Step 1: Understanding the Question:
The question asks for the number of chlorine atoms in the final products of two different reactions of benzene. Both reactions involve chlorine, but the conditions are different: one involves a Lewis acid catalyst in the dark, and the other involves UV light. These different conditions trigger two entirely different mechanisms: electrophilic substitution and free-radical addition.
Step 2: Key Formula or Approach:
Reaction 1: Benzene $+ Cl_2$ (excess) $+ AlCl_3$ (Lewis acid) $\rightarrow$ Electrophilic substitution.
Reaction 2: Benzene $+ Cl_2 + UV$ light ($h\nu$) $\rightarrow$ Radical addition reaction.
Step 3: Detailed Explanation:
Product X (Substitution): When benzene is treated with excess chlorine in the presence of $AlCl_3$ (anhydrous) in the dark, it undergoes electrophilic aromatic substitution. The $AlCl_3$ helps generate $Cl^+$ electrophiles. Since chlorine is in excess, all six hydrogen atoms on the benzene ring are substituted by chlorine atoms.
$C_6H_6 + 6Cl_2 \rightarrow C_6Cl_6 + 6HCl$. Product $X$ is Hexachlorobenzene. It has 6 chlorine atoms.
Product Y (Addition): When benzene reacts with chlorine in the presence of sunlight ($h\nu$), the mechanism changes to addition. The aromaticity is lost as chlorine atoms add across each of the three double bonds.
$C_6H_6 + 3Cl_2 \xrightarrow{h\nu} C_6H_6Cl_6$. Product $Y$ is Benzene Hexachloride (BHC), also known as Gammexane or Lindane. It also has 6 chlorine atoms.
Note the difference in the formula: $X$ is $C_6Cl_6$ and $Y$ is $C_6H_6Cl_6$. However, both molecules contain exactly six chlorine atoms.
Step 4: Final Answer:
Both $X$ and $Y$ contain $6$ chlorine atoms each. So the correct option is (C).