Step 1: Understanding the Concept:
Oxidation states are usually integers. However, "average oxidation states" in molecules where an element is present in different environments or bonding states can sometimes result in fractional values.
Step 2: Detailed Explanation:
Nitrogen (\( \text{N} \)) is unique in Group 15 for its ability to form a vast variety of compounds with oxidation states ranging from \( -3 \) to \( +5 \).
Nitrogen shows a fractional oxidation state in Hydrazoic acid (\( \text{N}_{3}\text{H} \)).
In \( \text{N}_{3}\text{H} \):
Let the oxidation state of N be \( x \).
The oxidation state of H is \( +1 \).
Sum of oxidation states \( = 0 \):
\[ 3x + (+1) = 0 \]
\[ 3x = -1 \implies x = -1/3 \]
Thus, Nitrogen exhibits a fractional average oxidation state of \( -1/3 \) in Hydrazoic acid.
Step 3: Final Answer:
The element is Nitrogen (N).