Variations in average atomic mass may be observed for elements obtained from different sources. Lithium provides an example of this. The isotopic composition of lithium from naturally occurring minerals is \(7.5 \%^{6} \mathrm{Li}\) and 92.5\% \(^{7}\) Li, which have masses of 6.01512 amu and 7.01600 amu, respectively. A commercial source of lithium, recycled from a military source, was \(3.75 \%^{6} \mathrm{Li}\) (and the rest \(^{7} \mathrm{Li}\) ). Calculate the average atomic mass values for each of these two sources.

The atomic mass is a fundamental concept in chemistry which refers to the mass of a single atom, usually expressed in atomic mass units (amu). It accounts for both, the mass of the protons and neutrons in the atom's nucleus, and the tiny mass of the electrons orbiting around it. Although the mass of an electron is negligible in comparison to protons and neutrons, it is accounted for in the calculation of the atomic mass.

For most elements, the atomic mass listed on the periodic table is not a whole number because it is actually a weighted average of all the naturally occurring isotopes of that element. This calculated value reflects both, the masses of the different isotopes and their relative abundance on Earth.

Isotopes are variants of a particular chemical element which differ in neutron number, but have the same number of protons in their atomic nuclei. Despite this difference in neutron count, isotopes of an element exhibit nearly identical chemical behavior. This is because chemical properties are primarily determined by the number of protons and electrons involved in bonding, not the number of neutrons.

However, the atomic masses of isotopes are different - for instance, Carbon-12 has 12 amu because it has 6 protons and 6 neutrons, while Carbon-14 has 14 amu because it has 6 protons and 8 neutrons. Medical treatments, dating techniques such as Carbon dating, and studies in physics and chemistry heavily rely on isotopic differences.

A chemical element is a pure substance consisting entirely of one type of atom characterized by its specific number of protons in the atomic nucleus, known as the atomic number. For example, all atoms with 6 protons in their nuclei are atoms of the chemical element carbon.

The Periodic Table of Elements organizes all known chemical elements based on their atomic number and groups them into categories based on shared properties. Each element has unique characteristics and, in many cases, exists in multiple isotopic forms in nature.

The abundance of isotopes describes how much of each isotope of an element is present in a sample or in the Earth's crust as a whole. This natural abundance varies for different elements and their respective isotopes. One isotope might be dominant and thus will have a greater impact on the average atomic mass. For example, Carbon-12 is much more abundant than Carbon-13 or Carbon-14, making it the major contributor to carbon's average atomic mass.

Isotopic abundance is essential in various scientific fields, including geology, where isotopic variations in materials can provide information regarding the age and formation conditions of minerals or other geological samples.

Isotopic composition refers to the relative proportions of isotopes of a given element in a specific sample, which can differ from the average isotopic abundance found in nature. This is of particular interest when calculating the average atomic mass of a commercial product or a sample with a known isotopic concentration, such as the lithium example from the textbook exercise.

The isotopic composition is calculated by taking into account the individual mass of each isotope and its fractional abundance in a sample. By multiplying the mass of each isotope by its corresponding abundance and summing these products, we arrive at the average atomic mass for the sample in question. This calculation reveals variations in average atomic mass from different sources, as seen in various applications such as medical isotopes, where specific isotopic compositions are critical.