Question

the coulombic forces that hold the ions together in an ionic solid are characterized in terms of the lattice energy of the crystal. a high lattice energy results in high melting points, and in general, is indicative of a stable crystalline form. very stable crystalline materials that do not deform or shatter under extreme conditions are required for applications in electronic and photonic engineering. for example, the ionic solid magnesium fluoride (mgf₂ comprised of mg²⁺ and f⁻) is used as a coating for high - power laser mirrors. the coating, however is readily damaged by the high power beams. alternative materials are lanthanum fluoride (laf₃ comprised of la³⁺ and f⁻) and aluminum fluoride (alf₃ comprised of al³⁺ and f⁻). which of these three materials would you expect to have the highest lattice energy, i.e, the strongest ionic bonding?
mgf₂
laf₃
alf₃
dont test me yet, i am trying to gain an understanding before attempting to answer this question.

Explanation:

Step1: Recall lattice - energy factors

Lattice energy depends on ion - charge and ion - size. Higher ion - charge and smaller ion - size lead to higher lattice energy.

Step2: Analyze charges and sizes of ions in given compounds

In $MgF_2$, $Mg^{2 + }$ has a charge of + 2 and $F^-$ has a charge of - 1. In $AlF_3$, $Al^{3+}$ has a charge of + 3 and $F^-$ has a charge of - 1. In $LaF_3$, $La^{3+}$ has a charge of + 3 and $F^-$ has a charge of - 1. The ionic radius of $Mg^{2+}

Step3: Compare lattice energies

Since $AlF_3$ and $LaF_3$ have ions with higher charges (+ 3) compared to $MgF_2$ (+ 2), and $Al^{3+}$ is smaller than $La^{3+}$, $AlF_3$ has the highest lattice energy among the three due to the combination of high ion - charge and relatively small cation size.

Answer:

$AlF_3$