An element $X$ belongs to the $3rd$ period and group $13$ of the Modern Periodic Table.
$(a)$ Determine the valence electrons and the valency of $X$.
$(b)$ Determine the molecular formula of the compound formed when $X$ reacts with an element $Y$ (atomic number $= 8$).
$(c)$ Write the name and formula of the compound formed when $X$ combines with chlorine.

State whether the following statement is true or false: In $1913$,Dmitri Ivanovich Mendeleev showed that the atomic number of an element is a more fundamental property than its atomic mass.

Give reasons for the following:
$(a)$ Lithium atom is smaller than Sodium atom.
$(b)$ Chlorine (Atomic Number $17$) is more electronegative than Sulphur (Atomic Number $16$).

Complete the following crossword puzzle (Figure):
**Across:**
$(1)$ An element with atomic number $12$.
$(3)$ Metal used in making cans and member of Group $14$.
$(4)$ $A$ lustrous non-metal which has $7$ electrons in its outermost shell.
**Down:**
$(2)$ Highly reactive and soft metal which imparts yellow colour when subjected to flame and is kept in kerosene.
$(5)$ The first element of second Period.
$(6)$ An element which is used in making fluorescent bulbs and is second member of Group $18$ in the Modern Periodic Table.
$(7)$ $A$ radioactive element which is the last member of halogen family.
$(8)$ Metal which is an important constituent of steel and forms rust when exposed to moist air.
$(9)$ The first metalloid in Modern Periodic Table whose fibres are used in making bullet-proof vests.

The elements $A, B, C, D$ and $E$ have atomic numbers $9, 11, 17, 12$ and $13$ respectively. Which pair of elements belong to the same group?

Elements have been arranged in the following sequence on the basis of their increasing atomic masses.
$F, Na, Mg, Al, Si, P, S, Cl, Ar, K$
$(a)$ Pick two sets of elements which have similar properties.
$(b)$ The given sequence represents which law of classification of elements?