The energy is lowest for the orbital

Options

A. 3d
B. 4p
C. 4s
D. 4f

Explanation

To determine which orbital has the lowest energy, we can use the n + l rule. This rule states that the energy of an orbital is determined by the sum of the principal quantum number (n) and the azimuthal quantum number (l). The orbital with the lowest n + l value has the lowest energy.

### Step-by-Step Solution:

1. **Identify the Orbitals**: We are given four orbitals to compare: 3D, 4P, 4S, and 4F.

2. **Calculate n + l for Each Orbital**:
- For **3D**:
- n = 3 (principal quantum number)
- l = 2 (for D orbitals)
- n + l = 3 + 2 = **5**

- For **4P**:
- n = 4
- l = 1 (for P orbitals)
- n + l = 4 + 1 = **5**

- For **4S**:
- n = 4
- l = 0 (for S orbitals)
- n + l = 4 + 0 = **4**

- For **4F**:
- n = 4
- l = 3 (for F orbitals)
- n + l = 4 + 3 = **7**

3. **Compare the n + l Values**:
- 3D: n + l = 5
- 4P: n + l = 5
- 4S: n + l = 4
- 4F: n + l = 7

4. **Determine the Lowest Energy Orbital**:
- The lowest n + l value is **4** for the **4S** orbital.
- Therefore, the orbital with the lowest energy is **4S**.

### Final Answer:
The energy is lowest for the orbital **4S**.