If two sushells have the same value of n + 1, which shell will be filled first?

Answer

To determine which subshell will be filled first when two subshells have the same value of \( n + l \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the \( n + l \) Rule**: The \( n + l \) rule states that the subshell with the lower \( n + l \) value will be filled first. If two subshells have the same \( n + l \) value, we need to look at their principal quantum number \( n \).

2. **Identify the Subshells**: Let's consider two subshells, for example, \( 3p \) and \( 4s \).
- For \( 3p \):
- \( n = 3 \) (principal quantum number)
- \( l = 1 \) (azimuthal quantum number for p subshell)
- Therefore, \( n + l = 3 + 1 = 4 \).
- For \( 4s \):
- \( n = 4 \) (principal quantum number)
- \( l = 0 \) (azimuthal quantum number for s subshell)
- Therefore, \( n + l = 4 + 0 = 4 \).

3. **Compare the Values of \( n \)**: Since both \( 3p \) and \( 4s \) have the same \( n + l \) value of 4, we need to compare their \( n \) values.
- \( 3p \) has \( n = 3 \).
- \( 4s \) has \( n = 4 \).

4. **Determine Which Subshell is Filled First**: According to the \( n + l \) rule, when two subshells have the same \( n + l \) value, the subshell with the lower \( n \) value will be filled first because it has lower energy.
- Since \( n = 3 \) (for \( 3p \)) is less than \( n = 4 \) (for \( 4s \)), \( 3p \) will be filled before \( 4s \).

### Final Conclusion:
The subshell with the lower value of \( n \) will be filled first when two subshells have the same value of \( n + l \). Therefore, in our example, \( 3p \) will be filled before \( 4s \).

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