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 the subshells (5D, 6S, 4F, and 5P), we can use the n + l rule, which states that the subshell with the higher value of n + l has higher energy. Let's break down the steps:

### Step-by-Step Solution:

1. **Identify the values of n and l for each subshell:**
- For **5D**:
- n = 5
- l = 2 (since l = 2 for D)
- n + l = 5 + 2 = **7**
- For **6S**:
- n = 6
- l = 0 (since l = 0 for S)
- n + l = 6 + 0 = **6**
- For **4F**:
- n = 4
- l = 3 (since l = 3 for F)
- n + l = 4 + 3 = **7**
- For **5P**:
- n = 5
- l = 1 (since l = 1 for P)
- n + l = 5 + 1 = **6**

2. **Compare the n + l values:**
- 5D: n + l = 7
- 6S: n + l = 6
- 4F: n + l = 7
- 5P: n + l = 6

3. **Order the subshells based on n + l values:**
- The subshells with the lowest n + l value will have the lowest energy.
- 6S and 5P both have n + l = 6, while 5D and 4F both have n + l = 7.

4. **Resolve ties in n + l values:**
- For **6S (n=6)** and **5P (n=5)**: Since 6 > 5, **6S** has higher energy than **5P**.
- For **5D (n=5)** and **4F (n=4)**: Since 5 > 4, **5D** has higher energy than **4F**.

5. **Final order of increasing energy:**
- 5P (lowest energy)
- 6S
- 4F
- 5D (highest energy)

Thus, the correct order for increasing energy of the subshells is:
**5P < 6S < 4F < 5D**