Lattice energy is directly proportional to charge of the ion and is inversely proportional to size of ion. Therefore, NaF, as F^- is smallest all other anion.

NaF has the highest lattice energy among the given options. Lattice energy is a measure of the strength of the ionic bond in a compound and is defined as the energy released when one mole of an ionic compound is formed from its constituent ions in the gas phase. It is influenced by factors such as the charge of the ions and the size of the ions involved.

Ionic compounds are formed through the transfer of electrons from a metal atom to a non-metal atom. The resulting ions are held together by electrostatic attractions, forming a lattice structure. The lattice energy is the energy required to separate the ions in the lattice to an infinite distance.

Charge of Ions:
The lattice energy is directly proportional to the charge of the ions involved. In the given options, NaF and KCl both involve monovalent ions (Na+ and K+), while NaBr involves a divalent ion (Br-), and AgCl involves a monovalent ion (Ag+). Since the lattice energy increases with the charge of the ions, NaBr and AgCl will have lower lattice energies compared to NaF and KCl.

Size of Ions:
The lattice energy is inversely proportional to the size of the ions involved. Smaller ions can pack more closely together, resulting in stronger electrostatic attractions. In the given options, NaF involves smaller ions (Na+ and F-) compared to KCl (K+ and Cl-). Therefore, NaF will have a higher lattice energy compared to KCl.

Combining the influence of ion charges and sizes, NaF has the highest lattice energy among the given options. The combination of a monovalent cation (Na+) and a highly electronegative anion (F-) results in a strong ionic bond with a high lattice energy.