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Curve Fitting to Find Missing Elements in Mendeleev's Periodic Table

The first graphic (click "periodic table") shows a 5×5 fragment of Mendeleev's periodic table of the elements, ordered by increasing atomic weights, such that elements with chemical similarities occur in vertical groups. The headings give the formulas for the most stable oxide for elements in each group. Also shown in blue are the specific gravities of the elements. Mendeleev surmised that there must be missing elements in the three orange boxes, to which he gave the provisional names Ekaboron, Ekaaluminum, and Ekasilicon.
As an exercise in curve fitting, the known elements in the third and fourth rows are fitted to second-order polynomials in an attempt to locate the undiscovered elements. The third row gives an atomic-weight fit and a specific-gravity fit . The atomic weight and specific-gravity of Ekaboron are predicted to be and , respectively. These agree reasonably well with the later-discovered element Scandium: 45 and 2.99, shown as blue stars. For the fourth row, the corresponding fits give and . The predictions for Ekaaluminum are and , compared with Gallium: 69.7 and 5.90. For Ekasilicon, and , compared with Germanium: 72.6 and 5.32.

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Reference
[1] S. M. Blinder, Introduction to Quantum Mechanics, Amsterdam: Elsevier, 2004 p. 124.
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