# Question #3c081

Feb 15, 2018

${m}_{l} = \left\{- 3 , - 2 , - 1 , 0 , 1 , 2 , 3\right\}$

#### Explanation:

The values that the magnetic quantum number, ${m}_{l}$ can take depend on the value of the angular momentum quantum number, $l$.

${m}_{l} = \left\{- l , - \left(l - 1\right) , \ldots , - 1 , 0 , 1 , \ldots , \left(l - 1\right) , l\right\}$

This is the case because the angular momentum quantum number describes the energy subshell, i.e. the type of orbital, in which an electron is located inside an atom.

The magnetic quantum number describes the orientation of the orbital in which the electron is located, so it makes sense to have the type of the orbitals dictate the possible values that can describe their orientation.

.$l = 3$

and so

${m}_{l} = \left\{- 3 , - 2 , - 1 , 0 , 1 , 2 , 3\right\}$

The number of values that the magnetic quantum number can take tells you the number of orbitals present in the given energy subshell.

In this case, the $f$ subshell, which is described by $l = 3$, can hold seven $f$ orbitals because the magnetic quantum number can take seven possible values.

${m}_{l} = \left\{- 3 , - 2 , - 1 , 0 , 1 , 2 , 3\right\} \to \text{7 values = 7 orbitals}$