The query concerns the element among Chlorine, Fluorine, Bromine, and Iodine that does not display a variable oxidation state.
The solution requires an understanding of halogen oxidation states. Halogens typically exhibit varied oxidation states, with Fluorine being the sole exception. The reasoning is as follows:
- Fluorine: As the most electronegative element (electronegativity of 3.98 on the Pauling scale), Fluorine exclusively exhibits an oxidation state of -1. It cannot attain positive oxidation states as it is incapable of electron loss. Consequently, Fluorine's oxidation state is invariably -1.
- Chlorine: Chlorine demonstrates multiple oxidation states, ranging from -1 to +7, due to its ability to gain, lose, or share electrons under varying circumstances. It occurs in negative states like -1 and positive states such as +1, +3, +5, and +7.
- Bromine: Analogous to Chlorine, Bromine can display various oxidation states, including -1, +1, +3, +5, and +7.
- Iodine: Iodine also exhibits variable oxidation states akin to other halogens (excluding Fluorine), such as -1, +1, +3, +5, and +7.
In summary, of the provided options, Fluorine is the element that maintains a constant oxidation state of -1, thus not displaying variable oxidation states. Therefore, Fluorine is the correct answer.