What is the maximum number of orbitals that can be identified with the following quantum numbers? n =3, l= 1, m =0

Options

A. 1
B. 2
C. 3
D. 4

Answer

To determine the maximum number of orbitals that can be identified with the given quantum numbers \( n = 3 \), \( l = 1 \), and \( m = 0 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number (n)**:
- The principal quantum number \( n \) indicates the energy level of the electron in an atom. Here, \( n = 3 \) means we are looking at the third energy level.

**Hint**: The principal quantum number \( n \) determines the shell of the electron.

2. **Identify the Azimuthal Quantum Number (l)**:
- The azimuthal quantum number \( l \) defines the subshell and its shape. For \( l = 1 \), this corresponds to a p subshell.

**Hint**: The value of \( l \) can range from \( 0 \) to \( n-1 \). For \( l = 1 \), it indicates a p subshell.

3. **Determine the Magnetic Quantum Number (m)**:
- The magnetic quantum number \( m \) specifies the orientation of the orbital. For a p subshell (\( l = 1 \)), the possible values of \( m \) are \( -1, 0, +1 \). This means there are three possible orientations for the p orbitals: \( p_x \), \( p_y \), and \( p_z \).

**Hint**: The magnetic quantum number \( m \) can take values from \( -l \) to \( +l \), including zero.

4. **Analyze the Given Magnetic Quantum Number**:
- In this case, we are given \( m = 0 \). This means we are only interested in the orbital that corresponds to this orientation, which is \( p_z \).

**Hint**: If \( m = 0 \), it indicates a specific orientation of the orbital.

5. **Conclusion**:
- Since \( m = 0 \) corresponds to only one specific orbital (the \( p_z \) orbital), the maximum number of orbitals that can be identified with the given quantum numbers \( n = 3 \), \( l = 1 \), and \( m = 0 \) is **1**.

**Final Answer**: The maximum number of orbitals is **1**.