Elements are arranged in decreasing atomic size in picometers (pm = 10E -12):
Na (227 pm) > Si (210 pm) > P (195 pm) > Ar (188 pm) > Al (184 pm) > S (180 pm) > Cl (175 pm) > Mg (173 pm)
Bryan B.
tutor
A publication from J. Phys. Chem. A in 2009 (https://pubs.acs.org/doi/10.1021/jp8111556) provides a table of van der Waals radius for the main group elements. The values I used originate from Table 12 in the article expressed in Angstroms (10E -10). If you're assuming covalent radius then yes, Ar (106 +/- 10 pm) is smaller than Al (121 +/- 4 pm).
Covalent radius describes the internuclear distance between two atoms forming a chemical bond. Van der Waals radius describes the separation between two non-bonding atoms in a crystal lattice while also accounting for intermolecular forces. Ultimately, the values you choose depends on the nature of your problem, covalent or non-covalent.
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06/29/20
Bryan B.
tutor
Here are the covalent radii for the 8 elements listed in descending order: Na (154 pm) > Mg (136 pm) > Al (118 pm) > Si (111 pm) > P (106 pm) > S (102 pm) Cl ( 99 pm) > Ar (98 pm). The periodic trends (i.e., atomic size, electronegativity, ...) have been discussed in texts frequently with little context. The covalent radii measurements follow the periodic trend, however, it is erroneous to say "atomic size" increases from right to left and top to bottom of the periodic table. Electron clouds can be distorted by local interactions and deviations from expected bond angles. The problem with measuring atomic size is the assumption that atoms are treated as hard spheres leading to a single measurement (as is the case for covalent radii for which the atomic size trend relies upon).
Hopefully these covalent radii results clarify any confusion I have caused.
Best,
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06/29/20
J.R. S.
06/29/20