The number of optical isomers formed by hydrogenation of the compound `(CH_3)_2C=CHCH_3` are

Options

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

Explanation

To determine the number of optical isomers formed by the hydrogenation of the compound `(CH_3)_2C=CHCH_3`, we will follow these steps:

### Step 1: Identify the Compound and Its Structure
The given compound is `(CH_3)_2C=CHCH_3`, which can be represented structurally as follows:

```
CH3
|
CH3-C=CH-CH3
```

### Step 2: Perform Hydrogenation
Hydrogenation involves the addition of hydrogen (H2) across the double bond. In this case, the double bond between the second and third carbon atoms will be saturated by adding hydrogen atoms.

The reaction can be represented as:
```
(CH3)2C=CHCH3 + H2 → (CH3)2C-CH-CH3
```

After hydrogenation, the structure becomes:
```
CH3
|
CH3-C-CH2-CH3
```

### Step 3: Identify Chiral Centers
To determine the number of optical isomers, we need to identify any chiral (asymmetric) carbon atoms in the product. A carbon atom is chiral if it is bonded to four different groups.

In our hydrogenated product:
- The first carbon (C1) is bonded to two CH3 groups and one H, so it is not chiral.
- The second carbon (C2) is bonded to two CH3 groups and one CH2 group, so it is not chiral.
- The third carbon (C3) is bonded to one CH3, one CH2, and one H, making it chiral.

### Step 4: Count the Number of Chiral Centers
In the product, we have identified one chiral center (C3). The presence of one chiral center means that we can have optical isomers.

### Step 5: Calculate the Number of Optical Isomers
The number of optical isomers can be calculated using the formula:
\[ \text{Number of optical isomers} = 2^n \]
where \( n \) is the number of chiral centers.

Since we have 1 chiral center:
\[ \text{Number of optical isomers} = 2^1 = 2 \]

### Conclusion
The number of optical isomers formed by the hydrogenation of the compound `(CH_3)_2C=CHCH_3` is **2**.

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