Atomic mass: Difference between revisions

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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.
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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.
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). 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 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.
The difference between atomic mass and relative atomic mass is that the former has a dimension (u), while the latter is dimensionless.
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.)  
==Handling of isotopic masses==
Different [[isotopes]] of an element have different numbers of neutrons and the same number (the [[atomic number]] ''Z'') of protons. So, different isotopes of a given element have the same charge but differ in mass. For example, the element [[carbon]] (atomic number ''Z'' = 6, i.e., 6 protons) 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 those three isotopes are, respectively, the dimensionless numbers 12, 13.0033548378, and 14.003241988.
 
In practice there are two ways of dealing with the different masses of [[isotope]]s:
#In [[high resolution spectroscopy]] and [[mass spectrometry]] masses of isotopes are observed in the spectra. That is, one can distinguish the spectral peaks arising from the different  [[isotopologue]]s, (same molecule, different isotopic composition) in the sample. In these fields it is common to consider the samples as mixtures of of different isotopologues, in much the same way as when the sample consists of different compounds. Hydrogen chloride,  for instance, would be seen as a mixture of  the following isotopologues: H&ndash;<sup>35</sup>Cl, D&ndash;<sup>35</sup>Cl,  H&ndash;<sup>37</sup>Cl, and D&ndash;<sup>37</sup>Cl.
#In most of practical [[chemistry]] different isotopologues&mdash;always present in  "off-the-shelf" chemicals&mdash;are of no concern whatsoever. In off-the-shelf chemicals the concentrations of different isotopologues are determined by the terrestrial ''natural abundances'' of the isotopes. 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.) In most of practical chemistry the standard weight is used as "the" mass of an element. By using averaged masses the chemist accounts for the fact that different isotopes occur in nature. For instance, the HCl molecule has standard atomic weight 1.00794 + 35.453 = 36.461, which is the value used in almost all chemical calculations.


==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:
The concept of "relative atomic mass" is in principle a simple one, yet there is some confusion about its definition. [http://physics.nist.gov/PhysRefData/Compositions/notes.html NIST] clearly and unambiguously defines the ''relative mass'' of an ''isotope'':
<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, ''CODATA recommended values of the fundamental physical constants: 2002'', Reviews of Modern Physics, vol. '''77''', p. 1  (2005)</ref> who state that (the [[atomic mass constant]] ''m''<sub>u</sub> is a twelfth of the mass of <sup>12</sup>C):  
who state that (they define ''m''<sub>u</sub> as 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 stated  explicitly in the Goldbook what is meant by "average mass", it is likely and plausible that the averaging is over different isotopes weighted by terrestrial isotopic abundance. Hence, according to IUPAC's definition, the ''relative atomic mass'' is the dimensionless version of 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'', which suggests that the recommended value may change in the future when more accurate data become available.


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.
The confusion is created by too many international committees addressing the same, basically very simple, problem of definition.<ref> [http://www.iupac.org/publications/pac/1992/pdf/6410x1535.pdf Article about Atomic Weights] </ref>


==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 of the chemical elements (= for each element, the average atomic mass of all isotopes each weighted by their terrestrial abundance). The uncertainties in the last given decimal are in parentheses.  Parenthesis around the entire number indicate the mass number of the most stable isotope. CS stands for chemical symbol. ''Z'' is the [[atomic number]]. See [[Chemical elements|here]] 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. 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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<tr><th colspan="12"><hr> </tr>
<tr><th colspan="12"><hr> </tr>
<tr><td align="left ">  1  <td>  H    <td width="5%" >  1.00794(7)   <td width="15%"> <td align="left "> 38  <td>  Sr  <td width="5%" >  87.62(1)       <td width="15%">  <td align="left "> 75  <td>  Re  <td width="5%" >  186.207(1)
<tr><td align="left ">  1  <td>  [[Hydrogen|H]]   <td width="5%" >  [[Hydrogen/Atomic mass|{{:Hydrogen/Atomic mass}}]]   <td width="15%"> <td align="left "> 38  <td>  [[Strontium|Sr]] <td width="5%" >  [[Strontium/Atomic mass|{{:Strontium/Atomic mass}}]]       <td width="15%">  <td align="left "> 75  <td>  [[Rhenium|Re]]   <td width="5%" >  [[Rhenium/Atomic mass|{{:Rhenium/Atomic mass}}]]
<tr><td align="left ">  2  <td>  He  <td width="5%" >  4.002602(2)   <td width="15%"> <td align="left "> 39  <td>  Y  <td width="5%" >  88.90585(2)   <td width="15%">  <td align="left "> 76  <td>  Os  <td width="5%" >  190.23(3)
<tr><td align="left ">  2  <td>  [[Helium|He]]   <td width="5%" >  [[Helium/Atomic mass|{{:Helium/Atomic mass}}]]   <td width="15%"> <td align="left "> 39  <td>  [[Yttrium|Y]]   <td width="5%" >  [[Yttrium/Atomic mass|{{:Yttrium/Atomic mass}}]]   <td width="15%">  <td align="left "> 76  <td>  [[Osmium|Os]]   <td width="5%" >  [[Osmium/Atomic mass|{{:Osmium/Atomic mass}}]]
<tr><td align="left ">  3  <td>  Li  <td width="5%" >  6.941(2)     <td width="15%"> <td align="left "> 40  <td>  Zr  <td width="5%" >  91.224(2)     <td width="15%">  <td align="left "> 77  <td>  Ir  <td width="5%" >  192.217(3)
<tr><td align="left ">  3  <td>  [[Lithium|Li]]   <td width="5%" >  [[Lithium/Atomic mass|{{:Lithium/Atomic mass}}]]     <td width="15%"> <td align="left "> 40  <td>  [[Zirconium|Zr]] <td width="5%" >  [[Zirconium/Atomic mass|{{:Zirconium/Atomic mass}}]]     <td width="15%">  <td align="left "> 77  <td>  [[Iridium|Ir]]   <td width="5%" >  [[Iridium/Atomic mass|{{:Iridium/Atomic mass}}]]
<tr><td align="left ">  4  <td>  Be  <td width="5%" >  9.012182(3)   <td width="15%"> <td align="left "> 41  <td>  Nb  <td width="5%" >  92.90638(2)   <td width="15%">  <td align="left "> 78  <td>  Pt  <td width="5%" >  195.078(2)
<tr><td align="left ">  4  <td>  [[Beryllium|Be]]   <td width="5%" >  [[Beryllium/Atomic mass|{{:Beryllium/Atomic mass}}]]   <td width="15%"> <td align="left "> 41  <td>  [[Niobium|Nb]] <td width="5%" >  [[Niobium/Atomic mass|{{:Niobium/Atomic mass}}]]   <td width="15%">  <td align="left "> 78  <td>  [[Platinum|Pt]]   <td width="5%" >  [[Platinum/Atomic mass|{{:Platinum/Atomic mass}}]]
<tr><td align="left ">  5  <td>  B    <td width="5%" >  10.811(7)     <td width="15%"> <td align="left "> 42  <td>  Mo  <td width="5%" >  95.94(2)       <td width="15%">  <td align="left "> 79  <td>  Au  <td width="5%" >  196.96655(2)
<tr><td align="left ">  5  <td>  [[Boron|B]]   <td width="5%" >  {{Atomic mass|Boron}}     <td width="15%"> <td align="left "> 42  <td>  [[Molybdenum|Mo]] <td width="5%" >  {{Atomic mass|Molybdenum}}       <td width="15%">  <td align="left "> 79  <td>  [[Gold|Au]]   <td width="5%" >  {{Atomic mass|Gold}}
<tr><td align="left ">  6  <td>  C    <td width="5%" >  12.0107(8)    <td width="15%"> <td align="left "> 43  <td>  Tc  <td width="5%" >  [98]           <td width="15%">  <td align="left "> 80  <td>  Hg  <td width="5%" >  200.59(2)
<tr><td align="left ">  6  <td>  [[Carbon|C]]   <td width="5%" >  {{Atomic mass|Carbon}}    <td width="15%"> <td align="left "> 43  <td>  [[Technetium|Tc]] <td width="5%" >  {{Atomic mass|Technetium}}           <td width="15%">  <td align="left "> 80  <td>  [[Mercury (element)|Hg]]   <td width="5%" >  {{Atomic mass|Mercury (element)}}
<tr><td align="left ">  7  <td>  N    <td width="5%" >  14.0067(2)   <td width="15%"> <td align="left "> 44  <td>  Ru  <td width="5%" >  101.07(2)     <td width="15%">  <td align="left "> 81  <td>  Tl  <td width="5%" >  204.3833(2)
<tr><td align="left ">  7  <td>  [[Nitrogen|N]]   <td width="5%" >  {{Atomic mass|Nitrogen}}   <td width="15%"> <td align="left "> 44  <td>  [[Ruthenium|Ru]] <td width="5%" >  {{Atomic mass|Ruthenium}}     <td width="15%">  <td align="left "> 81  <td>  [[Thallium|Tl]]   <td width="5%" >  {{Atomic mass|Thallium}}
<tr><td align="left ">  8  <td>  O    <td width="5%" >  15.9994(3)   <td width="15%"> <td align="left "> 45  <td>  Rh  <td width="5%" >  102.90550(2)   <td width="15%">  <td align="left "> 82  <td>  Pb  <td width="5%" >  207.2(1)
<tr><td align="left ">  8  <td>  [[Oxygen|O]]   <td width="5%" >  {{Atomic mass|Oxygen}}   <td width="15%"> <td align="left "> 45  <td>  [[Rhodium|Rh]] <td width="5%" >  {{Atomic mass|Rhodium}}   <td width="15%">  <td align="left "> 82  <td>  [[Lead|Pb]]   <td width="5%" >  {{Atomic mass|Lead}}
<tr><td align="left ">  9  <td>  F    <td width="5%" >  18.9984032(5) <td width="15%"> <td align="left "> 46  <td>  Pd  <td width="5%" >  106.42(1)     <td width="15%">  <td align="left "> 83  <td>  Bi  <td width="5%" >  208.98038(2)
<tr><td align="left ">  9  <td>  [[Fluorine|F]]   <td width="5%" >  {{Atomic mass|Fluorine}} <td width="15%"> <td align="left "> 46  <td>  [[Palladium|Pd]] <td width="5%" >  {{Atomic mass|Palladium}}     <td width="15%">  <td align="left "> 83  <td>  [[Bismuth|Bi]]   <td width="5%" >  {{Atomic mass|Bismuth}}
<tr><td align="left "> 10  <td>  Ne  <td width="5%" >  20.1797(6)   <td width="15%"> <td align="left "> 47  <td>  Ag  <td width="5%" >  107.8682(2)   <td width="15%">  <td align="left "> 84  <td>  Po  <td width="5%" >  [209]
<tr><td align="left "> 10  <td>  [[Neon|Ne]]   <td width="5%" >  {{Atomic mass|Neon}}   <td width="15%"> <td align="left "> 47  <td>  [[Silver|Ag]] <td width="5%" >  {{Atomic mass|Silver}}   <td width="15%">  <td align="left "> 84  <td>  [[Polonium|Po]]   <td width="5%" >  {{Atomic mass|Polonium}}
<tr><td align="left "> 11  <td>  Na  <td width="5%" >  22.989770(2) <td width="15%"> <td align="left "> 48  <td>  Cd  <td width="5%" >  112.411(8)    <td width="15%">  <td align="left "> 85  <td>  At  <td width="5%" >  [210]
<tr><td align="left "> 11  <td>  [[Sodium|Na]]   <td width="5%" >  {{Atomic mass|Sodium}} <td width="15%"> <td align="left "> 48  <td>  [[Cadmium|Cd]] <td width="5%" >  {{Atomic mass|Cadmium}}    <td width="15%">  <td align="left "> 85  <td>  [[Astatine|At]]   <td width="5%" >  {{Atomic mass|Astatine}}
<tr><td align="left "> 12  <td>  Mg  <td width="5%" >  24.3050(6)   <td width="15%"> <td align="left "> 49  <td>  In  <td width="5%" >  114.818(3)     <td width="15%">  <td align="left "> 86  <td>  Rn  <td width="5%" >  [222]
<tr><td align="left "> 12  <td>  [[Magnesium|Mg]]   <td width="5%" >  {{Atomic mass|Magnesium}}   <td width="15%"> <td align="left "> 49  <td>  [[Indium|In]] <td width="5%" >  {{Atomic mass|Indium}}     <td width="15%">  <td align="left "> 86  <td>  [[Radon|Rn]]   <td width="5%" >  {{Atomic mass|Radium}}
<tr><td align="left "> 13  <td>  Al  <td width="5%" >  26.981538(2) <td width="15%"> <td align="left "> 50  <td>  Sn  <td width="5%" >  118.710(7)     <td width="15%">  <td align="left "> 87  <td>  Fr  <td width="5%" >  [223]
<tr><td align="left "> 13  <td>  [[Aluminium|Al]]   <td width="5%" >  {{Atomic mass|Aluminium}} <td width="15%"> <td align="left "> 50  <td>  [[Tin|Sn]] <td width="5%" >  {{Atomic mass|Tin}}     <td width="15%">  <td align="left "> 87  <td>  [[Francium|Fr]]   <td width="5%" >  {{Atomic mass|Francium}}
<tr><td align="left "> 14  <td>  Si  <td width="5%" >  28.0855(3)   <td width="15%"> <td align="left "> 51  <td>  Sb  <td width="5%" >  121.760(1)     <td width="15%">  <td align="left "> 88  <td>  Ra  <td width="5%" >  [226]
<tr><td align="left "> 14  <td>  [[Silicon|Si]]   <td width="5%" >  {{Atomic mass|Silicon}}   <td width="15%"> <td align="left "> 51  <td>  [[Antimony|Sb]] <td width="5%" >  {{Atomic mass|Antimony}}     <td width="15%">  <td align="left "> 88  <td>  [[Radium|Ra]]   <td width="5%" >  {{Atomic mass|Radium}}
<tr><td align="left "> 15  <td>  P    <td width="5%" >  30.973761(2) <td width="15%"> <td align="left "> 52  <td>  Te  <td width="5%" >  127.60(3)     <td width="15%">  <td align="left "> 89  <td>  Ac  <td width="5%" >  [227]
<tr><td align="left "> 15  <td>  [[Phosphorus|P]]   <td width="5%" >  {{Atomic mass|Phosphorus}} <td width="15%"> <td align="left "> 52  <td>  [[Tellurium|Te]] <td width="5%" >  {{Atomic mass|Tellurium}}     <td width="15%">  <td align="left "> 89  <td>  [[Actinium|Ac]]   <td width="5%" >  {{Atomic mass|Actinium}}
<tr><td align="left "> 16  <td>  S    <td width="5%" >  32.065(5)     <td width="15%"> <td align="left "> 53  <td>  I  <td width="5%" >  126.90447(3)   <td width="15%">  <td align="left "> 90  <td>  Th  <td width="5%" >  232.0381(1)
<tr><td align="left "> 16  <td>  [[Sulphur|S]]   <td width="5%" >  {{Atomic mass|Sulfur}}     <td width="15%"> <td align="left "> 53  <td>  [[Iodine|I]]   <td width="5%" >  {{Atomic mass|Iodine}}   <td width="15%">  <td align="left "> 90  <td>  [[Thorium|Th]]   <td width="5%" >  {{Atomic mass|Thorium}}
<tr><td align="left "> 17  <td>  Cl  <td width="5%" >  35.453(2)     <td width="15%"> <td align="left "> 54  <td>  Xe  <td width="5%" >  131.293(6)     <td width="15%">  <td align="left "> 91  <td>  Pa  <td width="5%" >  231.03588(2)
<tr><td align="left "> 17  <td>  [[Chlorine|Cl]]   <td width="5%" >  {{Atomic mass|Chlorine}}     <td width="15%"> <td align="left "> 54  <td>  [[Xenon|Xe]] <td width="5%" >  {{Atomic mass|Xenon}}     <td width="15%">  <td align="left "> 91  <td>  [[Protactinium|Pa]]   <td width="5%" >  {{Atomic mass|Protactinium}}
<tr><td align="left "> 18  <td>  Ar  <td width="5%" >  39.948(1)     <td width="15%"> <td align="left "> 55  <td>  Cs  <td width="5%" >  132.90545(2)   <td width="15%">  <td align="left "> 92  <td>  U    <td width="5%" >  238.02891(3)
<tr><td align="left "> 18  <td>  [[Argon|Ar]]   <td width="5%" >  {{Atomic mass|Argon}}     <td width="15%"> <td align="left "> 55  <td>  [[Caesium|Cs]] <td width="5%" >  {{Atomic mass|Caesium}}   <td width="15%">  <td align="left "> 92  <td>  [[Uranium|U]]   <td width="5%" >  {{Atomic mass|Uranium}}
<tr><td align="left "> 19  <td>  K    <td width="5%" >  39.0983(1)   <td width="15%"> <td align="left "> 56  <td>  Ba  <td width="5%" >  137.327(7)     <td width="15%">  <td align="left "> 93  <td>  Np  <td width="5%" >  [237]
<tr><td align="left "> 19  <td>  [[Potassium|K]]   <td width="5%" >  {{Atomic mass|Potassium}}   <td width="15%"> <td align="left "> 56  <td>  [[Barium|Ba]] <td width="5%" >  {{Atomic mass|Barium}}     <td width="15%">  <td align="left "> 93  <td>  [[Neptunium|Np]]   <td width="5%" >  {{Atomic mass|Neptunium}}
<tr><td align="left "> 20  <td>  Ca  <td width="5%" >  40.078(4)     <td width="15%"> <td align="left "> 57  <td>  La  <td width="5%" >  138.9055(2)   <td width="15%">  <td align="left "> 94  <td>  Pu  <td width="5%" >  [244]
<tr><td align="left "> 20  <td>  [[Calcium|Ca]]   <td width="5%" >  {{Atomic mass|Calcium}}     <td width="15%"> <td align="left "> 57  <td>  [[Lanthanum|La]] <td width="5%" >  {{Atomic mass|Lanthanum}}   <td width="15%">  <td align="left "> 94  <td>  [[Plutonium|Pu]]   <td width="5%" >  {{Atomic mass|Plutonium}}
<tr><td align="left "> 21  <td>  Sc  <td width="5%" >  44.955910(8) <td width="15%"> <td align="left "> 58  <td>  Ce  <td width="5%" >  140.116(1)     <td width="15%">  <td align="left "> 95  <td>  Am  <td width="5%" >  [243]
<tr><td align="left "> 21  <td>  [[Scandium|Sc]]   <td width="5%" >  {{Atomic mass|Scandium}} <td width="15%"> <td align="left "> 58  <td>  [[Cerium|Ce]] <td width="5%" >  {{Atomic mass|Cerium}}     <td width="15%">  <td align="left "> 95  <td>  [[Americium|Am]]   <td width="5%" >  {{Atomic mass|Americium}}
<tr><td align="left "> 22  <td>  Ti  <td width="5%" >  47.867(1)     <td width="15%"> <td align="left "> 59  <td>  Pr  <td width="5%" >  140.90765(2)   <td width="15%">  <td align="left "> 96  <td>  Cm  <td width="5%" >  [247]
<tr><td align="left "> 22  <td>  [[Titanium|Ti]]   <td width="5%" >  {{Atomic mass|Titanium}}     <td width="15%"> <td align="left "> 59  <td>  [[Praseodymium|Pr]] <td width="5%" >  {{Atomic mass|Praseodymium}}   <td width="15%">  <td align="left "> 96  <td>  [[Curium|Cm]]   <td width="5%" >  {{Atomic mass|Curium}}
<tr><td align="left "> 23  <td>  V    <td width="5%" >  50.9415(1)   <td width="15%"> <td align="left "> 60  <td>  Nd  <td width="5%" >  144.24(3)      <td width="15%">  <td align="left "> 97  <td>  Bk  <td width="5%" >  [247]
<tr><td align="left "> 23  <td>  [[Vanadium|V]]   <td width="5%" >  {{Atomic mass|Vanadium}}   <td width="15%"> <td align="left "> 60  <td>  [[Neodymium|Nd]] <td width="5%" >  {{Atomic mass|Neodymium}}      <td width="15%">  <td align="left "> 97  <td>  [[Berkelium|Bk]]   <td width="5%" >  {{Atomic mass|Berkelium}}
<tr><td align="left "> 24  <td>  Cr  <td width="5%" >  51.9961(6)   <td width="15%"> <td align="left "> 61  <td>  Pm  <td width="5%" >  [145]         <td width="15%">  <td align="left "> 98  <td>  Cf  <td width="5%" >  [251]
<tr><td align="left "> 24  <td>  [[Chromium|Cr]]   <td width="5%" >  {{Atomic mass|Chromium}}   <td width="15%"> <td align="left "> 61  <td>  [[Promethium|Pm]] <td width="5%" >  {{Atomic mass|Promethium}}         <td width="15%">  <td align="left "> 98  <td>  [[Californium|Cf]]   <td width="5%" >  {{Atomic mass|Californium}}
<tr><td align="left "> 25  <td>  Mn  <td width="5%" >  54.938049(9) <td width="15%"> <td align="left "> 62  <td>  Sm  <td width="5%" >  150.36(3)     <td width="15%">  <td align="left "> 99  <td>  Es  <td width="5%" >  [252]
<tr><td align="left "> 25  <td>  [[Manganese|Mn]]   <td width="5%" >  {{Atomic mass|Manganese}} <td width="15%"> <td align="left "> 62  <td>  [[Samarium|Sm]] <td width="5%" >  {{Atomic mass|Samarium}}     <td width="15%">  <td align="left "> 99  <td>  [[Einsteinium|Es]]   <td width="5%" >  {{Atomic mass|Einsteinium}}
<tr><td align="left "> 26  <td>  Fe  <td width="5%" >  55.845(2)     <td width="15%"> <td align="left "> 63  <td>  Eu  <td width="5%" >  151.964(1)     <td width="15%">  <td align="left ">100  <td>  Fm  <td width="5%" >  [257]
<tr><td align="left "> 26  <td>  [[Iron|Fe]]   <td width="5%" >  {{Atomic mass|Iron}}     <td width="15%"> <td align="left "> 63  <td>  [[Europium|Eu]] <td width="5%" >  {{Atomic mass|Europium}}     <td width="15%">  <td align="left ">100  <td>  [[Fermium|Fm]]   <td width="5%" >  {{Atomic mass|Fermium}}
<tr><td align="left "> 27  <td>  Co  <td width="5%" >  58.933200(9) <td width="15%"> <td align="left "> 64  <td>  Gd  <td width="5%" >  157.25(3)     <td width="15%">  <td align="left ">101  <td>  Md  <td width="5%" >  [258]
<tr><td align="left "> 27  <td>  [[Cobalt|Co]]   <td width="5%" >  {{Atomic mass|Cobalt}} <td width="15%"> <td align="left "> 64  <td>  [[Gadolinium|Gd]] <td width="5%" >  {{Atomic mass|Gadolinium}}     <td width="15%">  <td align="left ">101  <td>  [[Mendelevium|Md]]   <td width="5%" >  {{Atomic mass|Mendelevium}}
<tr><td align="left "> 28  <td>  Ni  <td width="5%" >  58.6934(2)   <td width="15%"> <td align="left "> 65  <td>  Tb  <td width="5%" >  158.92534(2)   <td width="15%">  <td align="left ">102  <td>  No  <td width="5%" >  [259]
<tr><td align="left "> 28  <td>  [[Nickel|Ni]]   <td width="5%" >  {{Atomic mass|Nickel}}   <td width="15%"> <td align="left "> 65  <td>  [[Terbium|Tb]] <td width="5%" >  {{Atomic mass|Terbium}}   <td width="15%">  <td align="left ">102  <td>  [[Nobelium|No]]   <td width="5%" >  {{Atomic mass|Nobelium}}
<tr><td align="left "> 29  <td>  Cu  <td width="5%" >  63.546(3)     <td width="15%"> <td align="left "> 66  <td>  Dy  <td width="5%" >  162.500(1)     <td width="15%">  <td align="left ">103  <td>  Lr  <td width="5%" >  [262]
<tr><td align="left "> 29  <td>  [[Copper|Cu]]   <td width="5%" >  {{Atomic mass|Copper}}     <td width="15%"> <td align="left "> 66  <td>  [[Dysprosium|Dy]] <td width="5%" >  {{Atomic mass|Dysprosium}}     <td width="15%">  <td align="left ">103  <td>  [[Lawrencium|Lr]]   <td width="5%" >  {{Atomic mass|Lawrencium}}
<tr><td align="left "> 30  <td>  Zn  <td width="5%" >  65.409(4)     <td width="15%"> <td align="left "> 67  <td>  Ho  <td width="5%" >  164.93032(2)   <td width="15%">  <td align="left ">104  <td>  Rf  <td width="5%" >  [261]
<tr><td align="left "> 30  <td>  [[Zinc|Zn]]   <td width="5%" >  {{Atomic mass|Zinc}}     <td width="15%"> <td align="left "> 67  <td>  [[Holmium|Ho]] <td width="5%" >  {{Atomic mass|Holmium}}   <td width="15%">  <td align="left ">104  <td>  [[Rutherfordium|Rf]]   <td width="5%" >  {{Atomic mass|Rutherfordium}}
<tr><td align="left "> 31  <td>  Ga  <td width="5%" >  69.723(1)     <td width="15%"> <td align="left "> 68  <td>  Er  <td width="5%" >  167.259(3)    <td width="15%">  <td align="left ">105  <td>  Db  <td width="5%" >  [262]
<tr><td align="left "> 31  <td>  [[Gallium|Ga]]   <td width="5%" >  {{Atomic mass|Gallium}}     <td width="15%"> <td align="left "> 68  <td>  [[Erbium|Er]] <td width="5%" >  {{Atomic mass|Erbium}}    <td width="15%">  <td align="left ">105  <td>  [[Dubnium|Db]]   <td width="5%" >  {{Atomic mass|Dubnium}}
<tr><td align="left "> 32  <td>  Ge  <td width="5%" >  72.64(1)     <td width="15%"> <td align="left "> 69  <td>  Tm  <td width="5%" >  168.93421(2)   <td width="15%">  <td align="left ">106  <td>  Sg  <td width="5%" >  [266]
<tr><td align="left "> 32  <td>  [[Germanium|Ge]]   <td width="5%" >  {{Atomic mass|Germanium}}     <td width="15%"> <td align="left "> 69  <td>  [[Thulium|Tm]] <td width="5%" >  {{Atomic mass|Thulium}}   <td width="15%">  <td align="left ">106  <td>  [[Seaborgium|Sg]]   <td width="5%" >  {{Atomic mass|Seaborgium}}
<tr><td align="left "> 33  <td>  As  <td width="5%" >  74.92160(2)   <td width="15%"> <td align="left "> 70  <td>  Yb  <td width="5%" >  173.04(3)     <td width="15%">  <td align="left ">107  <td>  Bh  <td width="5%" >  [264]
<tr><td align="left "> 33  <td>  [[Arsenic|As]]   <td width="5%" >  {{Atomic mass|Arsenic}}   <td width="15%"> <td align="left "> 70  <td>  [[Ytterbium|Yb]] <td width="5%" >  {{Atomic mass|Ytterbium}}     <td width="15%">  <td align="left ">107  <td>  [[Bohrium|Bh]]   <td width="5%" >  {{Atomic mass|Bohrium}}
<tr><td align="left "> 34  <td>  Se  <td width="5%" >  78.96(3)     <td width="15%"> <td align="left "> 71  <td>  Lu  <td width="5%" >  174.967(1)     <td width="15%">  <td align="left ">108  <td>  Hs  <td width="5%" >  [277]
<tr><td align="left "> 34  <td>  [[Selenium|Se]]   <td width="5%" >  {{Atomic mass|Selenium}}     <td width="15%"> <td align="left "> 71  <td>  [[Lutetium|Lu]] <td width="5%" >  {{Atomic mass|Lutetium}}     <td width="15%">  <td align="left ">108  <td>  [[Hassium|Hs]]   <td width="5%" >  {{Atomic mass|Hassium}}
<tr><td align="left "> 35  <td>  Br  <td width="5%" >  79.904(1)     <td width="15%"> <td align="left "> 72  <td>  Hf  <td width="5%" >  178.49(2)     <td width="15%">  <td align="left ">109  <td>  Mt  <td width="5%" >  [268]
<tr><td align="left "> 35  <td>  [[Bromine|Br]]   <td width="5%" >  {{Atomic mass|Bromine}}     <td width="15%"> <td align="left "> 72  <td>  [[Hafnium|Hf]] <td width="5%" >  {{Atomic mass|Hafnium}}     <td width="15%">  <td align="left ">109  <td>  [[Meitnerium|Mt]]   <td width="5%" >  {{Atomic mass|Meitnerium}}
<tr><td align="left "> 36  <td>  Kr  <td width="5%" >  83.798(2)     <td width="15%"> <td align="left "> 73  <td>  Ta  <td width="5%" >  180.9479(1)   <td width="15%">  <td align="left ">110  <td>  Ds  <td width="5%" >  [281]
<tr><td align="left "> 36  <td>  [[Krypton|Kr]]   <td width="5%" >  {{Atomic mass|Krypton}}     <td width="15%"> <td align="left "> 73  <td>  [[Tantalum|Ta]] <td width="5%" >  {{Atomic mass|Tantalum}}   <td width="15%">  <td align="left ">110  <td>  [[Darmstadtium|Ds]]   <td width="5%" >  {{Atomic mass|Darmstadtium}}
<tr><td align="left "> 37  <td>  Rb  <td width="5%" >  85.4678(3)   <td width="15%"> <td align="left "> 74  <td>  W  <td width="5%" >  183.84(1)     <td width="15%">  <td align="left ">111  <td>  Rg  <td width="5%" >  [272]
<tr><td align="left "> 37  <td>  [[Rubidium|Rb]]   <td width="5%" >  {{Atomic mass|Rubidium}}   <td width="15%"> <td align="left "> 74  <td>  [[Tungsten|W]]   <td width="5%" >  {{Atomic mass|Tungsten}}     <td width="15%">  <td align="left ">111  <td>  [[Roentgenium|Rg]]   <td width="5%" >  {{Atomic mass|Roentgenium}}
<tr><td colspan="12" ><hr> </tr>
<tr><td colspan="12" ><hr> </tr>
</table>
</table>
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==Notes==
==Notes==
<references />
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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 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.

The difference between atomic mass and relative atomic mass is that the former has a dimension (u), while the latter is dimensionless.

Handling of isotopic masses

Different isotopes of an element have different numbers of neutrons and the same number (the atomic number Z) of protons. So, different isotopes of a given element have the same charge but differ in mass. For example, the element carbon (atomic number Z = 6, i.e., 6 protons) 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 those three isotopes are, respectively, the dimensionless numbers 12, 13.0033548378, and 14.003241988.

In practice there are two ways of dealing with the different masses of isotopes:

  1. In high resolution spectroscopy and mass spectrometry masses of isotopes are observed in the spectra. That is, one can distinguish the spectral peaks arising from the different isotopologues, (same molecule, different isotopic composition) in the sample. In these fields it is common to consider the samples as mixtures of of different isotopologues, in much the same way as when the sample consists of different compounds. Hydrogen chloride, for instance, would be seen as a mixture of the following isotopologues: H–35Cl, D–35Cl, H–37Cl, and D–37Cl.
  2. In most of practical chemistry different isotopologues—always present in "off-the-shelf" chemicals—are of no concern whatsoever. In off-the-shelf chemicals the concentrations of different isotopologues are determined by the terrestrial natural abundances of the isotopes. 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.) In most of practical chemistry the standard weight is used as "the" mass of an element. By using averaged masses the chemist accounts for the fact that different isotopes occur in nature. For instance, the HCl molecule has standard atomic weight 1.00794 + 35.453 = 36.461, which is the value used in almost all chemical calculations.

Note on nomenclature

The concept of "relative atomic mass" is in principle a simple one, yet there is some confusion about its definition. NIST clearly and unambiguously defines the relative mass of an isotope:

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 stated explicitly in the Goldbook what is meant by "average mass", it is likely and plausible that the averaging is over different isotopes weighted by terrestrial isotopic abundance. Hence, according to IUPAC's definition, the relative atomic mass is the dimensionless version of 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, which suggests that the recommended value may change in the future when more accurate data become available.

The confusion is created by too many international committees addressing the same, basically very simple, problem of definition.[2]

Standard atomic weights of the elements

The following table[3] lists the standard atomic weights of the chemical elements (= for each element, the average atomic mass of all isotopes each weighted by their terrestrial abundance). The uncertainties in the last given decimal are in parentheses. Parenthesis around the entire number indicate the mass number of the most stable isotope. CS stands for chemical symbol. Z is the atomic number. See here 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 98.9062 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 226
13 Al 26.981538(2) 50 Sn 118.710(7)g/mol 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 237.0462
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 265
31 Ga 69.723(1) 68 Er 167.259(3) 105 Db 268
32 Ge 72.64(1) 69 Tm 168.93421(2) 106 Sg 271
33 As 74.92160(2) 70 Yb 173.04(3) 107 Bh 272
34 Se 78.96(3) 71 Lu 174.967(1) 108 Hs 270
35 Br 79.904(1) 72 Hf 178.49(2) 109 Mt 276
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 280

Notes

  1. ↑ P. J. Mohr and B. N. Taylor, CODATA recommended values of the fundamental physical constants: 2002, 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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