`A` wave function for an atomic orbital is given as `Psi_(2,1,0)` Recogine the orbital

Answer

To recognize the orbital represented by the wave function \( \Psi_{2,1,0} \), we will analyze the quantum numbers provided in the notation.

### Step-by-Step Solution:

1. **Identify the Quantum Numbers**:
The wave function \( \Psi_{2,1,0} \) corresponds to three quantum numbers:
- \( n = 2 \) (Principal quantum number)
- \( l = 1 \) (Azimuthal quantum number)
- \( m = 0 \) (Magnetic quantum number)

2. **Determine the Principal Quantum Number \( n \)**:
The principal quantum number \( n \) indicates the energy level or shell of the electron. Here, \( n = 2 \) means the electron is in the second energy level.

3. **Determine the Azimuthal Quantum Number \( l \)**:
The azimuthal quantum number \( l \) defines the shape of the orbital:
- \( l = 0 \) corresponds to an s orbital
- \( l = 1 \) corresponds to a p orbital
- \( l = 2 \) corresponds to a d orbital
Since \( l = 1 \), we conclude that the orbital is a p orbital.

4. **Determine the Magnetic Quantum Number \( m \)**:
The magnetic quantum number \( m \) specifies the orientation of the orbital:
- For \( l = 1 \) (p orbital), \( m \) can take the values -1, 0, or +1.
Here, \( m = 0 \) indicates the specific orientation of the p orbital along the z-axis, which is commonly referred to as the \( 2p_z \) orbital.

5. **Final Recognition of the Orbital**:
Based on the values of \( n \), \( l \), and \( m \), we can identify the orbital as \( 2p_z \).

### Conclusion:
The wave function \( \Psi_{2,1,0} \) corresponds to the \( 2p_z \) orbital.

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