`Psi_420` represents

Options

A. `4 p_z`
B. `4d_(z^2)`
C. 4s
D. `5 P_x`

Answer

To solve the question regarding what `Psi_420` represents, we will break down the components of the notation step by step.

### Step-by-Step Solution:

1. **Understanding the Notation**:
The notation `Psi_nlm` represents a wave function in quantum mechanics, where:
- `n` is the principal quantum number,
- `l` is the angular momentum quantum number,
- `m` is the magnetic quantum number.

2. **Identifying the Values**:
From `Psi_420`, we can identify:
- \( n = 4 \)
- \( l = 2 \)
- \( m = 0 \)

3. **Interpreting the Principal Quantum Number (n)**:
The principal quantum number \( n = 4 \) indicates that the electron is in the fourth energy level or shell.

4. **Interpreting the Angular Momentum Quantum Number (l)**:
The angular momentum quantum number \( l = 2 \) corresponds to the type of orbital:
- \( l = 0 \) corresponds to an s orbital,
- \( l = 1 \) corresponds to a p orbital,
- \( l = 2 \) corresponds to a d orbital.
Therefore, \( l = 2 \) indicates that we are dealing with a d orbital.

5. **Interpreting the Magnetic Quantum Number (m)**:
The magnetic quantum number \( m = 0 \) specifies the orientation of the orbital. For \( l = 2 \) (d orbitals), the possible values of \( m \) can be -2, -1, 0, +1, +2. The value \( m = 0 \) corresponds to the \( d_{z^2} \) orbital.

6. **Conclusion**:
Combining all the information:
- The principal quantum number \( n = 4 \) indicates the fourth shell.
- The angular momentum quantum number \( l = 2 \) indicates a d orbital.
- The magnetic quantum number \( m = 0 \) indicates the \( d_{z^2} \) orbital.

Thus, `Psi_420` represents the **4d_z^2 orbital**.

### Final Answer:
`Psi_420` represents the **4d_z^2 orbital**.