Final answer:
I₃⁻ exists due to the larger size of iodine atoms allowing for the accommodation of extra electrons, while F₃⁻ does not form because the high electronegativity and small size of fluorine do not permit stable extra electron accommodation.
Step-by-step explanation:
The key difference between I3- and F3- lies in the size and electronegativity of the atoms. Iodine is a larger atom, which can accommodate extra electrons and thus facilitates the existence of I₃⁻ ion. Fluorine, on the other hand, is the most electronegative element and it does not favor the formation of a F₃⁻ ion due to its high electron density and smaller atomic radius, which prevents the accommodation of additional electrons.
Moreover, fluorine, being highly electronegative, prefers to form the highest possible oxidation states when it reacts and is more effective as an oxidizing agent, thus making it less likely to form a stable F₃⁻ ion.