Step 1: Identifying Bond Types.
In the given molecule, the sigma bonds (\(\sigma\)) are formed by the head-on overlap of orbitals, while pi bonds (\(\pi\)) are formed by the sidewise overlap of p-orbitals. By counting the single and double bonds in the molecule, we can calculate the total number of sigma and pi bonds. Typically, for a molecule with alternating single and double bonds, the number of pi bonds will be equal to the number of double bonds, and sigma bonds will be counted for both single and double bonds.
Step 2: Analyzing the options.
(A) 5\(\pi\), 14 \(\sigma\)-bonds: Incorrect. This is too many pi bonds for the given structure.
(B) 3\(\pi\), 17 \(\sigma\)-bonds: Incorrect. The number of sigma bonds is too high.
(C) 3\(\pi\), 16 \(\sigma\)-bonds: Correct. This is the correct count based on the given structure of alternating single and double bonds.
(D) 2\(\pi\), 17 \(\sigma\)-bonds: Incorrect. The number of pi bonds is too low for this structure.
Step 3: Conclusion.
The correct count is 3\(\pi\), 16 \(\sigma\)-bonds, which corresponds to option (C).