# Lattice energy of NaCl and MgCl [sic]

In an exam paper it says that the lattice energy of NaCl is more exothermic than MgCl [sic] as the Na+ cation has a smaller ionic radius than Mg+. Here are the resources given:

What is the reasoning for for Na+ having a smaller ionic radius even though Mg+ has a higher proton number?

• Mg+ is not a thing at all. Oct 16, 2018 at 4:47
• It was part of a CIE A - level chemistry exam Oct 16, 2018 at 5:14
• I'd agree with Ivan. You must be making a mistake. It should be $\ce{Mg^{2+}}$ and $\ce{MgCl2}$.
– MaxW
Oct 16, 2018 at 5:51
• In the exam I think it was asked as hypothetical situation, so hypothetically how would you reason the ionic radius of Mg+? Oct 16, 2018 at 5:55
• We wouldn't. It makes no sense. Oct 16, 2018 at 6:01

We actually do mean $$\ce{Mg^+}$$ here. The idea is to show what factors are involved when an alkaline earth metal forms stable compounds with $$\ce{M^{2+}}$$ ions whereas an alkali metal favors $$\ce{M^+}$$. In this case, as pointed out in some of the comments, $$\ce{Mg^+}$$ is bulked up by the electron that remains in the relatively diffuse, loosely held $$3s$$ subshell. You need to remove that electron, making $$\ce{Mg^{2+}}$$, to get a compact ion that gives good lattice energies in ionic crystals.
Although $$\ce{MgCl}$$ and monatomic $$\ce{Mg^+}$$ are not real materials, the case of scandium monosulfude, $$\ce{ScS}$$ is instructive. A simple ionic model proposing $$\ce{Sc^{2+}}$$ and $$\ce{S^{2-}}$$ would require the scandium to retain a valence electron in an outer-shell orbital, apparently $$3d$$. In an early-group metal such orbitals are diffuse and, if occupied, would inhibit tight binding of the oppositely charged ions. Instead, according to Ref. [1] which identifies $$\ce{ScS}$$ as a metallic conductor, the extra electron per scandium atom is delocalized into a conduction band. This allows the sulfide ions to bind tightly with compact $$\ce{Sc^{3+}}$$. Thus scandium monosulfide is stable not as a conventional ionic salt, but as a compound that combines ionic and metallic characteristics.