Step 1: Understanding the Concept:
In \(\text{KO}_2\), potassium is an alkali metal with oxidation state +1. The compound contains the superoxide ion \(\text{O}_2^-\).
Step 2: Key Formula or Approach:
The sum of oxidation numbers in a neutral compound is zero.
Step 3: Detailed Explanation:
Let the oxidation number of each O be \(x\).
\[ (+1) + 2x = 0 \Rightarrow x = -\frac{1}{2} \]
A fractional value arises because two oxygen atoms share one negative charge in the superoxide ion.
Option (A) \(-2\) is for oxides, option (C) \(-1\) is for peroxides like \(\text{Na}_2\text{O}_2\), and option (D) \(+2\) is found only in \(\text{OF}_2\).
Step 4: Final Answer:
The oxidation number of oxygen is \(-1/2\), option (B).
Final Answer:
Superoxide oxygen has oxidation state -1/2.
\[ \boxed{\text{(B) }-\tfrac{1}{2}} \]