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

1 Answer
Stefan V.
Mar 25, 2018

Seven.

Explanation:

The number of values that the magnetic quantum number, m_lml, can take tells you the number of orbitals present in an energy subshell described by the angular momentum quantum number ll.

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"))

Related questions
See all questions in Quantum Numbers
Impact of this question
39117 views around the world
You can reuse this answer
Creative Commons License