Question

Which of the following magnetic quantum number, ml, cannot be found in d-orbitals?

A) ml=0

B) ml=1

C) ml=2

D) ml=3

Answer 1

The magnetic quantum number ml for d-orbitals, which have an angular momentum quantum number l of 2, can range from -2 to +2. Hence, an ml value of 3 is not possible for d-orbitals since it exceeds the given range.

Step-by-step explanation:

The magnetic quantum number, ml, is crucial for determining the orientation of an electron's orbital in space. It is heavily dependent on the angular momentum quantum number l. When discussing d-orbitals, which correspond to l=2, the possible values for ml range from -l to +l, i.e., -2, -1, 0, +1, and +2. Therefore, an ml value of 3 is not permissible for d-orbitals, as it exceeds the maximum value of +2.

This is in line with the general rule for any given l value, where the magnetic quantum number can take on 2l+1 values. For instance, with l=0 for s-orbitals, ml can only be 0; with l=1 for p-orbitals, ml can be -1, 0, or +1; and with l=3 for f-orbitals, ml ranges from -3 to +3. Values outside these ranges are not allowed and do not exist within the confines of quantum mechanics for electron orbitals.