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To determine the optically inactive compound, we need to recall that optical inactivity occurs when a compound does not rotate the plane of polarized light. This typically happens if the molecule is achiral, meaning it either lacks a chiral center or possesses a plane of symmetry. A chiral center is a carbon atom bonded to four different groups. Let's analyze each option step by step.
Starting with Option A: 2-chloropropanal. The structure is $$CH_{3}-CHCl-CHO$$. The carbon at position 2 is bonded to four groups: hydrogen (H), chlorine (Cl), methyl group ($$CH_{3}$$), and aldehyde group ($$CHO$$). Since $$CH_{3}$$ and $$CHO$$ are different, and all four groups are distinct (H, Cl, $$CH_{3}$$, $$CHO$$), this carbon is a chiral center. The molecule has no plane of symmetry, so it is chiral and optically active.
Next, Option B: 2-chloro-2-methylbutane. The structure is $$CH_{3}-C(Cl)(CH_{3})-CH_{2}-CH_{3}$$, which can be written as:
Moving to Option C: 2-chlorobutane. The structure is $$CH_{3}-CHCl-CH_{2}-CH_{3}$$. The carbon at position 2 is bonded to H, Cl, $$CH_{3}$$, and $$CH_{2}CH_{3}$$. These groups are all different: methyl ($$CH_{3}$$) and ethyl ($$CH_{2}CH_{3}$$) have different sizes and compositions. Thus, carbon-2 is a chiral center, and the molecule lacks a plane of symmetry, making it chiral and optically active.
Finally, Option D: 2-chloropentane. The structure is $$CH_{3}-CHCl-CH_{2}-CH_{2}-CH_{3}$$. The carbon at position 2 is bonded to H, Cl, $$CH_{3}$$, and propyl group ($$CH_{2}CH_{2}CH_{3}$$). All four groups are distinct (H, Cl, $$CH_{3}$$, $$CH_{2}CH_{2}CH_{3}$$), so carbon-2 is a chiral center. The molecule has no plane of symmetry, rendering it chiral and optically active.
Therefore, the only optically inactive compound is Option B, 2-chloro-2-methylbutane, due to its plane of symmetry and absence of a chiral center.
Hence, the correct answer is Option B.
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