An element $X$ (atomic number $17$) reacts with an element $Y$ (atomic number $20$) to form a divalent halide.
$(a)$ Where in the periodic table are elements $X$ and $Y$ placed?
$(b)$ Classify $X$ and $Y$ as metal$(s)$,non-metal$(s)$,or metalloid$(s)$.

(A-D) The electronic configuration of element $X$ $(Z=17)$ is $2, 8, 7$. Since it has $7$ valence electrons,it belongs to Group $17$ and the $3^{rd}$ period.
The electronic configuration of element $Y$ $(Z=20)$ is $2, 8, 8, 2$. Since it has $2$ valence electrons,it belongs to Group $2$ and the $4^{th}$ period.
$(b)$ Element $X$ is a non-metal because it gains electrons to complete its octet. Element $Y$ is a metal because it loses $2$ electrons to form a stable cation.