# What values of m_l are permitted for an electron with l=3 ?

Mar 25, 2018

Seven.

#### Explanation:

The number of values that the magnetic quantum number, ${m}_{l}$, can take tells you the number of orbitals present in an energy subshell described by the angular momentum quantum number $l$.

The values that the magnetic quantum number can take depend on the value of the angular momentum quantum number as described by the relation

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

$l = 3$
This value of the angular momentum quantum number describes the $f$ subshell. Consequently, you can say that magnetic quantum number can take the following values
${m}_{l} = \left\{- 3 , - 2 , - 1 , 0 , 1 , 2 , 3\right\}$
The fact that the magnetic quantum number can take $7$ possible values for an $f$ subshell tells you that this subshell holds a total of $7$ orbitals, each described by a value of the magnetic quantum number.
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