Chemical Bonding - Metallic Bonding-advanced

Why does Aluminum ($Al$) have a higher melting point than Sodium ($Na$)?

Aluminum has $3$ valence electrons and forms $Al^{3+}$ ions, whereas Sodium has only $1$ valence electron and forms $Na^+$ ions. The charge density on $Al^{3+}$ is much higher than on $Na^+$.

Based on the formula $F \propto \frac{q_1 q_2}{r^2}$, the greater charge ($q = +3$ vs $+1$) and smaller ionic radius of Aluminum lead to a much stronger attraction between the cations and the delocalized electrons, resulting in a higher melting point.

Explain why metals are good conductors of electricity in terms of the electron sea model.

In a metallic lattice, valence electrons are delocalized. When a voltage is applied, these electrons flow toward the positive terminal, creating an electric current.

Since the electrons are not localized to any specific nucleus, they are free to move throughout the structure. The conductivity is proportional to the number of free electrons ($n$) per unit volume.

Compare the metallic bond strength of $Group\ 1$ metals: Lithium ($Li$), Sodium ($Na$), and Potassium ($K$).

$Li > Na > K$

In $Group\ 1$, all these metals contribute $1$ electron to the sea. However, the atomic radius ($r$) increases down the group ($r_{Li} < r_{Na} < r_{K}$). Since $Bond\ Strength \propto \frac{1}{r}$, Lithium has the strongest metallic bond among them.