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

Options

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

Explanation

To determine the maximum number of electrons that can be associated with the given set of quantum numbers \( (n = 3, l = 1, m = -1) \), we can follow these steps:

### Step 1: Identify the Principal Quantum Number (n)
The principal quantum number \( n \) indicates the energy level or shell of the electron. In this case, \( n = 3 \) means we are looking at the third energy level.

**Hint:** The principal quantum number \( n \) tells us which shell the electrons are in.

### Step 2: Identify the Azimuthal Quantum Number (l)
The azimuthal quantum number \( l \) defines the subshell. The values of \( l \) correspond to different subshells as follows:
- \( l = 0 \) corresponds to the s subshell
- \( l = 1 \) corresponds to the p subshell
- \( l = 2 \) corresponds to the d subshell
- \( l = 3 \) corresponds to the f subshell

Since \( l = 1 \), we are dealing with the p subshell.

**Hint:** The azimuthal quantum number \( l \) determines the shape of the orbital and the type of subshell.

### Step 3: Identify the Magnetic Quantum Number (m)
The magnetic quantum number \( m \) specifies the orientation of the orbital within the subshell. For \( l = 1 \) (p subshell), the possible values of \( m \) are:
- \( m = -1 \) (3p orbital)
- \( m = 0 \) (3p orbital)
- \( m = +1 \) (3p orbital)

In this case, \( m = -1 \) refers to one specific orbital in the p subshell, which is the 3p orbital.

**Hint:** The magnetic quantum number \( m \) indicates the specific orbital orientation.

### Step 4: Determine the Maximum Number of Electrons
Each orbital can hold a maximum of 2 electrons (one with spin up and one with spin down). Since \( m = -1 \) corresponds to one specific orbital (3p), the maximum number of electrons that can occupy this orbital is 2.

**Hint:** Each orbital can hold a maximum of 2 electrons due to the Pauli exclusion principle.

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

**Final Answer:** 2 electrons.