The mass number is written either after the element name or as asuperscript to the left of an element's symbol. For example, the most common isotope ofcarbon iscarbon-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.[3]
Different types ofradioactive decay are characterized by their changes in mass number as well asatomic number, according to theradioactive displacement law of Fajans and Soddy. For example,uranium-238 usually 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-234 and an alpha particle (4 2He2+ ):[4]
238 92U
→
234 90Th
+
4 2He2+
On the other hand,carbon-14 decays bybeta decay, whereby one neutron is transmuted into a proton with the emission of anelectron and 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).[5] The resulting atom isnitrogen-14, with seven protons and seven neutrons:
14 6C
→
14 7N
+
e−
+
ν e
Beta decay is possible because differentisobars[6] have 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 ray from anuclear isomer ormetastable 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.
The mass number gives an estimate of theisotopic mass measured indaltons (Da). For12C, the isotopic mass is exactly 12, since the dalton is defined as 1/12 of the mass of12C. For other isotopes, the isotopic mass is usually within0.1 Da of the mass number. For example,35Cl (17 protons and 18 neutrons) has a mass number of 35 and an isotopic mass of34.96885.[7] The difference of the actual isotopic mass minus the mass number of an atom is known as themass excess,[8] which for35Cl is –0.03115. Mass excess should not be confused withmass defect, which is the difference between the mass of an atom and its constituent particles (namelyprotons,neutrons andelectrons).
There are two reasons for mass excess, both stemming from the fact that thedalton is based on coercing12 C to 12 daltons:
A neutron's mass is1.00866491606(40) Da[9], which is greater than a proton's,1.0072764665789(83) Da[10]. Thedalton ignores this by assuming equal proportions of each (the reason both protonsand neutrons out-mass 1 Da is explained below), so it inherently loses accuracy as the balance between protons shifts in either direction, such as1 H (0 neutrons) or238 U (significantly more neutrons than protons).
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'smass–energy equivalence relationE =mc2. Thedalton assumes12 C's binding energy of92161.753±0.014 keV, so with more energy, such as62 Ni's545262.286±0.434 keV, actual mass drops, and with less energy, such as1 H's 0, it goes up.
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.[11] The atomic weight is amass ratio, while the mass number is acounted 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 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 (actually35.4527 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,bromine has 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),[12] even though theisotope80Br with such mass is unstable.
^Wang, M.; Audi, G.; Kondev, F. G.; Huang, W. J.; Naimi, S.; Xu, X. (2017). "The AME2016 atomic mass evaluation (II). Tables, graphs, and references".Chinese Physics C.41 (3) 030003.doi:10.1088/1674-1137/41/3/030003.
