Which of the following orbitals has the highest energy?

Options

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

Explanation

To determine which of the given orbitals has the highest energy, we need to analyze the s-character of each hybridized orbital. The s-character is inversely related to the energy of the orbital: the more s-character an orbital has, the more stable it is, and thus the lower its energy. Conversely, the less s-character, the higher the energy.

### Step-by-Step Solution:

1. **Identify the s-character of each orbital:**
- **sp orbital:**
- Contains 50% s-character and 50% p-character.
- **sp² orbital:**
- Contains 33.33% s-character and 66.67% p-character.
- **sp³ orbital:**
- Contains 25% s-character and 75% p-character.
- **sp³d orbital:**
- Contains 20% s-character (from the sp³ part) and 80% p-character, plus the d-orbital which is higher in energy.

2. **Determine the stability order based on s-character:**
- The stability order (from most stable to least stable) based on s-character is:
- sp > sp² > sp³ > sp³d
- This means that sp is the most stable and has the lowest energy, while sp³d is the least stable and has the highest energy.

3. **Establish the energy order:**
- Since stability is inversely related to energy, the energy order (from lowest to highest) is:
- sp < sp² < sp³ < sp³d

4. **Conclusion:**
- Therefore, the orbital with the highest energy among the given options is **sp³d**.

### Final Answer:
The orbital with the highest energy is **sp³d**.

---