(a) the Bohr–Sommerfeld “solar system” atomic model (with electron spin and the Madelung principle), which provides the magic-number elements that end each row of the table and gives the number of elements in each row,
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(1) In general, whatever the total number of constituent atomic valence electrons, data for isoelectronic molecules tend to be more similar than for adjacent molecules that have more or fewer valence electrons; for triatomic molecules, the electron count is the sum of the atomic group numbers (the sum of the column numbers 1 to 8 in the p-block of the periodic chart of the elements, C1+C2+C3).
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