Which of the following has been arranged in increasing order of size of the hybrid orbitals ?

Options

A. `sp lt sp^2 lt sp^3`
B. `sp^3 lt sp^2 lt sp`
C. `sp^2 lt sp^3 lt sp`
D. `sp^2 lt sp lt sp^3`

Answer

To solve the question regarding the increasing order of size of hybrid orbitals, we will analyze the hybridization types (sp, sp², sp³) and their corresponding s-character percentages.

### Step-by-Step Solution:

1. **Understand Hybridization Types**:
- Hybridization involves the mixing of atomic orbitals to form new hybrid orbitals. The common types are sp, sp², and sp³.

2. **Calculate the Percentage of s-Character**:
- For **sp hybridization**:
- There is 1 s orbital and 1 p orbital.
- Total orbitals = 1 (s) + 1 (p) = 2.
- Percentage of s-character = (1/2) × 100 = 50%.
- For **sp² hybridization**:
- There is 1 s orbital and 2 p orbitals.
- Total orbitals = 1 (s) + 2 (p) = 3.
- Percentage of s-character = (1/3) × 100 = 33.33%.
- For **sp³ hybridization**:
- There is 1 s orbital and 3 p orbitals.
- Total orbitals = 1 (s) + 3 (p) = 4.
- Percentage of s-character = (1/4) × 100 = 25%.

3. **Relate s-Character to Orbital Size**:
- The size of hybrid orbitals is inversely proportional to the percentage of s-character. This means:
- More s-character → smaller orbital size.
- Less s-character → larger orbital size.

4. **Determine the Order of Sizes**:
- From the percentages calculated:
- sp has the highest s-character (50%), hence the smallest size.
- sp² has a lower s-character (33.33%), hence a larger size than sp.
- sp³ has the least s-character (25%), hence the largest size.
- Therefore, the order of sizes from smallest to largest is:
- sp < sp² < sp³.

5. **Final Increasing Order of Size**:
- The increasing order of size of the hybrid orbitals is:
- sp < sp² < sp³.

### Final Answer:
The correct increasing order of size of the hybrid orbitals is:
**sp < sp² < sp³**.