Question

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

• A. 2
• B. 3
• C. 4
• D. 1

Answer 1

The Correct Option is D

The question asks for the maximum number of orbitals identified by a set of quantum numbers values: n = 3, l = 1, and m_l = 0. Let's go through a step-by-step analysis of this set of quantum numbers:

1. Principal Quantum Number (n): This number specifies the energy level or shell and can be any positive integer. In this case, n = 3, meaning we are dealing with the third shell.
2. Azimuthal Quantum Number (l): Also known as the angular momentum quantum number, it defines the shape of the orbital. It can take values from 0 to n-1. Here, l = 1, which corresponds to the 'p' subshell.
3. Magnetic Quantum Number (m_l): This number describes the orientation of the orbital within a subshell. It ranges from -l to +l. Given l = 1, m_l can be -1, 0, or +1. The question specifies m_l = 0, indicating the center 'p' orbital.

From the above analysis:

• The p subshell (l = 1) in any shell has 3 orbitals: p_x, p_y, and p_z, corresponding to m_l = -1, 0, and +1.
• Here, only one orbital has m_l = 0 within the given set of quantum numbers, specifically the p_z orbital.

Therefore, there is only one orbital that matches the given set of quantum numbers. Thus, the maximum number of orbitals that can be identified with the given quantum numbers is 1.

Hence, the correct answer is:

• 1