Step 1: Understanding the Topic
The question asks to compare the melting points of four ionic/covalent bromides. The melting point of a substance is related to the strength of the forces holding its constituent particles together. For ionic compounds, this is primarily the lattice energy. However, the degree of covalent character can significantly affect the melting point.
Step 2: Key Approach - Lattice Energy and Fajan's Rules
Lattice Energy: For purely ionic compounds, lattice energy increases with higher ionic charges and decreases with larger ionic radii. Higher lattice energy generally leads to a higher melting point.
Fajan's Rules (Covalent Character): Covalent character is favored by:
Small, highly charged cations.
Large anions.
A higher degree of covalent character leads to weaker intermolecular forces (van der Waals forces) compared to strong electrostatic forces in an ionic lattice, thus lowering the melting point.
Step 3: Detailed Analysis of Each Compound
The anion ($Br^-$) is the same in all compounds, so we compare the cations: $Li^+$, $Na^+$, $Mg^{2+}$, and $Al^{3+}$.
(D) AlBr$_3$: $Al^{3+}$ is a very small and highly charged cation. According to Fajan's rules, it has a very high polarizing power, leading to significant covalent character in the Al-Br bond. $AlBr_3$ is a molecular solid with a low melting point (97.5 °C).
(C) MgBr$_2$: $Mg^{2+}$ has a +2 charge and is smaller than $Na^+$. It also has considerable polarizing power, giving $MgBr_2$ significant covalent character. Its melting point (711 °C) is high but is influenced by this covalent nature.
(A) LiBr: $Li^+$ is the smallest of the alkali metal cations. Its small size gives it a higher polarizing power than $Na^+$, introducing more covalent character into the Li-Br bond compared to the Na-Br bond. Its melting point is 552 °C.
(B) NaBr: $Na^+$ is larger than $Li^+$ and has a lower charge than $Mg^{2+}$ and $Al^{3+}$. It has the least polarizing power among the given cations. Therefore, $NaBr$ is the most ionic compound in the list. Purely ionic compounds form strong crystal lattices, which require a large amount of energy to break, resulting in a very high melting point (747 °C).
Step 4: Final Answer
Comparing the compounds, $NaBr$ has the most ionic character and the weakest covalent influence, resulting in the strongest crystal lattice and therefore the highest melting point.