# Chapter 6 - Electronic Structure of Atoms - Exercises: 6.56a

For $n=3$, there are 3 possible values for $l$ and 9 possible values for $m_l$.

#### Work Step by Step

*NOTES TO REMEMBER: - The angular momentum quantum number $l$ can have values from $0$ to $(n−1)$ for each value of $n$. - The magnetic quantum number $m_l$ can have integral values from $−l$ to $l$, including $0$. For $n=3$, there are 3 possible values for $l$ $(0, 1, 2)$. - For $l=0$, there is 1 possible value for $m_l$ $(0)$. - For $l=1$, there are 3 possible values for $m_l$ $(-1, 0, 1)$. - For $l=2$, there are 5 possible values for $m_l$ $(-2, -1, 0, 1, 2)$. Overall, there are 9 possible values for $m_l$.

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