what is the maximum number of electrons that can be associated with the following set of quantum numbers ? ` n=3 , l=1 and m=-1`

Options

A. 6
B. 4
C. 2
D. 10

Answer

To determine the maximum number of electrons that can be associated with the given set of quantum numbers \( n = 3 \), \( l = 1 \), and \( m = -1 \), 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. Here, \( n = 3 \).

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

3. **Determine the Magnetic Quantum Number (m)**:
- The magnetic quantum number \( m \) specifies the orientation of the orbital. The values of \( m \) can range from \( -l \) to \( +l \). Therefore, for \( l = 1 \), \( m \) can take the values \( -1, 0, +1 \). In this case, \( m = -1 \) corresponds to one specific orbital within the p subshell.

4. **Determine the Number of Orbitals in the p Subshell**:
- The p subshell consists of three orbitals: \( p_x \), \( p_y \), and \( p_z \). Each of these orbitals can hold a maximum of 2 electrons.

5. **Calculate the Maximum Number of Electrons**:
- Since each orbital can hold 2 electrons, and we are considering only the orbital corresponding to \( m = -1 \) (which is one of the three p orbitals), the maximum number of electrons that can be associated with this specific orbital is:
\[ \text{Maximum electrons} = 2 \]

### Final Answer:
The maximum number of electrons that can be associated with the quantum numbers \( n = 3 \), \( l = 1 \), and \( m = -1 \) is **2**.

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