## Chemistry: The Central Science (13th Edition)

For $n=5$, there are 5 possible values for $l$ and 25 possible values for $m_l$.
*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 $n=5$, there are 5 possible values for $l$ $(0, 1, 2, 3, 4)$. - 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 $m_l$ $(-2, -1, 0, 1, 2)$. - For $l=3$, there are 7 possible values for $m_l$ $(-3, -2, -1, 0, 1, 2, 3)$. - For $l=4$, there are 9 possible values for $m_l$ $(-4, -3, -2, -1, 0, 1, 2, 3, 4)$. Overall, there are 25 possible values for $m_l$.