Concept:
Dienes are hydrocarbons containing two carbon-carbon double bonds. Depending upon the relative positions of the double bonds, dienes are classified into three categories:
• Conjugated dienes: Double bonds are separated by one single bond.
\[
C=C-C=C
\]
• Isolated dienes: Double bonds are separated by two or more single bonds.
\[
C=C-C-C=C
\]
• Cumulated dienes: Two double bonds share a common carbon atom.
\[
C=C=C
\]
Conjugated dienes are particularly stable because the \(\pi\)-electrons are delocalized over four carbon atoms.
Step 1: Examine hepta-1,6-diene.
Structure:
\[
CH_2=CH-CH_2-CH_2-CH_2-CH=CH_2
\]
The two double bonds are separated by four single bonds.
Therefore, it is an isolated diene and not a conjugated diene.
Step 2: Examine hepta-1,3-diene.
Structure:
\[
CH_2=CH-CH=CH-CH_2-CH_2-CH_3
\]
The double bonds are separated by exactly one single bond.
\[
C=C-C=C
\]
This is the characteristic arrangement of a conjugated diene.
Therefore, hepta-1,3-diene contains conjugated double bonds.
Step 3: Examine hepta-1,4-diene.
Structure:
\[
CH_2=CH-CH_2-CH=CH-CH_2-CH_3
\]
The double bonds are separated by two single bonds.
Hence it is an isolated diene.
Step 4: Examine hepta-1,5-diene.
Structure:
\[
CH_2=CH-CH_2-CH_2-CH=CH-CH_3
\]
Again, the double bonds are separated by more than one single bond.
Therefore, it is also an isolated diene.
Step 5: Conclusion.
Only hepta-1,3-diene possesses the arrangement
\[
C=C-C=C
\]
which represents conjugation.
Hence the correct answer is
\[
\boxed{\text{hepta-1,3-diene}}
\]