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 1: Identify the Quantum Numbers
The wave function \( \Psi_{431} \) can be broken down into three quantum numbers:
- \( n = 4 \) (principal quantum number)
- \( l = 3 \) (azimuthal quantum number)
- \( m = 1 \) (magnetic quantum number)

### Step 2: Understand the Principal Quantum Number (n)
The principal quantum number \( n \) indicates the energy level or shell of the electron. In this case, \( n = 4 \) means we are looking at the fourth energy level.

### Step 3: Understand the Azimuthal Quantum Number (l)
The azimuthal quantum number \( l \) determines the shape of the orbital and is related to the subshell:
- \( l = 0 \) 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

Since \( l = 3 \), this indicates that we are dealing with an f subshell.

### Step 4: Combine the Information
Now that we have both \( n \) and \( l \):
- The principal quantum number \( n = 4 \) indicates the fourth energy level.
- The azimuthal quantum number \( l = 3 \) indicates the f subshell.

### Step 5: Write the Subshell Notation
Combining these two pieces of information, we can represent the subshell as \( 4f \).

### Conclusion
Thus, the subshell represented by the wave function \( \Psi_{431} \) is \( 4f \).

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