Why is the atomic mass of carbon not listed as 12 on the periodic table if the universal standard is that \({ }_{6}^{12} \mathrm{C}\) has an atomic mass of exactly 12 amu?

When we talk about atomic mass, what we're really discussing is the average weight of all the isotopes of a given element. Isotopes are variations of an element that contain the same number of protons but differ in the number of neutrons. This variance in neutron count leads to different atomic weights for each isotope. The atomic mass you find on the periodic table isn't just a simple number—it represents the collective heft of these isotopes, weighted according to how often they're found in nature.

For instance, even though one of carbon's isotopes, \( ^{12}\mathrm{C} \), has an atomic mass of exactly 12 atomic mass units (amu), the atomic mass reported for carbon on the periodic table isn't 12. This is because it's the average mass derived from all carbon isotopes and their relative abundances, not just \( ^{12}\mathrm{C} \).

Delving into carbon isotopes, we recognize that carbon doesn't come in just one form. It's blessed with three different ones, namely, \( ^{12}\mathrm{C} \), \( ^{13}\mathrm{C} \), and \( ^{14}\mathrm{C} \). The numbers here signal the sum total of protons and neutrons in the nucleus. With \( ^{12}\mathrm{C} \) being the run-of-the-mill variety, accounting for approximately 98.89% of all carbon, its atomic mass carries the most weight in the average. The next, \( ^{13}\mathrm{C} \), makes up about 1.1% and barely affects the atomic mass. Finally, \( ^{14}\mathrm{C} \) is a whisper in the winds of carbon isotopes, being so rare that its impact on the overall atomic mass is minimal.

The notion of a weighted average is paramount when calculating atomic mass. This math reflects the idea that not all isotopes are created, or found, equally. To get the weighted average, we take each isotope's atomic mass and multiply it by its abundance as a percentage—turned into a decimal for simplicity's sake. Such multiplication results in a scaled value, representing the isotope's actual contribution to the average atomic mass.

After doing this for each isotope, we add these scaled values together. For carbon, with \( ^{12}\mathrm{C} \) being so abundant, its multiplicative product overwhelmingly shapes the final average—this is why the minor isotopes, like \( ^{14}\mathrm{C} \), with their paltry presence, do little to shift the mean. This intricate dance delivers an atomic mass value that truly reflects carbon’s isotopic portfolio.

The periodic table is a mosaic of information, telling us not only about atomic masses but also about the behaviors and properties of elements. Every element's box in the table is a treasure trove. It houses not just the atomic mass, but also the atomic number, which is the count of protons and defines the element, as well as the electron configuration which influences chemical reactivity.

The atomic mass featured on each element's box is the weighted average mass based on the element's naturally occurring isotopes, as in the case for carbon we've discussed. This number gives us a more practical understanding since it accounts for the full spectrum of an element's forms as found in nature. The periodic table is the chemistry student's best friend, the guide to the elements, and the trustee of atomic information—a single tableau playing host to the entire known chemical universe.