 u (eight neutrons). The relative atomic mass of e.g. the isotope 13C is the dimensionless number 13.0033548378.

In high resolution spectroscopy and mass spectrometry masses of different isotopes are observed in the spectra, and in these fields computations are usually done for isotopically pure substances.

In most of practical chemistry chemicals are used that are isotopic mixtures: different molecules contain different isotopes. The concentration of different isotopes is determined by the terrestrial natural abundance of the isotope.

Take the element chlorine as an example. It has two stable isotopes:  35Cl (with a mass of 34.96885271 u) and 37Cl (with a mass of 36.96590260 u). Of all the chlorine atoms occurring on earth 75.78 % is of the lighter kind, while 24.22 % is the heavier isotope. The average mass of the Cl atom is

(34.969×75.78 + 36.966×24.22)/100 = 35.453 u.

The atomic mass averaged over isotopic abundances is called the standard atomic weight. (For historical reasons the term "weight" is still used here.)

Note on nomenclature

Although the concept "relative atomic mass" is in principle simple, yet there is some confusion about its definition. We followed NIST, see the NIST web site, where clearly and unambiguously the relative mass is defined of an isotope. The site states:

Relative Atomic Mass (of the isotope): Ar(X), where X is an isotope

This usage is followed by Mohr and Taylor[1] who state that (the atomic mass constant mu is a twelfth of the mass of 12C):

The relative atomic mass Ar(X) of an elementary particle, atom, or more generally an entity X, is defined by Ar(X) = m(X) /mu, where m(X) is the mass of X. Thus Ar(X) is the numerical value of m(X) when m(X) is expressed in u, and evidently Ar(12C)=12.

On the other hand, the official IUPAC publication, IUPAC Goldbook, defines:

relative atomic mass (atomic weight), Ar
The ratio of the average mass of the atom to the unified atomic mass unit

Although it is not explicitly stated in the Goldbook what the average mass is, it is likely and plausible that the averaging is over different isotopes weighted by terrestrial isotopic abundance. Hence, acccording to IUPAC's definition, the relative atomic mass is almost synonymous with the standard atomic weight defined above.

IUPAC also defines standard atomic weight, but adds recommended to its definition, that is, IUPAC defines standard atomic weight as recommended relative atomic mass, implying that the value may change in the future.

From reading Ref. [2] it becomes clear that the confusion is created by too many international comittees addressing this, basically very simple, problem of definition.

Standard Atomic Weights of the Elements

The following table [3] lists the standard atomic weights. The uncertainties in the last given decimal are in parentheses. Square brackets [ ] indicate the mass number of the most stable isotope. CS stands for chemical symbol. Z is the atomic number. See this article for a list of the full names of the elements.

ZCS Mass ZCS Mass ZCS Mass
1 H 1.00794(7) 38 Sr 87.62(1) 75 Re 186.207(1)
2 He 4.002602(2) 39 Y 88.90585(2) 76 Os 190.23(3)
3 Li 6.941(2) 40 Zr 91.224(2) 77 Ir 192.217(3)
4 Be 9.012182(3) 41 Nb 92.90638(2) 78 Pt 195.078(2)
5 B 10.811(7) 42 Mo 95.94(2) 79 Au 196.96655(2)
6 C 12.0107(8) 43 Tc [98] 80 Hg 200.59(2)
7 N 14.0067(2) 44 Ru 101.07(2) 81 Tl 204.3833(2)
8 O 15.9994(3) 45 Rh 102.90550(2) 82 Pb 207.2(1)
9 F 18.9984032(5) 46 Pd 106.42(1) 83 Bi 208.98038(2)
10 Ne 20.1797(6) 47 Ag 107.8682(2) 84 Po [209]
11 Na 22.989770(2) 48 Cd 112.411(8) 85 At [210]
12 Mg 24.3050(6) 49 In 114.818(3) 86 Rn [222]
13 Al 26.981538(2) 50 Sn 118.710(7) 87 Fr [223]
14 Si 28.0855(3) 51 Sb 121.760(1) 88 Ra [226]
15 P 30.973761(2) 52 Te 127.60(3) 89 Ac [227]
16 S 32.065(5) 53 I 126.90447(3) 90 Th 232.0381(1)
17 Cl 35.453(2) 54 Xe 131.293(6) 91 Pa 231.03588(2)
18 Ar 39.948(1) 55 Cs 132.90545(2) 92 U 238.02891(3)
19 K 39.0983(1) 56 Ba 137.327(7) 93 Np [237]
20 Ca 40.078(4) 57 La 138.9055(2) 94 Pu [244]
21 Sc 44.955910(8) 58 Ce 140.116(1) 95 Am [243]
22 Ti 47.867(1) 59 Pr 140.90765(2) 96 Cm [247]
23 V 50.9415(1) 60 Nd 144.24(3) 97 Bk [247]
24 Cr 51.9961(6) 61 Pm [145] 98 Cf [251]
25 Mn 54.938049(9) 62 Sm 150.36(3) 99 Es [252]
26 Fe 55.845(2) 63 Eu 151.964(1) 100 Fm [257]
27 Co 58.933200(9) 64 Gd 157.25(3) 101 Md [258]
28 Ni 58.6934(2) 65 Tb 158.92534(2) 102 No [259]
29 Cu 63.546(3) 66 Dy 162.500(1) 103 Lr [262]
30 Zn 65.409(4) 67 Ho 164.93032(2) 104 Rf [261]
31 Ga 69.723(1) 68 Er 167.259(3) 105 Db [262]
32 Ge 72.64(1) 69 Tm 168.93421(2) 106 Sg [266]
33 As 74.92160(2) 70 Yb 173.04(3) 107 Bh [264]
34 Se 78.96(3) 71 Lu 174.967(1) 108 Hs [277]
35 Br 79.904(1) 72 Hf 178.49(2) 109 Mt [268]
36 Kr 83.798(2) 73 Ta 180.9479(1) 110 Ds [281]
37 Rb 85.4678(3) 74 W 183.84(1) 111 Rg [272]

Notes

  1. ↑ P. J. Mohr and B. N. Taylor, Reviews of Modern Physics, vol. 77, p. 1 (2005)
  2. ↑ Article about Atomic Weights
  3. ↑ Physical Reference Data. The numbers in this table are taken from the web site of NIST on December 2, 2007.
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