The correct orders of increasing energy of atomic orbitals is

Options

A. ` 5p gt 4f lt 6s lt5d`
B. `5plt6s lt 4f lt5d `
C. `4f lt 5p lt5d lt6s`
D. `5plt 5d lt4flt6s`

Answer

To determine the correct order of increasing energy of atomic orbitals, we can use the n + l rule, where n is the principal quantum number and l is the azimuthal quantum number. Let's go through the solution step by step.

### Step-by-Step Solution:

1. **Identify the Atomic Orbitals**: The atomic orbitals we need to analyze are 5p, 4f, 6s, and 5d.

2. **Determine n and l Values**:
- For **5p**:
- n = 5 (principal quantum number)
- l = 1 (for p orbitals)
- For **4f**:
- n = 4
- l = 3 (for f orbitals)
- For **6s**:
- n = 6
- l = 0 (for s orbitals)
- For **5d**:
- n = 5
- l = 2 (for d orbitals)

3. **Calculate n + l Values**:
- For **5p**: n + l = 5 + 1 = 6
- For **4f**: n + l = 4 + 3 = 7
- For **6s**: n + l = 6 + 0 = 6
- For **5d**: n + l = 5 + 2 = 7

4. **Compare n + l Values**:
- We have:
- 5p: n + l = 6
- 6s: n + l = 6
- 4f: n + l = 7
- 5d: n + l = 7

5. **Determine the Order**:
- Since 5p and 6s have the same n + l value (6), we compare their n values:
- 5p (n = 5) < 6s (n = 6), so 5p has lower energy than 6s.
- For 4f and 5d, both have n + l = 7, we compare their n values:
- 4f (n = 4) < 5d (n = 5), so 4f has lower energy than 5d.

6. **Final Order of Increasing Energy**:
- Combining all the comparisons, we get the increasing order of energy:
- 5p < 6s < 4f < 5d

### Conclusion:
The correct order of increasing energy of the atomic orbitals is:
**5p < 6s < 4f < 5d**