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For example, Magnesium has a higher charge density compared to Sodium, therefore its metallic lattice is stronger and it has a higher melting point. Does that mean that Magnesium has more protons and a smaller atomic radius or is it about its charge (2+), that makes its lattice stronger?

What does charge density show?

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There are really two separate things here - "does having a higher ionic charge make magnesium's metallic bonding stronger", and "what is charge density". You might want to clarify exactly what your real question is. – Aesin Jan 12 at 11:48

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If it was about the number of protons in the nucleus, then Mercury would hardly be liquid at room temperature, would it?

Actually, it is about the density of free electrons, i.e. the density of the "electron gas" that makes up the metallic bonding. Obviously, this density has to be the negative of the ions' charge, so you might equivalently say it's about magnesium's (2+) charge, though that doesn't make much sense physically unless you also consider the conduction electrons, as the ions themselves of course repulse each other.

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So at my level it means the charge, like Magnesium's charge density is 2+ and sodium's in 1+. – Cyrus Jan 6 at 13:28

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