Which subshell is represented by the wave function `Psi_(431)` ?

Options

A. 4f
B. 3d
C. 4d
D. 7s

Answer

To determine which subshell is represented by the wave function \( \Psi_{431} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Notation**: The wave function notation \( \Psi_{nlm} \) consists of three quantum numbers:
- \( n \): Principal quantum number
- \( l \): Azimuthal quantum number
- \( m \): Magnetic quantum number

2. **Identify the Quantum Numbers**: From the wave function \( \Psi_{431} \):
- \( n = 4 \)
- \( l = 3 \)
- \( m = 1 \)

3. **Determine the Subshell from \( l \)**:
- The azimuthal quantum number \( l \) corresponds to specific subshells:
- \( l = 0 \) corresponds to the s subshell
- \( l = 1 \) corresponds to the p subshell
- \( l = 2 \) corresponds to the d subshell
- \( l = 3 \) corresponds to the f subshell

4. **Combine \( n \) and \( l \)**:
- Since \( n = 4 \) and \( l = 3 \), we have the 4f subshell.

5. **Conclusion**: The subshell represented by the wave function \( \Psi_{431} \) is **4f**.

### Final Answer:
The subshell represented by the wave function \( \Psi_{431} \) is **4f**.

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