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The existence of electron shells was first observed experimentally in Charles Barkla's and Henry Moseley's X-ray absorption studies. Barkla labelled them with the letters K, L, M, etc. (The origin of this terminology was alphabetic. K and L were originally called B and A, but were later renamed to leave room for hypothetical spectral lines that were never discovered.) These letters were later found to correspond to the n-values 1, 2, 3, etc. They are used in the spectroscopic Siegbahn notation.
The name for electron shells originates from the Bohr model, in which groups of electrons were believed to orbit the nucleus at certain distances, so that their orbits formed "shells".
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