$(i)$ An atomic orbital has $n=3$. What are the possible values of $l$ and $m_l$?
$(ii)$ List the quantum numbers ($m_l$ and $l$) of electrons for $3d$ orbital.
$(iii)$ Which of the following orbitals are possible? $1p$,$2s$,$2p$,and $3f$.

(N/A) $(i)$ $n=3$ (Given).
For a given value of $n$,$l$ can have values from $0$ to $(n-1)$.
$\therefore$ For $n=3$,$l=0, 1, 2$.
For a given value of $l$,$m_l$ can have $(2l+1)$ values ranging from $-l$ to $+l$.
For $l=0$,$m_l=0$; for $l=1$,$m_l=-1, 0, 1$; for $l=2$,$m_l=-2, -1, 0, 1, 2$.
$(ii)$ For $3d$ orbital,$n=3$ and $l=2$.
For $l=2$,$m_l$ can have $5$ values: $-2, -1, 0, 1, 2$.
$(iii)$ Among the given orbitals,only $2s$ and $2p$ are possible.
$1p$ is not possible because for $p$-orbital $(l=1)$,the minimum value of $n$ is $2$.
$3f$ is not possible because for $f$-orbital $(l=3)$,the minimum value of $n$ is $4$.