Arrange the following in the order of increasing stability:
`PhC^(+)H_(2) , Ph_(3)C^(+), Me^(+), Ph_(2)C^(+)H`

Options

A. `Me^(+) lt PhC^(+)He lt Ph_(2)C^(+)H lt Ph_(3)C^(+)`
B. `PhC^(+)H_(2) lt Me^(+) lt Ph_(3)C^(+) lt Ph_(2)C^(+)H`
C. `PhC^(+)H_(2) lt Ph_(3)C^(+) lt Me^(+) lt Ph_(2)C^(+)H`
D. `PhC^(+)H_(2) lt Ph_(2)C^(+)H lt Ph_(3)C^(+) lt Me^(+)`

Answer

To determine the order of increasing stability of the given carbocations, we need to analyze each structure based on the number of phenyl (Ph) groups attached and their ability to stabilize the positive charge through resonance.

### Step-by-Step Solution:

1. **Identify the Structures**:
- **PhC^(+)H₂**: A phenyl group attached to a carbocation (C^+).
- **Ph₃C^(+)**: A carbocation with three phenyl groups attached.
- **Me^(+)**: A methyl carbocation (C^+ with three hydrogens).
- **Ph₂C^(+)H**: A carbocation with two phenyl groups and one hydrogen.

2. **Assess Stability**:
- **Stability of Carbocations**: Carbocations are stabilized by electron-donating groups. The more resonance structures that can be drawn, the more stable the carbocation.
- **PhC^(+)H₂**: Has one phenyl group, which can stabilize the positive charge through resonance, but not very effectively.
- **Ph₃C^(+)**: Has three phenyl groups, which can delocalize the positive charge very effectively through resonance. This is the most stable carbocation.
- **Me^(+)**: A methyl carbocation has no resonance stabilization and is the least stable.
- **Ph₂C^(+)H**: Has two phenyl groups, providing some resonance stabilization, but not as much as Ph₃C^(+).

3. **Rank the Stability**:
- **Least Stable**: Me^(+) (no resonance stabilization)
- **Next**: PhC^(+)H₂ (one phenyl group)
- **Next**: Ph₂C^(+)H (two phenyl groups)
- **Most Stable**: Ph₃C^(+) (three phenyl groups)

### Final Order of Increasing Stability:
1. Me^(+) < PhC^(+)H₂ < Ph₂C^(+)H < Ph₃C^(+)