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. 2
B. 4
C. 6
D. 10

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: Understand the quantum numbers
- The principal quantum number (n) indicates the energy level of the electron. Here, n = 3 means we are looking at the third energy level.
- The azimuthal quantum number (l) defines the subshell. For l = 1, this corresponds to the p subshell.
- The magnetic quantum number (m) specifies the orientation of the orbital. For l = 1, the possible values of m are -1, 0, and +1.

### Step 2: Identify the subshell and orbitals
- Since l = 1, we are dealing with the 3p subshell. The 3p subshell has three orbitals corresponding to the values of m:
- m = -1
- m = 0
- m = +1

### Step 3: Determine the maximum number of electrons
- Each orbital can hold a maximum of 2 electrons (due to the Pauli exclusion principle).
- Therefore, for the 3p subshell, which has 3 orbitals, the maximum number of electrons is calculated as follows:
\[ \text{Maximum electrons} = \text{Number of orbitals} \times 2 = 3 \times 2 = 6 \]

### Step 4: Consider the specific m value
- The question specifies m = -1. However, this does not limit the number of electrons in the subshell; it only specifies one of the orbitals. The 3p subshell can still hold a total of 6 electrons, regardless of the specific m value.

### Conclusion
Thus, the maximum number of electrons that can be associated with the quantum numbers (n = 3, l = 1, m = -1) is **6 electrons**.

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