Lattice energy of NaCl and MgCl

In an exam paper it says that the lattice energy of NaCl is more exothermic than MgCl 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?

Thanks.

• Mg+ is not a thing at all. – Ivan Neretin Oct 16 '18 at 4:47
• It was part of a CIE A - level chemistry exam – Devansh Shah Oct 16 '18 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 '18 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+? – Devansh Shah Oct 16 '18 at 5:55
• We wouldn't. It makes no sense. – Ivan Neretin Oct 16 '18 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.