Zinc and mercury do not show variable valency like d-block elements because

their d-shells are complete.

Explanation:

Zinc (Zn) and mercury (Hg) are d-block elements with atomic numbers 30 and 80, respectively. Their electronic configurations are:

• Zinc: [Ar] 3d¹⁰ 4s²
• Mercury: [Xe] 4f¹⁴ 5d¹⁰ 6s²

In both elements, the d-subshells are completely filled with 10 electrons, resulting in a stable electronic arrangement. This full d-subshell configuration leads to the following characteristics:

• Limited oxidation states: The stability of the filled d-subshells means that Zn and Hg predominantly exhibit a +2 oxidation state, corresponding to the loss of their two outermost s-electrons. This is in contrast to other transition metals, which often have partially filled d-orbitals and can exhibit multiple oxidation states.
• Absence of variable valency: Due to their complete d-subshells, Zn and Hg lack unpaired d-electrons that could participate in bonding, thereby limiting their ability to exhibit variable valency. This distinguishes them from other d-block elements, which commonly show variable valency due to the involvement of d-electrons in bonding.

Therefore, the correct explanation is that zinc and mercury do not show variable valency like other d-block elements because their d-shells are complete.