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’.

(a) Positions of 'X', 'Y' and 'Z' in the Modern Periodic Table:

• 'X' (Atomic number 7): Electronic configuration is $2, 5$. It has $2$ shells and $5$ valence electrons.
• Period: $2$
• Group: $10 + 5 = 15$
• 'Y' (Atomic number 8): Electronic configuration is $2, 6$. It has $2$ shells and $6$ valence electrons.
• Period: $2$
• Group: $10 + 6 = 16$
• 'Z' (Atomic number 9): Electronic configuration is $2, 7$. It has $2$ shells and $7$ valence electrons.
• Period: $2$
• Group: $10 + 7 = 17$

(b) Decreasing order of atomic radii:

• Order: $X > Y > Z$
• Reason: All three elements belong to the same period (Period 2). As we move from left to right across a period, the nuclear charge increases due to the addition of protons in the nucleus. This stronger nuclear charge pulls the valence electrons closer to the nucleus, thereby decreasing the atomic radius.

(c) Formula of the compound formed when 'X' combines with 'Z':

• Element 'X' (Nitrogen) has $5$ valence electrons, so its valency is $8 - 5 = 3$.
• Element 'Z' (Fluorine) has $7$ valence electrons, so its valency is $8 - 7 = 1$.
• By crossing over their valencies:

$$\text{Element } X \quad \text{Element } Z$$

$$\text{Valency: } 3 \quad\quad\quad\quad 1$$

• Formula: $XZ_3$ (which represents Nitrogen trifluoride, $NF_3$).