Lattice energy of `BeCO_(3)(I), MgCO_(3)(II)` and `CaCO_(3)(III)` is in order.

Options

A. `I gt II gt III`
B. `III gt II gt I`
C. `II gt III gt I`
D. `III gt I gt II`

Explanation

To determine the lattice energy of beryllium carbonate (BeCO₃), magnesium carbonate (MgCO₃), and calcium carbonate (CaCO₃), we need to consider the factors that affect lattice energy, which are the size of the ions and the charge of the ions.

### Step-by-Step Solution:

1. **Understanding Lattice Energy**:
Lattice energy is the amount of energy released when one mole of an ionic compound is formed from its gaseous ions. It is also the energy required to separate one mole of an ionic compound into its gaseous ions.

2. **Factors Affecting Lattice Energy**:
- **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.
- **Size of the Ions**: Lattice energy is inversely proportional to the size of the ions. Smaller ions can get closer together, resulting in stronger attractions and higher lattice energy.

3. **Analyzing the Cations**:
- Beryllium ion (Be²⁺) is smaller than magnesium ion (Mg²⁺), which in turn is smaller than calcium ion (Ca²⁺).
- The order of ionic sizes is: Be²⁺ < Mg²⁺ < Ca²⁺.

4. **Analyzing the Anion**:
- The carbonate ion (CO₃²⁻) is the same in all three compounds, so we only need to consider the cations for our comparison.

5. **Determining Lattice Energy Order**:
- Since Be²⁺ is the smallest cation, it will have the highest lattice energy due to stronger attraction.
- Mg²⁺ is larger than Be²⁺, so it will have a lower lattice energy than beryllium carbonate.
- Ca²⁺ is the largest among the three cations, leading to the lowest lattice energy.

6. **Final Order of Lattice Energy**:
- Therefore, the order of lattice energy for the carbonates is:
- BeCO₃ (highest lattice energy)
- MgCO₃ (middle lattice energy)
- CaCO₃ (lowest lattice energy)

### Conclusion:
The correct order of lattice energy for the compounds is:
1. BeCO₃ (I)
2. MgCO₃ (II)
3. CaCO₃ (III)

### Answer:
The order of lattice energy is: BeCO₃ > MgCO₃ > CaCO₃.

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