Answer
a) $n=5$, $l=3$, $m_{l}$ can be $-3$, $-2$, $-1$, $0$, $1$, $2$ or $3$;
b) $n=4$, $l=2$, $m_{l}$ can be $-2$, $-1$, $0$, $1$ or $2$;
c) $n=2$, $l=0$, $m_{l}=0$.
Work Step by Step
a) For $5f$ orbital, $n=5$, and since we have the $f$ sublevel, $l=3$. Magnetic quantum number has to be between $-l$ and $l$, so it can be either $-3$, $-2$, $-1$, $0$, $1$, $2$ or $3$.
b) Using the same idea as in the previous example, we can conclude that $n=4$, $l=2$ and $m_{l}$ can be either $-2$, $-1$, $0$, $1$ or $2$.
c) As shown before, $n=2$, $l=0$ and $m_{l}=0$.
