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Q. What are the possible values of $l$ and $m_l$ for an atomic orbital $4f$?

Structure of Atom

Solution:

For $n ^{\text {th }}$ orbital possible values of azimuthal quantum number, 1 are from 0 to $( n -1)$. Total of $n$ values.
In $4 f$ orbital, $n =4$ and $f$-orbital has $1=3$
Magnetic quantum number $m_{1}$ have values from $-1$ to $+1$ and total of $21+1$ values.
For $1=3$ total; values of $m_{1}$ are 7 and are:
For $1=3, m _{1}=-3-2,-1,0,1,2,3$