Question

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

• A. 4
• B. 2
• C. 10
• D. 6

Answer 1

The Correct Option is B

To determine the maximum number of electrons that can be associated with the given set of quantum numbers: \( n = 3 \), \( l = 1 \), and \( m = -1 \), let's interpret these quantum numbers and their implications:

• Principal Quantum Number (n): It specifies the main energy level occupied by the electron. In this case, \( n = 3 \), which means the electron is in the third energy level or shell.
• Azimuthal Quantum Number (l): It defines the shape of the orbital and is sometimes called the angular momentum quantum number. The value of \( l \) can range from 0 to \( n-1 \). For \( n = 3 \), possible values of \( l \) are 0, 1, and 2. Here, \( l = 1 \) indicates a 'p' subshell.
• Magnetic Quantum Number (m): It indicates the orientation of the orbital in space. Its values range from \(-l\) to \(+l\), inclusive. Given \( l = 1 \), \( m \) can be -1, 0, +1. Here, \( m = -1 \) specifies one of the possible orientations of the p orbital.

Each orbital can hold a maximum of 2 electrons, each with opposite spins. Therefore, for the orbital defined by \( n = 3 \), \( l = 1 \), and \( m = -1 \), the maximum number of electrons is 2.

Thus, the correct answer is 2.

This solution uses the fundamental principles of quantum mechanics concerning the arrangement of electrons in atoms, based on their quantum numbers.