Number of isomers of molecular formula `C_(2)H_(2)Br_(2)` are

Options

A. `1`
B. `2`
C. `3`
D. `0`

Explanation

To determine the number of isomers for the molecular formula \( C_2H_2Br_2 \), we can follow these steps:

### Step 1: Determine the Degree of Unsaturation
The degree of unsaturation (DU) can be calculated using the formula:
\[ DU = \frac{(2C + 2 + N - H - X)}{2} \]
where \( C \) is the number of carbon atoms, \( H \) is the number of hydrogen atoms, \( N \) is the number of nitrogen atoms, and \( X \) is the number of halogens (in this case, bromine).

For \( C_2H_2Br_2 \):
- \( C = 2 \)
- \( H = 2 \)
- \( Br = 2 \) (considered as halogens)

Plugging in the values:
\[ DU = \frac{(2 \times 2 + 2 + 0 - 2 - 2)}{2} = \frac{(4 + 2 - 4)}{2} = \frac{2}{2} = 1 \]
This indicates that there is one degree of unsaturation, which suggests the presence of a double bond or a ring.

### Step 2: Identify Possible Structures
Given that we have two carbon atoms and one degree of unsaturation, the simplest structure would involve a double bond between the two carbon atoms. The general structure can be represented as:
\[ C=C \]

### Step 3: Consider Substituents
Now we need to consider the placement of the bromine atoms and hydrogen atoms around the double bond. The possible structures can be:

1. **Cis Isomer**:
\[ HBr \quad Br \]
\[ H \quad C=C \quad H \]

2. **Trans Isomer**:
\[ H \quad Br \]
\[ Br \quad C=C \quad H \]

3. **1,1-Dibromoethene**:
\[ Br \quad C=C \quad Br \]
\[ H \quad H \]

### Step 4: Count the Isomers
From the structures identified, we have:
1. **Cis-1,2-dibromoethene**
2. **Trans-1,2-dibromoethene**
3. **1,1-dibromoethene**

Thus, the total number of isomers for \( C_2H_2Br_2 \) is **3**.

### Final Answer
The number of isomers of molecular formula \( C_2H_2Br_2 \) is **3**.

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