Three elements $X$,$Y$,and $Z$ have atomic numbers $7$,$8$,and $9$ respectively.
$(a)$ State their positions (Group number and period number both) in the Modern Periodic Table.
$(b)$ Arrange these elements in the decreasing order of their atomic radii.
$(c)$ Write the formula of the compound formed when $X$ combines with $Z$.

(N/A) Electronic configuration of elements:
$X (Z=7): 2, 5$. It has $2$ shells,so it belongs to Period $2$. Since it has $5$ valence electrons,its Group number is $5 + 10 = 15$.
$Y (Z=8): 2, 6$. It has $2$ shells,so it belongs to Period $2$. Since it has $6$ valence electrons,its Group number is $6 + 10 = 16$.
$Z (Z=9): 2, 7$. It has $2$ shells,so it belongs to Period $2$. Since it has $7$ valence electrons,its Group number is $7 + 10 = 17$.
$(b)$ Atomic radius decreases across a period from left to right due to an increase in effective nuclear charge. Since all three elements belong to Period $2$ and their atomic numbers increase from $X$ to $Y$ to $Z$,the decreasing order of atomic radii is $X > Y > Z$.
$(c)$ $X$ has a valency of $3$ (needs $3$ electrons to complete its octet) and $Z$ has a valency of $1$ (needs $1$ electron to complete its octet). By cross-multiplying their valencies,the formula of the compound formed is $XZ_3$.