# If atomic electron is in $f$-state, what values of the total angular momentum are allowed?

What I know is total angular momentum $$\vec{j}= \vec{\ell}+\vec{s}$$, here $$\ell=3$$ for $$f$$ state, $$s=1/2$$ for spin, so the total angular momentum should be $$7/2$$, is this correct? is there any other allowed values?

If $$l=3$$ and $$s=1/2$$ then the values of total angular momentum can take lie within the following range:
$$|l-s|\leq J\leq l+s$$
With $$J$$ incrementing by 1 between these two bounds.
$$\therefore 5/2\leq J\leq7/2$$
$$J$$ can take values $$5/2$$ and $$7/2$$