Which is the correct order for increasing the energy of subshells ?

Options

A. `5p lt 4f lt 6s lt 5d`
B. `5p lt 6s lt 4f lt 5d`
C. `4f lt 5p lt 5d lt 6s`
D. `5p lt 5d lt 4f lt 6s`

Answer

To determine the correct order for increasing energy of subshells, we will use the n + l rule. This rule states that the energy of subshells increases with the increasing value of n + l, where n is the principal quantum number and l is the azimuthal quantum number. If two subshells have the same n + l value, the subshell with the lower n value has lower energy.

Let's analyze the given subshells: 5p, 4f, 6s, and 5d.

### Step-by-Step Solution:

1. **Identify the values of n and l for each subshell:**
- For **5p**: n = 5, l = 1 (p subshell)
- For **4f**: n = 4, l = 3 (f subshell)
- For **6s**: n = 6, l = 0 (s subshell)
- For **5d**: n = 5, l = 2 (d subshell)

2. **Calculate n + l for each subshell:**
- 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

3. **Compare the n + l values:**
- 5p: n + l = 6
- 6s: n + l = 6
- 4f: n + l = 7
- 5d: n + l = 7

4. **Determine the order based on n + l values:**
- Both 5p and 6s have the same n + l value (6), but since n for 5p (5) is less than n for 6s (6), 5p will have lower energy than 6s.
- Between 4f and 5d, both have the same n + l value (7), but since n for 4f (4) is less than n for 5d (5), 4f will have lower energy than 5d.

5. **Establish the increasing order of energy:**
- First: 5p (lowest energy)
- Second: 6s
- Third: 4f
- Fourth: 5d (highest energy)

Thus, the correct order for increasing energy of the subshells is:
**5p < 6s < 4f < 5d**

### Final Answer:
The correct option for increasing order of energy of the subshells is:
**5p, 6s, 4f, 5d**

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