To determine the ratio of sigma ($\sigma$) and pi ($\pi$)-bonds in 1-butene-3-yne, we first need to draw its structural formula.

The name 1-butene-3-yne indicates a four-carbon chain with a double bond at position 1 and a triple bond at position 3.

The structure is: $C{H}_2=CH-C\equiv CH$

Step 1: Count the sigma bonds.

• C1-H bonds: 2
• C1-C2 bond: 1
• C2-H bond: 1
• C2-C3 bond: 1
• C3-C4 bond: 1
• C4-H bond: 1

Total sigma bonds = $2+1+1+1+1+1=7$

Step 2: Count the pi bonds.

• In the double bond ($C_1=C_2$), there is 1 pi bond.
• In the triple bond ($C_3\equiv C_4$), there are 2 pi bonds.

Total pi bonds = $1+2=3$

Step 3: Calculate the ratio of sigma to pi bonds.

Ratio $rac\sigma \pi =\frac{7}{3}$

Option Analysis:

• A) $\frac{6}{4}$: Incorrect. This would imply 6 sigma and 4 pi bonds, which is not the case.
• B) 4: Incorrect. This is a single number, not a ratio, and does not represent the bond counts.
• C) $\frac{7}{3}$: Correct. This matches our calculated ratio of 7 sigma bonds to 3 pi bonds.
• D) 1: Incorrect. This would imply an equal number of sigma and pi bonds, which is not true for this molecule.

Correct Answer: (C)