Answer
For $n=5$, there are 5 possible values for $l$ and 25 possible values for $m_l$.
Work Step by Step
*NOTES TO REMEMBER:
- The angular momentum quantum number $l$ can have values from $0$ to $(nā1)$ for each value of $n$.
- The magnetic quantum number $m_l$ can have integral values from $āl$ 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 $m_l$.