How many sterioisomers does the following compound have ?
`CH_(3)-CH_(2)-underset(overset(|)(Br))(C)H-CH_(2)-CH=CH-CH_(3)`

Options

A. None
B. 2
C. 4
D. 6

Answer

To determine the number of stereoisomers for the given compound `CH3-CH2-(Br)C-CH2-CH=CH-CH3`, we will follow a systematic approach:

### Step 1: Identify the Structure
The compound can be represented as follows:
```
CH3
|
CH2-C(Br)-CH2-CH=CH-CH3
```
Here, we have a bromine (Br) substituent on a carbon chain.

### Step 2: Identify Chiral Carbons
A chiral carbon is defined as a carbon atom that has four different groups attached to it. We will analyze each carbon atom in the structure:

1. **First Carbon (C1)**: Attached to three hydrogens (not chiral).
2. **Second Carbon (C2)**: Attached to two hydrogens (not chiral).
3. **Third Carbon (C3)**: Attached to one bromine, one hydrogen, one ethyl group (C2H5), and one CH2-CH=CH-CH3 (chiral).
4. **Fourth Carbon (C4)**: Attached to two CH2 groups (not chiral).
5. **Fifth Carbon (C5)**: Attached to one hydrogen, one CH2, and one double bond (not chiral).
6. **Sixth Carbon (C6)**: Attached to three hydrogens (not chiral).

From this analysis, we find that there is **one chiral carbon** (C3).

### Step 3: Identify Double Bonds
Next, we need to identify the number of double bonds in the compound. There is **one double bond** between C5 and C6.

### Step 4: Calculate the Total Number of Stereoisomers
Using the formula for calculating stereoisomers:
\[ \text{Number of stereoisomers} = 2^{(n + m)} \]
where:
- \( n \) = number of chiral carbons
- \( m \) = number of double bonds

In our case:
- \( n = 1 \) (one chiral carbon)
- \( m = 1 \) (one double bond)

Substituting the values:
\[ \text{Number of stereoisomers} = 2^{(1 + 1)} = 2^2 = 4 \]

### Conclusion
The total number of stereoisomers for the given compound is **4**.