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 order of lattice energy for the compounds BeCO₃ (I), MgCO₃ (II), and CaCO₃ (III), we need to consider the factors that influence lattice energy, particularly the size of the cations and the arrangement of ions in the crystal lattice.

### Step-by-Step Solution:

1. **Understand Lattice Energy**:
Lattice energy is the energy released when gaseous ions combine to form an ionic solid. It is influenced by the charge and size of the ions involved. Smaller ions can pack more closely together, leading to higher lattice energy.

2. **Identify the Size of Cations**:
- Beryllium (Be²⁺) is the smallest cation among the three.
- Magnesium (Mg²⁺) is larger than Be²⁺.
- Calcium (Ca²⁺) is the largest cation among the three.

3. **Consider the Anion Size**:
The carbonate ion (CO₃²⁻) is a relatively large anion. The size of the cation relative to the anion is crucial for determining how well they can pack together in the crystal lattice.

4. **Evaluate the Packing**:
- Be²⁺ being the smallest cation will fit more snugly with the carbonate ion, leading to a more stable and stronger lattice.
- Mg²⁺, being larger than Be²⁺, will not pack as efficiently, resulting in lower lattice energy compared to BeCO₃.
- Ca²⁺, being the largest, will have the least effective packing with the carbonate ion, leading to the lowest lattice energy among the three.

5. **Order of Lattice Energy**:
Based on the above reasoning, the order of lattice energy from highest to lowest is:
- BeCO₃ > MgCO₃ > CaCO₃

### Final Answer:
The order of lattice energy is: **BeCO₃ (I) > MgCO₃ (II) > CaCO₃ (III)**.