Answer
$n=1$, $l=0$, $m_l=0$, orbital $1s$.
$n=3$, $l=-3$, $m_l=2$, not allowed.
$n=3$, $l=2$, $m_l=-2$, orbital $3d$.
$n=2$, $l=0$, $m_l=-1$, not allowed.
$n=0$, $l=0$, $m_l=0$, not allowed.
$n=4$, $l=2$, $m_l=1$, orbital $4d$.
$n=5$, $l=3$, $m_l=0$, orbital $5f$.
Work Step by Step
*NOTES TO REMEMBER:
In an orbital designation,
- the number represents the value of $n$.
- the letter represents the value of $l$, according to the following rule:
$l=0$, the letter used is $s$.
$l=1$, the letter used is $p$.
$l=2$, the letter used is $d$.
$l=3$, the letter used is $f$.
- The value of $l$ cannot exceed or even be equal with the value of $n$ and cannot be negative.
- The value of $n$ must be that $n\gt0$.
- The values of $m_l$ only range from $-l$ to $l$, including $0$.
$n=1$, $l=0$, $m_l=0$, orbital $1s$.
$n=3$, $l=-3$, $m_l=2$, not allowed since $l\lt0$.
$n=3$, $l=2$, $m_l=-2$, orbital $3d$.
$n=2$, $l=0$, $m_l=-1$, not allowed since for $l=0$, the only possible value of $m_l$ is $0$.
$n=0$, $l=0$, $m_l=0$, not allowed since $n\gt0$ is obligatory.
$n=4$, $l=2$, $m_l=1$, orbital $4d$.
$n=5$, $l=3$, $m_l=0$, orbital $5f$.
