Calcium, Carbon, and Oxygen in the form of CaCO3 are the dominate ones. A full list would be over a dozen times as long and varies from shell to shell. The origin of a shell can be identified by the exact elemental composition.
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Stable elements do not react because they don't need to. Elements react so that they can gain stability( as stability is gained by filling the outer most shell of the atom). As stable elements already have full outer shells and are stable , they do not react.
The chemical nature of an element is determined (mainly) by the electronic configuration in the outermost shells. However, most elements have isotopes - atomic configurations that have the same outer shells, but which may have a different number of neutrons in the atom core. This gives them the same chemical nature, but a different mass. Many isotopes are unstable in the long run - they will spontaneously disintegrate.
The noble gases are the chemical family composed of elements that have full valence shells. These elements include helium, neon, argon, krypton, xenon, and radon. Due to their full valence shells, noble gases are known for their stability and lack of reactivity with other elements. This stability is attributed to the fact that their outermost energy levels are completely filled with electrons.
The number of shells varies. The row number of the element is the number of shells. They don't really have names, but they're referred to by how many levels they are away from the nucleus.