Direct Dependence of Covalent, Van Der Waals, and Valence Shell Radii of Atoms on their Bohr Radii for the Main Group Elements
Institute of Biophysics, Academy of Sciences on the Czech Republic
Královopolská, Brno, Czech Republic
Recent work by the author has shown that ionic, atomic, and the ground state Bohr radii (aB) of elements are inter-related. An earlier work by others has shown that the ratio, van der Waals radii/de Broglie wavelengths is nearly constant for each group of some non-metallic elements. Since aB and the de Broglie wavelength are directly related, the author shows here that, in fact, for all the main group elements from 1A – 8A, the van der Waals radii are directly proportional to aB. It was found that the valence shell and covalent radii also vary linearly with aB. Thus, all the above radii (R) can be unified by a single linear equation, R = maB + c. Therefore, aB can be considered as a unit of length for the above radii as much as for the smaller Compton wavelength and classical radii (sum) of electron and proton.
It was pointed out (Bondi 1964; Morrison 1955) over 40 years ago, with the available data then, that the ratio of the van der Waals radii (RvdW) of atoms to their de Broglie wavelengths (λdB) is nearly a constant for each group of non-metallic elements. The de Broglie wavelength (λdB = 2πaB) is related to the ground state Bohr radius (aB) and, aB, in turn, to ground state energy (or the ionization potential). Using existing data (Bondi 1964; Batsanov 2001; www.webelements.com), it was found that RvdW varies linearly with aB not only for the non-metallic elements, but also for all the elements from Group 1A to 8A. The straight lines have different slopes and non-zero intercepts (unlike in Bondi 1964; Morrison 1955). In Batsanov (2001), which has data for elements of groups 1A – 7A, two sets of data are given for the van der Waals radii, one from crystallographic data [which are comparable with the values given by Bondi (1964) and in www.webelements.com for elements of Groups 5A – 7A], and the other, denoted as equilibrium values, are for the isolated atoms. The latter are larger since the atoms have more free space than in the crystalline lattices. For elements of other groups, the graphs are not linear and are not considered here.
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