Mass number

Not to be confused withAtomic number,Atomic mass,orRelative atomic mass.

Themass number(symbolA,from the German word:Atomgewicht,"atomic weight" ),also calledatomic mass numberornucleon number,is the total number ofprotonsandneutrons(together known asnucleons) in anatomic nucleus.It is approximately equal to theatomic(also known asisotopic) massof theatomexpressed inatomic mass units.Since protons and neutrons are bothbaryons,the mass numberAis identical with thebaryon numberBof the nucleus (and also of the whole atom orion). The mass number is different for eachisotopeof a givenchemical element,and the difference between the mass number and theatomic numberZgives thenumber of neutrons(N) in the nucleus:N=A−Z.

The mass number is written either after the element name or as asuperscriptto the left of an element's symbol. For example, the most common isotope ofcarboniscarbon-12,or¹²
C
,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:¹²
₆C
.

Mass number changes in radioactive decay

Different types ofradioactive decayare characterized by their changes in mass number as well asatomic number,according to theradioactive displacement law of Fajans and Soddy. For example,uranium-238usually decays byAlpha decay,where the nucleus loses two neutrons and two protons in the form of anAlpha 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 ofthorium-234and an Alpha particle (⁴
₂He²⁺
):

238 92U

→

234 90Th

+

4 2He2+

On the other hand,carbon-14decays bybeta decay,whereby one neutron is transmuted into a proton with the emission of anelectronand anantineutrino.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).The resulting atom isnitrogen-14,with seven protons and seven neutrons:

14 6C

→

14 7N

+

e−

+

ν e

Beta decay is possible because differentisobarshave mass differences on the order of a fewelectron masses.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 theisobar with the lowest atomic mass.

Another type of radioactive decay without change in mass number is emission of agamma rayfrom anuclear isomerormetastableexcited 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 theisotopic massmeasured inatomic mass units(u). For¹²C, the isotopic mass is exactly 12, since the atomic mass unit is defined as 1/12 of the mass of¹²C. For other isotopes, the isotopic mass is usually within 0.1 u of the mass number. For example,³⁵Cl (17 protons and 18 neutrons) has a mass number of 35 and an isotopic mass of 34.96885.The difference of the actual isotopic mass minus the mass number of an atom is known as themass excess,which for³⁵Cl is –0.03115. Mass excess should not be confused withmass defectwhich is the difference between the mass of an atom and its constituent particles (namelyprotons,neutronsandelectrons).

There are two reasons for mass excess:

1. The neutron is slightly heavier than the proton. This increases the mass of nuclei with more neutrons than protons relative to the atomic mass unit scale based on¹²C with equal numbers of protons and neutrons.
2. Nuclearbinding energyvaries between nuclei. A nucleus with greater binding energy has a lower total energy, and therefore a lower mass according to Einstein'smass–energy equivalencerelationE=mc².For³⁵Cl, 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 thestandard atomic weight(also calledatomic weight) of an element, which is the ratio of the average atomic mass of the different isotopes of that element (weighted by abundance) to theatomic mass constant.The atomic weight is amassratio, while the mass number is acountednumber (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 mainisotopes 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 35.4527 g/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,brominehas only two stable isotopes,⁷⁹Br and⁸¹Br, naturally present in approximately equal fractions, which leads to the standard atomic mass of bromine close to 80 (79.904 g/mol),even though theisotope⁸⁰Brwith such mass is unstable.

Further reading

• Bishop, Mark."The Structure of Matter and Chemical Elements (ch. 3)".An Introduction to Chemistry.Chiral Publishing. p. 93.ISBN978-0-9778105-4-3.Retrieved2008-07-08.