Step 1: Understanding the Question:
The question asks for the orbital hybridization state of the carbon atoms in ethyne (acetylene). Step 2: Key Formula or Approach:
Hybridization can be determined by counting the number of sigma (\(\sigma\)) bonds and lone pairs around the atom (Steric Number). Step 3: Detailed Explanation:
The structure of Ethyne is \(H-C \equiv C-H\).
Each carbon atom is bonded to:
1. One Hydrogen atom via a \(\sigma\)-bond.
2. One Carbon atom via a triple bond (which consists of \(1 \sigma\)-bond and \(2 \pi\)-bonds).
Total sigma bonds per carbon = \(2\).
Lone pairs on carbon = \(0\).
Steric Number = \(2 + 0 = 2\).
A steric number of \(2\) corresponds to \(sp\) hybridization, resulting in a linear geometry (\(180^\circ\)). Step 4: Final Answer:
The hybridization is \(sp\).