The possible angular momentum quantum numbers that result from combining two angular momentum quantum numbers $j_1$ and $j_2$ are $\left|j_1 - j_2 \right|,\ldots, j_1 + j_2$ . The angular momentum quantum numbers that we need to combine in this problem are $s = 1/2$ , $s = 1/2$ , $s = 1/2$ , $l = 1$ , and $l = 1$ (three electrons with spin angular momentum quantum number $1/2$ two of which are in a state with orbital angular momentum quantum number $l = 1$ and one of which is in a state with orbital angular momentum quantum number $l = 0$ ). Therefore, the maximum total angular momentum quantum number is $1/2 + 1/2+ 1/2+1+1 = \boxed{7/2}$ .

Solution to 1992 Problem 76