Among the following , the orbitals that has the lowest energy is

Options

A. 5f
B. 4f
C. 6s
D. 6p

Answer

To determine which orbital has the lowest energy among the given options, we can use the n + l rule. This rule states that the energy of an orbital increases with increasing values of n + l, where n is the principal quantum number and l is the azimuthal quantum number.

### Step-by-Step Solution:

1. **Identify the Orbitals**: Let's assume the orbitals given in the question are:
- 5f
- 4d
- 6s
- 6p

2. **Assign Quantum Numbers**:
- For **5f**:
- n = 5
- l = 3 (since f corresponds to l = 3)
- n + l = 5 + 3 = 8
- For **4d**:
- n = 4
- l = 2 (since d corresponds to l = 2)
- n + l = 4 + 2 = 6
- For **6s**:
- n = 6
- l = 0 (since s corresponds to l = 0)
- n + l = 6 + 0 = 6
- For **6p**:
- n = 6
- l = 1 (since p corresponds to l = 1)
- n + l = 6 + 1 = 7

3. **Calculate n + l Values**:
- 5f: n + l = 8
- 4d: n + l = 6
- 6s: n + l = 6
- 6p: n + l = 7

4. **Determine the Lowest Energy**:
- The lowest energy orbital corresponds to the smallest n + l value.
- Here, both 4d and 6s have the same n + l value of 6, but since 4d has a lower principal quantum number (n = 4) compared to 6s (n = 6), 4d will have lower energy than 6s.

5. **Conclusion**:
- The orbital with the lowest energy among the options provided is **4d**.

### Final Answer:
The orbital that has the lowest energy is **4d**.