What accounts for the difference in bond lengths and similarities in bond energies of these diatomic molecules?

a$.$ The internuclear distance for $O_2$ is greater than that for $H_2$ because $O_2$ has a double bond and $H_2$ has a single bond. The bond energies are similar because they are both diatomic.

b$.$ The internuclear distance for $O_2$ is greater than that for $H_2$ because $O_2$ has a double bond and $H_2$ has a single bond. The bond energies are similar because the greater number of protons and greater bond length in $O_2$ creates approximately the same Coulombic attraction as that present in $H_2.$

c$.$ The internuclear distance for $O_2$ will be greater than that for $H_2$ because $O_2$ is using electrons from the second energy level to form covalent bonds while $H_2$ is using electrons from the first energy level. The bond energies are similar because the greater number of protons and greater bond length in $O_2$ creates approximately the same Coulombic attraction as that present in $H_2.$

d$.$ The internuclear distance for $O_2$ is greater than that for $H_2$ because $O_2$ is using electrons from the second energy level to form covalent bonds while $H_2$ is using electrons from the first energy level. The bond energies are similar because they are both diatomic.