Bond length is the distance between the nuclei of two bonded atoms. It generally increases as the size of the atoms involved in the bond increases. In this case, all the molecules involve hydrogen (\( H \)) bonded to a halogen (\( F, Cl, Br, I \)). The size of the halogen atom increases down the group in the periodic table due to the addition of electron shells.
Among the halogens, iodine (\( I \)) is the largest atom, followed by bromine (\( Br \)), chlorine (\( Cl \)), and fluorine (\( F \)). Consequently, the bond length of \( \text{H-I} \) is the longest, as the larger iodine atom results in a greater distance between the hydrogen and iodine nuclei.
Final Answer: The molecule with the highest bond length is \( \mathbf{\text{H-I}} \), which corresponds to option \( \mathbf{(4)} \).