The following carbocation rearranges to
`CH_(2)=underset(CH_(3))underset(|)C-overset(CH_(3))overset(|)C-overset(o+)CH-overset(CH_(3))overset(|)(CH)-CH_(3)`

Options

A. `CH_(2)=underset(Ch_(3))underset(|)C-underset(underset(o+)CH_(2))underset(|)CH-overset(CH_(3))overset(|)CH-overset(CH_(3))overset(|)CH-CH_(3)`
B. `CH_(2)=underset(CH_(3))underset(|)C-underset(CH_(3))underset(|)overset(CH_(3))overset(|)C-CH_(2)-underset(o+)overset(CH_(3))overset(|)C-CH_(3)`
C. `CH_(2)=underset(CH_(3))underset(|)C-underset(CH_(3))underset(|)overset(CH_(3))overset(|)C-overset(CH_(3))overset(|)CH-underset(H)underset(|)overset(o+)C-CH_(3)`
D. `CH_(3)=underset(CH_(3))underset(|)C-underset(CH_(3))underset(|)overset(o+)C-overset(CH_(3))overset(|)CH-overset(CH_(3))overset(|)CH-CH_(3)`

Answer

To solve the problem of rearranging the given carbocation, we will follow these steps:

### Step 1: Identify the Structure of the Given Carbocation
The given carbocation can be represented as follows:
```
CH3
|
CH2 = C - C^+ - C - CH3
|
CH3
```
Here, the positive charge is located on a secondary (2°) carbocation.

**Hint:** Always start by sketching the structure of the carbocation to visualize the rearrangement.

### Step 2: Determine the Stability of the Carbocation
The stability of carbocations is crucial for determining whether a rearrangement will occur. The order of stability is:
- Tertiary (3°) > Secondary (2°) > Primary (1°)

Since we have a secondary carbocation, it can rearrange to a more stable tertiary carbocation.

**Hint:** Remember that carbocations prefer to rearrange to a more stable form.

### Step 3: Perform the Rearrangement
To increase the stability, the secondary carbocation can rearrange to a tertiary carbocation. This can occur through a hydride shift or a methyl shift. In this case, a methyl shift is more favorable.

1. The methyl group from the adjacent carbon (C) can migrate to the positively charged carbon (C^+).
2. The positive charge will then shift to the carbon that originally had the methyl group.

The new structure after the rearrangement will be:
```
CH3
|
CH2 = C - C - C^+ - CH3
|
CH3
```
Now the positive charge is on a tertiary carbon.

**Hint:** Look for the adjacent carbon atoms to see which groups can migrate to stabilize the carbocation.

### Step 4: Final Structure
After the rearrangement, the final structure of the carbocation will be:
```
CH3
|
CH2 = C - C^+ - CH3
|
CH3
```
This structure shows the positive charge now on a tertiary carbon, which is more stable than the original secondary carbocation.

**Hint:** Always verify that the final structure has a more stable carbocation than the initial one.

### Conclusion
The rearrangement of the given carbocation results in a more stable tertiary carbocation. The final structure is confirmed to be more stable due to the positive charge being on a tertiary carbon.