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

1 Answer
Mar 25, 2018

Answer:

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 = {-l, -(l-1), ..., -1, 0, 1, ..., (l-1), l}#

In your case, you have

#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 = {-3, -2, -1, 0, 1, 2, 3}#

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.

#underbrace(l = 3)_ (color(blue)("the f subshell")) => m_l = underbrace( {-3, -2, -1, 0, 1, 2, 3} )_ (color(blue)("7 values for m"_l quad = quad "7 distinct f orbitals"))#