Element not showing variable oxidation state is :

Solution

Chemistry ma’am · 3 steps

Fluorine is the most electronegative element, so it never gives up electrons. That leaves it with only -1.

1. Why fluorine is stuck. Fluorine is the most electronegative element, so no other atom can pull electrons away from it. In every compound it takes one electron and shows only -1. It is 0 only in F₂ itself.
2. No d orbitals. Fluorine is in period 2, so it has no d orbitals in its valence shell. Its electrons cannot be unpaired and promoted, so it cannot form 3, 5 or 7 bonds the way the other halogens do.

   Halogen	Vacant d orbitals	Oxidation states	Examples
   F	none	only -1	HF, OF₂
   Cl	yes (3d)	-1, +1, +3, +5, +7	HCl, HOCl, HClO₄
   Br	yes (4d)	-1, +1, +3, +5, +7	HBr, BrF₃, HBrO₄
   I	yes (5d)	-1, +1, +3, +5, +7	HI, ICl, IF₇

3. So. Chlorine, bromine and iodine all show positive oxidation states with oxygen or fluorine. Fluorine shows only -1, so the answer is (d).

The idea to keep. Among the halogens, only fluorine is fixed at -1. It is the most electronegative element and has no d orbitals, so it can never take a positive oxidation state.

Answer from the NTA final answer key. Solution by PrepWiser.