Which orbit of the following is lower in energy in a many electron atom ?

Options

A. `2p`
B. `3d`
C. `4s`
D. `5f`

Explanation

To determine which orbital is lower in energy in a many-electron atom among the given options (2p, 3d, 4s, and 5f), we will use the Aufbau principle, which states that the energy of orbitals can be compared using the sum of the principal quantum number (n) and the azimuthal quantum number (l).

### Step-by-Step Solution:

1. **Identify the orbitals and their quantum numbers:**
- 2p: n = 2, l = 1 (since p corresponds to l = 1)
- 3d: n = 3, l = 2 (since d corresponds to l = 2)
- 4s: n = 4, l = 0 (since s corresponds to l = 0)
- 5f: n = 5, l = 3 (since f corresponds to l = 3)

2. **Calculate the n + l values for each orbital:**
- For 2p: n + l = 2 + 1 = 3
- For 3d: n + l = 3 + 2 = 5
- For 4s: n + l = 4 + 0 = 4
- For 5f: n + l = 5 + 3 = 8

3. **Compare the n + l values:**
- 2p: 3
- 3d: 5
- 4s: 4
- 5f: 8

4. **Determine the lowest n + l value:**
- The lowest value among 3, 5, 4, and 8 is 3 (from the 2p orbital).

5. **Conclusion:**
- Therefore, the orbital that is lower in energy in a many-electron atom is **2p**.

### Final Answer:
The lower energy orbital in a many-electron atom is **2p**.