Why does the beryllium 2+ ion have a larger radius than a helium atom?

Question

$\ce{Be^2+}$ has an ionic radius of $\pu{45 pm}$, while $\ce{He}$ has a radius of only $\pu{31 pm}$. If they are isoelectronic (they both have two elections in the $\mathrm{1p}$ orbital), and $\ce{Be}$ has more protons to attract them, why doesn't $\ce{Be^2+}$ have a smaller radius?

Answer 1

You are mixing apples and oranges. Or, to be more precise, an ionic radius for $\ce{Be^2+}$ with coordination number (C.N.) 6 and van der Waals radius of $\ce{He}$. To make it clear I compiled data for van der Waals and covalent radii [1, p. 9-58] as well as ionic radii [1, p. 12-13]:

$$ \begin{array}{lccccc} \hline \text{Element} & R_\mathrm{vdW}/\pu{Å} & R_\mathrm{cov}/\pu{Å} & \text{Ion} & \text{C.N.} & R_\mathrm{i}/\pu{Å} \\ \hline \ce{Be} & 1.52 & 0.99 & \ce{Be^2+} & 4 & 0.27 \\ & & & & 6 & 0.45 \\ \ce{He} & 1.40 & 0.37 & & & \\ \hline \end{array} $$

Apparently, there is no experimental ionic radii for helium to compare with as helium, well, represents one of the most non-reactive elements. Also, all radii set are determined using various methods and cannot be directly compared. From the foreword [1. p. 9-58]:

There are many scales of van der Waals radii, but they are not fully consistent with one another. The van der Waals radii determined by Bondi [...] from x-ray diffraction data, crystal densities, gas kinetic collision cross sections, critical densities, and liquid- state properties are the most widely used values. [...]

The covalent radii tabulated here are recommendations for single covalent bonds, and they are based on a comprehensive evaluation of experimental data [...].

Ionic radii are estimated first and foremost from the experimental crystal structure data, averaged and supplemented by empirical and theoretical calculations (extrapolations, e.g. using Zachariasen method).

References

1. Haynes, W. M.; Lide, D. R.; Bruno, T. J. CRC Handbook of Chemistry and Physics: A Ready-Reference Book of Chemical and Physical Data.; 2017; Vol. 97. ISBN 978-1-4987-5429-3.