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An electron shell is a region around an atom's nucleus where electrons can be found, with each shell corresponding to a specific energy level. Understanding electron shells matters because they determine how atoms bond with each other and behave chemically.
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Encyclopedic overview
In chemistry and atomic physics, an electron shell may be thought of as an orbit that electrons follow around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called the "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell"), and so on further and further from the nucleus. The shells correspond to the principal quantum numbers (n = 1, 2, 3, 4 ...) or are labeled alphabetically with the letters used in X-ray notation (K, L, M, ...). Each period on the conventional periodic table of elements represents an electron shell.
Each shell can contain only a fixed number of electrons: the first shell can hold up to two electrons, the second shell can hold up to eight electrons, the third shell can hold up to 18, continuing as the general formula of the nth shell being able to hold up to 2(n) electrons. For an explanation of why electrons exist in these shells, see electron configuration.
Excerpted from Wikipedia’s “electron shell” article, available under the CC BY-SA 4.0 licence.
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