Lattice energy of an ionic compounds depends upon

The strength of an ionic crystal is measured by its lattice energy, i.e. the energy released when one mole of the crystal is formed from its constituent gaseous ions.

According to the Born-Landé equation, the magnitude of lattice energy $$U$$ is given (in simplified form) by
$$U = \dfrac{N_A Z^{+} Z^{-} e^{2}}{4 \pi \varepsilon_0 r_0}\left(1-\dfrac{1}{n}\right)$$
where

• $$Z^{+}, Z^{-}$$ = charges on the cation and anion
• $$r_0$$ = distance between the ion centres (which depends on ionic sizes)
• $$n$$ = Born exponent (related to the compressibility of the ions)
• the remaining symbols have their usual meanings.

From the equation it is clear that

1. Larger magnitudes of ionic charge $$\left(Z^{+} Z^{-}\right)$$ increase the Coulombic attraction, thereby increasing lattice energy.
2. Smaller inter-ionic distance $$r_0$$ (which results from smaller ionic radii) places the opposite charges closer together, also increasing lattice energy.

No other factor listed (such as the specific way ions are packed) enters directly into the primary proportionality for lattice energy in a given type of crystal.

Therefore, lattice energy depends simultaneously on both the charge and the size (radius) of the ions.

Hence, the correct choice is
Option D which is: Charge on the ion and size of the ion