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Last updated date: 18th Jun 2024
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Hint: Lattice energy is the energy contained in the crystal lattice. Formation of Crystal lattice is an exothermic process thus $\Delta {H_{lattice}}$ is negative. According to Born-Lande equation, Lattice energy is directly proportional to charge of cation and anion and it is inversely proportional to interatomic distance.

The amount of energy released when cations and anions in their gaseous states are brought from infinity to their lattice sites in a crystal to form one mole of the ionic crystal.

This equation represents the formation of an ionic crystal from the constituent ions. There is a considerable amount of decrease in the potential energy of the system during the formation of an ionic crystal. That energy is released in the form of heat. Hence lattice energy U is negative. As the value of lattice energy increases, stability of the crystal also increases.
We can find the lattice energy by using Born-Lande equation. That is given by the formula
U= $\dfrac{{ - {N_0}A{\text{ }}\left| {{Z^ + }{Z^ - }} \right|}}{{{r_0}}}$ $\left[ {1 - 1/n} \right]$
Here A is known as Madelung Constant
N is the Born exponent
${Z^ + }$ is the charge of Cation.
${Z^ - }$ is the charge of Anion.
r is the distance between the ions.
The value of Madelung constant depends upon the geometry of the lattice and independent upon the ionic radius and charge. The Born exponent n depends upon the type of ion involved. Larger ions have higher electron densities and have high value of n.
From equation we can understand that Lattice energy $\alpha = \dfrac{{{Z^ + }{Z^ - }}}{{{r_0}}}$

Lattice energy is inversely proportional to the sum of radii of cation and anion

Hence, the correct answer is option (D) i.e. Sum of the radii of cation and anion

Note: Lattice energy can not be measured empirically, but it can be calculated using Born-Haber Cycle. Lattice energy is used to explain the stability of ionic solids. As the radius of ions increases the distance between their ions increases. Finally, less lattice energy is released during the process.