View source for Mass number

{{short description|Number of heavy particles in the atomic nucleus}}
{{distinguish|Atomic number|Atomic mass|Relative atomic mass}}
{{Nuclear physics|expanded=Nuclides' classification}}

The '''mass number''' (symbol ''A'', from the German word: ''Atomgewicht'', "atomic weight"),<ref>[[Jensen, William B.]] (2005). The Origins of the Symbols A and Z for Atomic Weight and Number. ''J. Chem. Educ.'' 82: 1764. [http://www.che.uc.edu/jensen/W.%20B.%20Jensen/Reprints/123.%20A%20&%20Z.pdf link].</ref> also called '''atomic mass number''' or '''nucleon number''', is the total number of [[proton]]s and [[neutron]]s (together known as [[nucleon]]s) in an [[atomic nucleus]]. It is approximately equal to the [[atomic mass|''atomic'' (also known as ''isotopic'') mass]] of the [[atom]] expressed in [[Dalton (unit)|dalton]]s. Since protons and neutrons are both [[baryon]]s, the mass number ''A'' is identical with the [[baryon number]] ''B'' of the nucleus (and also of the whole atom or [[ion]]). The mass number is different for each [[isotope]] of a given [[chemical element]], and the difference between the mass number and the [[atomic number]]&nbsp;''Z'' gives the [[Neutron number|number of neutrons]] (''N'') in the nucleus: {{nowrap|1=''N'' = ''A'' − ''Z''}}.<ref>{{cite web |url=http://education.jlab.org/qa/pen_number.html |title=How many protons, electrons and neutrons are in an atom of krypton, carbon, oxygen, neon, silver, gold, etc. ...? |publisher=Thomas Jefferson National Accelerator Facility |access-date=2008-08-27}}</ref>

The mass number is written either after the element name or as a [[superscript]] to the left of an element's symbol. For example, the most common isotope of [[carbon]] is [[carbon-12]], or {{SimpleNuclide|carbon|12}}, which has 6 protons and 6 neutrons. The full isotope symbol would also have the atomic number (''Z'') as a subscript to the left of the element symbol directly below the mass number: {{nuclide|carbon|12}}.<ref>{{cite web|url=http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson35.htm|title=Elemental Notation and Isotopes|publisher=Science Help Online|access-date=2008-08-27|url-status=dead|archive-url=https://web.archive.org/web/20080913063710/http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson35.htm|archive-date=2008-09-13}}</ref>

== Mass number changes in radioactive decay ==
Different types of [[radioactive decay]] are characterized by their changes in mass number as well as [[atomic number]], according to the [[radioactive displacement law of Fajans and Soddy]]. 
For example, [[uranium-238]] usually decays by [[alpha decay]], where the nucleus loses two neutrons and two protons in the form of an [[alpha particle]].  Thus the atomic number and the number of neutrons each decrease by 2 (''Z'': 92 → 90, ''N'': 146 → 144), so that the mass number decreases by 4 (''A'' = 238 → 234); the result is an atom of [[thorium-234]] and an alpha particle ({{nuclide|helium|4|charge=2+}}):<ref name="suchocki">Suchocki, John. ''Conceptual Chemistry'', 2007. Page 119.</ref>
: {| border="0"
|- style="height:2em;"
|{{nuclide|uranium|238}}&nbsp;||→&nbsp;||{{nuclide|thorium|234}}&nbsp;||+&nbsp;||{{nuclide|helium|4|charge=2+}}||
|}

On the other hand, [[carbon-14]] decays by [[beta decay]], whereby one neutron is transmuted into a proton with the emission of an [[electron]] and an [[antineutrino]].  Thus the atomic number increases by 1 (''Z'': 6 → 7) and the mass number remains the same (''A'' = 14), while the number of neutrons decreases by 1 (''N'': 8 → 7).<ref>
{{cite book
  | last = Curran
  | first = Greg
  | title = Homework Helpers
  | url = https://archive.org/details/homeworkhelpersc0000curr
  | url-access = registration
  | publisher = Career Press
  | year = 2004
  | pages = [https://archive.org/details/homeworkhelpersc0000curr/page/78 78–79]
  | isbn = 1-56414-721-5
}}</ref>  The resulting atom is [[nitrogen-14]], with seven protons and seven neutrons:
: {| border="0"
|- style="height:2em;"
|{{nuclide|carbon|14}}&nbsp;||→&nbsp;||{{nuclide|nitrogen|14}}&nbsp;||+&nbsp;||{{SubatomicParticle|Electron}}&nbsp;||+&nbsp;||{{SubatomicParticle|Electron Antineutrino}}
|}

Beta decay is possible because different [[isobar (nuclide)|isobars]]<ref name="isobar">Atoms with the same mass number.</ref> have mass differences on the order of a few [[electron mass]]es. If possible, a nuclide will undergo beta decay to an adjacent isobar with lower mass. In the absence of other decay modes, a cascade of beta decays terminates at the [[beta-stability line|isobar with the lowest atomic mass]].

Another type of radioactive decay without change in mass number is emission of a [[gamma ray]] from a [[nuclear isomer]] or [[metastable]] excited state of an atomic nucleus. Since all the protons and neutrons remain in the nucleus unchanged in this process, the mass number is also unchanged.

== Mass number and isotopic mass ==
The mass number gives an estimate of the [[isotopic mass]] measured in [[Dalton (unit)|dalton]]s (Da). For <sup>12</sup>C, the isotopic mass is exactly 12, since the dalton is defined as 1/12 of the mass of <sup>12</sup>C. For other isotopes, the isotopic mass is usually within {{val|0.1|u=Da}} of the mass number. For example, <sup>35</sup>Cl (17 protons and 18 neutrons) has a mass number of 35 and an isotopic mass of {{val|34.96885}}.{{AME2016 II|ref}} The difference of the actual isotopic mass minus the mass number of an atom is known as the [[mass excess]],<ref>{{cite book |doi=10.1351/goldbook.M03719 |doi-access=free  |chapter=Mass excess, Δ |title=The IUPAC Compendium of Chemical Terminology |year=2014 }}
</ref> which for <sup>35</sup>Cl is –0.03115. Mass excess should not be confused with [[mass defect]], which is the difference between the mass of an atom and its constituent particles (namely [[Proton|protons]], [[Neutron|neutrons]] and [[Electron|electrons]]).

There are two reasons for mass 
excess:
# The neutron is slightly heavier than the proton. This increases the mass of nuclei with more neutrons than protons relative to the dalton based on <sup>12</sup>C with equal numbers of protons and neutrons.
# Nuclear [[binding energy]] varies between nuclei. A nucleus with greater binding energy has a lower total energy, and therefore a lower mass according to Einstein's [[mass–energy equivalence]] relation {{nowrap|1=''E'' = ''mc''<sup>2</sup>}}. For <sup>35</sup>Cl, the isotopic mass is less than 35, so this must be the dominant factor.

== Relative atomic mass of an element ==

The mass number should also not be confused with the [[standard atomic weight]] (also called [[atomic weight]]) of an element, which is the ratio of the average atomic mass of the different isotopes of that element (weighted by abundance) to the [[atomic mass constant]].<ref>{{cite book |doi=10.1351/goldbook.R05258 |doi-access=free |chapter=Relative atomic mass (Atomic weight), A<sub>r</sub> |title=The IUPAC Compendium of Chemical Terminology |year=2014 }}
</ref> The atomic weight is a ''mass'' ratio, while the mass number is a ''counted'' number (and so an integer). 

This weighted average can be quite different from the near-integer values for individual isotopic masses. For instance, there are two main [[isotopes of chlorine]]: chlorine-35 and chlorine-37. In any given sample of chlorine that has not been subjected to mass separation there will be roughly 75% of chlorine atoms which are chlorine-35 and only 25% of chlorine atoms which are chlorine-37. This gives chlorine a relative atomic mass of 35.5 (actually {{val|35.4527|u=g/[[Mole (unit)|mol]]}}).

Moreover, the weighted average mass can be near-integer, but at the same time not corresponding to the mass of any natural isotope. For example, [[bromine]] has only two stable isotopes, <sup>79</sup>Br and <sup>81</sup>Br, naturally present in approximately equal fractions, which leads to the standard atomic mass of bromine close to 80 (79.904 g/mol),<ref>{{cite web |url=http://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl |title=Atomic Weights and Isotopic Compositions for All Elements |publisher=NIST}}</ref> even though the [[Isotopes of bromine|isotope <sup>80</sup>Br]] with such mass is unstable.

== References ==
{{reflist}}

== Further reading ==
* {{cite book |last=Bishop |first=Mark |title=An Introduction to Chemistry |url=http://preparatorychemistry.com |access-date=2008-07-08 |publisher=Chiral Publishing |isbn=978-0-9778105-4-3 |pages=93 |chapter=The Structure of Matter and Chemical Elements (ch. 3) |chapter-url=http://preparatorychemistry.com/Bishop_Book_atoms_3.html}}

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[[Category:Nuclear chemistry]]
[[Category:Chemical quantities]]
[[Category:Chemical properties]]