Hybridization state of the beryllium atom in $BeC{l_2}$ molecule is $x$ . The type of hybridization changes to $y$ when $BeC{l_2}$ transforms to the solid state. Then $x,y$ are respectively.
(A) $sp,s{p^2}$
(B) $sp,s{p^3}$
(C) $s{p^2},s{p^3}$
(D) $sp,sp$

Hint: Hybridization is defined as the concept of mixing two atomic orbitals with the same energy levels to give a degenerated new type of orbitals. The intermixing is based on quantum mechanics. The atomic orbitals of the same energy level can only take part in Hybridization and both full-filled and half-filled orbitals can also take part in this process, provided they have equal energy.

Complete step by step answer:
During the process of Hybridization, the atomic orbitals of similar energy are mixed together such as the mixing of two ’ $s$ ’ orbitals or two ’ $p$ ’ orbitals or mixing of ’ $s$ ’ orbital with a ’ $p$ ’ orbital or ’ $s$ ’ orbital with a ‘ $d$ ' orbital.
The structure of solid $BeC{l_2}$ is a polymeric chain; the local structure is an almost regular tetrahedron around the $Be$ atom and the bonding can be considered to be based on $s{p^3}$ Hybridization. In $BeC{l_2}$ , the chloride ion has sufficient electron density for $2c,2c$ covalent bonding takes place. Beryllium chloride is a Lewis acid, readily forming adducts with electron-pair donors such as diethyl ether.
In the vapor phase the compound tends to form a dinner based on $s{p^2}$ Hybridization and when temperature is above ${900^\circ }C$ linear monomers are formed, indicating $sp$ Hybridization

Therefore, option (A) is the correct option.

Additional information:
All the beryllium halides are covalent, expect $Be{F_2}$ , are insoluble in water, all other halides are soluble. $Be{F_2}$is prepared from the thermal decomposition of $\left\{ {{{\left( {N{H_4}} \right)}_2}Be{F_2}} \right\}$ and is a glassy solid that exists in several temperature dependent phases similar to those of $Si{O_2}$ . It is soluble in water, forming the hydrate $\left[ {Be{{\left( {OH} \right)}_2}} \right]_4^{2 + }$ . Beryllium chloride, $BeC{l_2}$ can be made from the oxide:
$Be{O_s} + C\left( s \right) + C{l_2}\left( g \right) \to BeC{l_2}\left( s \right) + CO\left( g \right)$
The chloride, as well as $BeB{r_2}$ and $Be{I_2}$ , can also be prepared from direct reaction of the elements at elevated temperature.

Note:
Beryllium chloride is an inorganic compound with the formula $BeC{l_2}$ . It is colorless, hygroscopic solid that dissolves well in many polar solvents. Its properties are similar to those of aluminium chloride. It is used as a raw material for the electrolysis of beryllium and as a catalyst for Friedal-crafts reaction.