The relationship between the magnetic quantum number (ml) and the azimuthal quantum number (l) is given by the following formula:
ml = -l, -l + 1, -l + 2, ..., 0, ..., l - 2, l - 1, l
In this formula, ml represents the magnetic quantum number, which specifies the orientation of the orbital in a given atomic or molecular system. The azimuthal quantum number, l, determines the shape of the orbital and is related to the total orbital angular momentum of the system.
The magnetic quantum number ml can take integer values between -l and l, inclusive, with a step size of 1. This means that there are 2l + 1 possible values for ml corresponding to a particular value of l. These values represent the different possible orientations of the orbital in three-dimensional space.
For example, if l = 2, the possible values of ml would be -2, -1, 0, 1, and 2, resulting in a total of 5 possible orientations for the orbital.