The degree of unsaturation or index of hydrogen deficiency in the following is :
i. `C_(6)H_(14)`
ii. `C_(4)H_(6)`
iii. `C_(6)H_(6)`

Options

A. 0,2,4
B. 1,0,2
C. 4,1,0
D. 2,0,4

Explanation

To determine the degree of unsaturation (also known as the index of hydrogen deficiency) for the given compounds, we can use the formula:

\[ \text{Degree of Unsaturation} = \frac{(2 \times \text{number of carbon atoms} + 2 - \text{number of hydrogen atoms})}{2} \]

Let's apply this formula step by step for each compound.

### Step 1: Calculate for C₆H₁₄
1. **Identify the number of carbon and hydrogen atoms**:
- Carbon (C) = 6
- Hydrogen (H) = 14

2. **Substitute into the formula**:
\[ \text{Degree of Unsaturation} = \frac{(2 \times 6 + 2 - 14)}{2} \]

3. **Calculate**:
- \(2 \times 6 = 12\)
- \(12 + 2 = 14\)
- \(14 - 14 = 0\)
- \(\frac{0}{2} = 0\)

**Result**: The degree of unsaturation for C₆H₁₄ is **0**.

### Step 2: Calculate for C₄H₆
1. **Identify the number of carbon and hydrogen atoms**:
- Carbon (C) = 4
- Hydrogen (H) = 6

2. **Substitute into the formula**:
\[ \text{Degree of Unsaturation} = \frac{(2 \times 4 + 2 - 6)}{2} \]

3. **Calculate**:
- \(2 \times 4 = 8\)
- \(8 + 2 = 10\)
- \(10 - 6 = 4\)
- \(\frac{4}{2} = 2\)

**Result**: The degree of unsaturation for C₄H₆ is **2**.

### Step 3: Calculate for C₆H₆
1. **Identify the number of carbon and hydrogen atoms**:
- Carbon (C) = 6
- Hydrogen (H) = 6

2. **Substitute into the formula**:
\[ \text{Degree of Unsaturation} = \frac{(2 \times 6 + 2 - 6)}{2} \]

3. **Calculate**:
- \(2 \times 6 = 12\)
- \(12 + 2 = 14\)
- \(14 - 6 = 8\)
- \(\frac{8}{2} = 4\)

**Result**: The degree of unsaturation for C₆H₆ is **4**.

### Final Summary of Results:
- For C₆H₁₄: Degree of Unsaturation = **0**
- For C₄H₆: Degree of Unsaturation = **2**
- For C₆H₆: Degree of Unsaturation = **4**