# When you see the atomic mass number for an element, does it take into account the atomic mass defect?

Sometimes I read that the official atomic mass number for an element on the periodic table only includes natural isotope ratios, other times I read that atomic mass defect, number of electrons, etc. is considered. I am confused.

It can depend on who has published the table; if you care about isotopic composition of your sample, or nuclide masses, you have to read the documentation carefully.

The periodic table provided by the IUPAC, who are the governing body that actually approve the names of new elements, reports two atomic weights for some elements: a "conventional" weight and a "standard" weight, the second of which seems to be a range for some elements. The explanatory text below the table refers to the publication Atomic weights of the elements 2013 (IUPAC Technical Report), which says:

The atomic mass, $m_\text a$, of an unbound neutral atom of carbon-12, $m_\text a ({}^{12}\rm C)$, in its nuclear and electronic ground states is $\rm 12\,Da$ exactly, where $\rm Da$ is the symbol for the unified atomic mass unit, and alternative symbol is $\rm u$. The atomic weight (also called the relative atomic mass) of isotope $^{i}\rm E$ of element $\rm E$, symbol $A_\text r ({}^i \rm E)$, in material $\rm P$ is

$$A_\text r ({}_i {\rm E)_P} = \frac{m_\text a ({}_i \rm E)_P}{m_a(_{12}\rm C)/12} = \frac{m_\text a ({}_i\rm E)_P}{\rm Da} \tag1$$

Thus, the atomic mass of $\rm^{12}C$ is $\rm 12\,Da$, and the atomic weight of $^{12}\rm C$ is $12$ exactly. All other atomic weight values are ratios to the $^{12}\rm C$ standard value and thus are dimensionless numbers. The atomic weight of element $\rm E$, $A_\text r(\rm E)$, in a material $P$ is determined from the relation

$$A_\text r({\rm E)_P} = \sum \left[ x({}^i{\rm E)_P} \times A_\text r({}^i{\rm E)} \right] \tag2$$ where $x({}^i{\rm E)_P}$ is the amount fraction of isotope $^i\rm E$ in material $\rm P$ (also called the isotopic abundance). [... T]he standard atomic weight is a quantity that represents the atomic weights of an element in normal terrestrial materials.

[...]

The Commission recognizes that some users of atomic-weight data only need single values with disregard to their uncertainties. Therefore, for those elements with standard atomic weights given as intervals, the Commission provides conventional atomic-weight values (Table 3). These conventional quantity values have been selected so that most or all atomic-weight variation in normal materials is covered in an interval of plus or minus one in the last digit.

So we have that the IUPAC atomic weights correspond to the weights of free, neutral atoms in their electronic ground states, weighted by the isotopic composition of the element when found naturally, with different published values corresponding to different levels of implied precision and a recipe for measuring the average atomic weight of an element in your sample if you are concerned that your sample is not "typical." For example, papers on historical climate data frequently use changing isotopic concentrations in old materials (such as the fraction of oxygen that is oxygen-18) as proxy measurements for historical biological activity and/or temperature.

The elements without stable isotopes don't have these conventional atomic weights; the relevant table has a footnote stating

*Element has no stable isotopes. One or more representative isotopes are given in Table 4 with the appropriate relative atomic mass and half-life. However, four such elements (Bi, Th, Pa, and U) do have a characteristic terrestrial isotopic composition, and for these elements, standard atomic weights are tabulated.

For more careful definitions of a "typical" isotopic abundance, see the IUPAC report and its references.

The Nuclear Wallet Cards, maintained by the National Nuclear Data Center, are one tabulation of the masses of all known isotopes. That publication tabulates the "mass excess," $\Delta$, which they define as the difference between an isotope's mass $M$ in atomic mass units and its atomic number $A=Z+N$. The definition $\Delta(^{12}\rm C) = 0$ suggests strongly that these are the same as the IUPAC masses --- that is, the masses of free, electrically neutral atoms in their electronic ground states. A homework project, if you want to make sure you believe this, would be to take the masses and "natural" abundances from the Nuclear Wallet Cards and reproduce the IUPAC "conventional" weights for a few interesting elements. The precision with which the mass excesses are tabulated suggests that essentially all of the uncertainties in the "conventional" atomic weights are due to variations in isotopic composition.