Question

What are the possible values of $m_l$ for an electron in the $n = 4$ state?

Final Answer

$m_l = -3, -2, -1, 0, 1, 2, 3$

### Solution video

# OpenStax College Physics for AP® Courses, Chapter 30, Problem 37 (Problems & Exercises)

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Video Transcript

This is College Physics Answers with Shaun Dychko. We are told that the principal quantum number for an electron around an atom is 4 and we are asked what are the possible values of the angular momentum projection quantum number,

*m l*. Now, we don't know what*l*is because we are not told but we can choose a maximum*l*such that we get the maximum number of possibilities for*m l*because*m l*is possibilities are constrained by whatever the value of*l*is. And so the maximum possible*l*is 3 because it follows the sequence starting from 0, 1 to up to a maximum of principal quantum number minus 1 so that is 4 minus 1. So the maximum possible angular momentum quantum number is 3. So with that being 3, the angular momentum projection quantum number can start from negative 3 which is negative*l*and increasing by 1's to negative 2, negative 1, 0, 1, 2 or a maximum of*l*so a maximum of 3. So these are the possible values for*m l*given a principal quantum number of 4.