`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 need to analyze the notation used in quantum mechanics, specifically in the context of wave functions.

### Step-by-Step Solution:

1. **Understanding the Notation**: The notation `Psi_420` can be broken down into three parts: the first digit (4), the second digit (2), and the letter (D). In quantum mechanics, the wave function is often denoted by the Greek letter Psi (Ψ).

2. **Identifying the Principal Quantum Number (n)**: The first digit (4) in `Psi_420` represents the principal quantum number (n). This quantum number indicates the energy level of the electron in an atom. Here, \( n = 4 \).

3. **Identifying the Azimuthal Quantum Number (l)**: The second digit (2) corresponds to the azimuthal quantum number (l). This quantum number determines the shape of the orbital. The values of l can be 0, 1, 2, and so on, corresponding to s, p, d, and f orbitals respectively. Here, \( l = 2 \).

4. **Determining the Orbital Type**: The letter D indicates the type of orbital. In quantum mechanics, the following correspondence exists:
- \( l = 0 \) corresponds to s orbitals
- \( l = 1 \) corresponds to p orbitals
- \( l = 2 \) corresponds to d orbitals
- \( l = 3 \) corresponds to f orbitals

Since \( l = 2 \), this indicates that the orbital is a d orbital.

5. **Conclusion**: Therefore, `Psi_420` represents a wave function for an electron in the 4th energy level (n = 4) and in a d orbital (l = 2).

### Final Answer:
`Psi_420` represents a wave function for an electron in the 4th energy level (n = 4) in a d orbital (l = 2).