The correct order of the lattice energies of the following ionic compounds is

Options

A. `NaClgtMgBr_2gtCaOgtAl_2O_3`
B. `NaClgtCaOgtMgBr_2gtAl_2O_3`
C. `Al_2O_3gtMgBr_2gtCaOgtNaCl`
D. `Al_2O_3gtCaOgtMgBr_2gtNaCl`

Explanation

To determine the correct order of lattice energies for the ionic compounds NaCl, MgBr2, CaO, and Al2O3, we need to consider the charges of the ions and the sizes of the ions involved. Lattice energy is influenced by two main factors:

1. **Charge of the ions**: Lattice energy is directly proportional to the charge of the ions. Higher charges lead to stronger electrostatic forces and thus higher lattice energy.

2. **Size of the ions**: Lattice energy is inversely proportional to the distance between the ions. Smaller ions can get closer together, resulting in stronger interactions and higher lattice energy.

### Step-by-Step Solution:

**Step 1: Identify the charges of the ions in each compound.**
- NaCl: Na⁺ (charge +1), Cl⁻ (charge -1)
- MgBr2: Mg²⁺ (charge +2), Br⁻ (charge -1)
- CaO: Ca²⁺ (charge +2), O²⁻ (charge -2)
- Al2O3: Al³⁺ (charge +3), O²⁻ (charge -2)

**Step 2: Determine the total charge for each compound.**
- NaCl: Total charge = +1 + (-1) = 0 (but we consider individual charges)
- MgBr2: Total charge = +2 + 2*(-1) = 0 (but we consider individual charges)
- CaO: Total charge = +2 + (-2) = 0 (but we consider individual charges)
- Al2O3: Total charge = 2*(+3) + 3*(-2) = 0 (but we consider individual charges)

**Step 3: Compare the charges.**
- Al2O3 has the highest charge (+3 for Al).
- CaO has a charge of +2 for Ca and -2 for O.
- MgBr2 has a charge of +2 for Mg and -1 for Br.
- NaCl has the lowest charge (+1 for Na and -1 for Cl).

**Step 4: Rank the compounds based on their charges.**
- Highest lattice energy: Al2O3 (due to +3 charge)
- Next: CaO (due to +2 charge)
- Then: MgBr2 (due to +2 charge but lower than CaO)
- Lowest: NaCl (due to +1 charge)

**Step 5: Final order of lattice energies.**
The correct order of lattice energies from highest to lowest is:
1. Al2O3
2. CaO
3. MgBr2
4. NaCl

### Final Answer:
The correct order of the lattice energies of the ionic compounds is:
**Al2O3 > CaO > MgBr2 > NaCl**