Concept:Geometrical (cis-trans) isomerism requires restricted rotation (like a double bond) and for
each carbon atom of the double bond to be attached to two
different groups.
Solution:- Let's analyze \( \text{C}_2\text{H}_2\text{Br}_2 \) (1,2-dibromoethene): \( \text{CHBr}=\text{CHBr} \).
- Carbon 1 is attached to one H and one Br. Carbon 2 is attached to one H and one Br.
- Because both carbons have distinct groups, they can be arranged with the two Bromine atoms on the same side (cis) or on opposite sides (trans) of the double bond.
- Note: Option C (\( \text{C}_2\text{H}_2\text{Cl}_2 \)) can also show it if it is 1,2-dichloroethene, but based on the provided Answer Key, D was the specifically intended valid option (likely distinguishing from a 1,1-isomer not explicitly ruled out in other contexts). Both C and D mathematically can, but D is keyed.
Why other options are incorrect:- \( \text{C}_2\text{H}_4 \) (Ethene) has identical hydrogen atoms on both carbons.
- \( \text{C}_2\text{HCl}_3 \) (Trichloroethene) has two identical chlorine atoms on one of its carbons, making cis-trans impossible.
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