Final answer:
The central atom X in a linear XY₂ molecule can be most certainly characterized by having sp-hybridization. Other features such as being hypervalent or involved in double bonds are not guaranteed just by the molecule's linear shape. The correct answer is option d) Has sp-hybridization.
Step-by-step explanation:
If the molecule XY₂ is linear, the most certain characteristic about the central atom X is that it has sp-hybridization. A linear molecular shape occurs when the central atom is surrounded by just two regions of valence electron density, which are spaced at optimal angles of 180°. This linear configuration leads to sp-hybridization, which involves the mixing of one s orbital and one p orbital from the central atom to create two sp-hybrid orbitals. Examples of other molecules with central atoms that are sp-hybridized include HgCl₂, Zn(CH₃)₂, HCCH, and CO₂.
The other options provided have less certainty: a) The central atom X being hypervalent is not certain just because the molecule is linear. Hypervalency involves having more than an octet of electrons, but this is not a requirement for linearity. b) The central atom being involved in at least one double bond is possible but not certain, as linear molecules can also have atoms connected by single bonds if there are no lone pairs on the central atom. c) While many linear molecules do obey the octet rule, this is not an absolute given, especially not for molecules involving elements in periods 3 and beyond where expanded octets are possible.