Which of the following statements correctly describes how differences in ionic radii affect lattice energy?

• A. Lattice energy increases as the ionic radii of the ions decrease.
• B. Lattice energy increases as the ionic radii of the ions increase.
• C. Lattice energy decreases as the ionic radii of the ions decrease.
• D. Lattice energy is independent of the ionic radii of the ions.

Answer: (A)

Verified step by step guidance

1. Recall that lattice energy is the energy released when gaseous ions combine to form an ionic solid, and it depends on the electrostatic attraction between the ions.
2. Understand that the electrostatic force between two ions is described by Coulomb's law: \(E = \dfrac{k \cdot Q_1 \cdot Q_2}{r}\), where \(E\) is the lattice energy, \(Q_1\) and \(Q_2\) are the charges of the ions, \(r\) is the distance between the centers of the ions (related to ionic radii), and \(k\) is a proportionality constant.
3. Recognize that as the ionic radii decrease, the distance \(r\) between the ions decreases, which increases the magnitude of the electrostatic attraction and thus increases the lattice energy.
4. Conversely, if the ionic radii increase, the distance \(r\) increases, reducing the electrostatic attraction and decreasing the lattice energy.
5. Therefore, the correct relationship is that lattice energy increases as the ionic radii of the ions decrease.