Hybridisation states of C in `CH_(3)^(+)` and `CH_(4)` are

Options

A. `sp^(2) & sp^(3)`
B. `sp^(2) & sp^(2)`
C. `sp^(2) & sp^(2)`
D. `sp^(3) & sp^(3)`

Explanation

To determine the hybridization states of carbon in `CH₃⁺` (methyl cation) and `CH₄` (methane), we will follow these steps:

### Step 1: Determine the Steric Number for `CH₃⁺`

1. **Identify the number of valence electrons for carbon**: Carbon has 4 valence electrons.
2. **Count the number of monovalent atoms attached**: In `CH₃⁺`, there are 3 hydrogen atoms.
3. **Consider the cationic charge**: Since it is a cation, we subtract 1 from the total.
4. **Anionic charge**: There is no anionic charge, so this is 0.

Using the formula for steric number:
\[ \text{Steric Number} = \frac{1}{2} \left( \text{Number of valence electrons} + \text{Number of monovalent atoms} - \text{Cationic charge} + \text{Anionic charge} \right) \]
Substituting the values:
\[ \text{Steric Number} = \frac{1}{2} \left( 4 + 3 - 1 + 0 \right) = \frac{1}{2} \left( 6 \right) = 3 \]

### Step 2: Determine the Hybridization for `CH₃⁺`

- A steric number of 3 corresponds to **sp² hybridization**.

### Step 3: Determine the Steric Number for `CH₄`

1. **Identify the number of valence electrons for carbon**: Carbon has 4 valence electrons.
2. **Count the number of monovalent atoms attached**: In `CH₄`, there are 4 hydrogen atoms.
3. **Consider the cationic charge**: There is no cationic charge, so this is 0.
4. **Anionic charge**: There is also no anionic charge, so this is 0.

Using the formula for steric number:
\[ \text{Steric Number} = \frac{1}{2} \left( \text{Number of valence electrons} + \text{Number of monovalent atoms} - \text{Cationic charge} + \text{Anionic charge} \right) \]
Substituting the values:
\[ \text{Steric Number} = \frac{1}{2} \left( 4 + 4 - 0 + 0 \right) = \frac{1}{2} \left( 8 \right) = 4 \]

### Step 4: Determine the Hybridization for `CH₄`

- A steric number of 4 corresponds to **sp³ hybridization**.

### Final Answer

- The hybridization state of carbon in `CH₃⁺` is **sp²**.
- The hybridization state of carbon in `CH₄` is **sp³**.

### Summary

- `CH₃⁺`: sp² hybridization
- `CH₄`: sp³ hybridization