For the given reaction how many monochloro products are optically active ( all isomers ) `:`
`CH_(3)-underset(" "CH_(3))underset(|)overset(" "CH_(3))overset(|)(C)-CH_(2)-overset(" "CH_(3))overset(|)(CH)-CH_(3) overset(Br_(2)//hv)(rarr)`

Answer

To determine how many monochloro products from the given reaction are optically active, we will analyze the structure and identify the chiral centers after chlorination.

### Step-by-Step Solution:

1. **Identify the Structure**: The compound given is a substituted alkane with multiple methyl groups and a central carbon chain. The structure can be represented as:
```
CH3
|
CH3-C-CH2-CH-CH3
|
CH3
```
Here, the central carbon (C) is connected to three identical methyl groups (CH3) and two other carbons.

2. **Monochlorination**: We will consider the monochlorination at different positions on the carbon chain. The possible positions for chlorination are the central carbon (C), the two adjacent carbons, and the terminal carbons.

3. **Chlorination at the Central Carbon (C)**:
- If chlorine is added to the central carbon, the resulting product will have no chiral centers since all substituents are identical (three CH3 groups).
- **Result**: Optically inactive.

4. **Chlorination at the First Adjacent Carbon (C1)**:
- If chlorine is added to one of the adjacent carbons (C1), we create a new chiral center at that carbon.
- The resulting product will have two different groups attached to the chiral carbon (the chlorine and the remaining carbon chain).
- **Result**: Optically active.

5. **Chlorination at the Second Adjacent Carbon (C2)**:
- If chlorine is added to the other adjacent carbon (C2), we again create a new chiral center.
- Similar to the previous case, this product will also have two different groups attached to the chiral carbon.
- **Result**: Optically active.

6. **Chlorination at the Terminal Carbons (C3 and C4)**:
- If chlorine is added to either of the terminal carbons (C3 or C4), the resulting product will have no chiral centers because the terminal carbons are connected to identical methyl groups.
- **Result**: Optically inactive.

7. **Count the Optically Active Products**:
- From the analysis, we found:
- 1 product from C1 (optically active)
- 1 product from C2 (optically active)
- 0 products from C (optically inactive)
- 0 products from C3 and C4 (optically inactive)
- Therefore, the total number of optically active monochloro products is **2**.

### Final Answer:
There are **2 optically active monochloro products** from the given reaction.