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I've often heard metals as having a "sea of electrons". I was wondering how the actual relationships between the electron shells of individual atoms are... do the electrons orbitals overlap the same space as each other, so the electrons are free to move or do they have to jump from the outermost orbital of their atom to another's? Is it something different entirely?

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    $\begingroup$ (Only) the outermost valence electrons occupy a huge set of closely-spaced orbitals (the overlapping valence and conducting band) that ideally span the whole piece of metal. All other electron shells are bound as usual to one nucleus. de:wp has a picture that i find most instructive de.wikipedia.org/wiki/Leitungsband $\endgroup$ – Karl Jan 5 '18 at 1:16
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The electrons do interact with eachother, and their orbitals do intersect, but electrons in higher orbitals will be, on average, further from the nucleus of the atom. Check out this page on wikipedia: https://en.wikipedia.org/wiki/Atomic_orbital

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