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Question #44255

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The Question

An optically pure sample of $(S)$ -3-methylhexane is subjected to free-radical bromination using $\ce{Br2}$ under photochemical conditions ( $h\nu$ ) at $373\text{ K}$ . The reaction yields a major monobrominated product fraction $\mathbf{P}$ via a carbon-centered radical intermediate.

Quantum mechanical analysis of the intermediate's singly occupied atomic orbital (SOMO) reveals it has $x$ planar nodes and $z$ radial nodes. Let $y$ be the optical purity (in %) of the major product fraction $\mathbf{P}$ .

Assuming ideal planar geometry for the intermediate, identify the correct set of $(x, z, y)$ and the stereochemical classification of $\mathbf{P}$ .

Options

A.
$x=1$ , $z=0$ , $y=0\%$ , Racemic mixture
B.
$x=0$ , $z=1$ , $y=100\%$ , Retention of configuration
C.
$x=1$ , $z=1$ , $y=0\%$ , Racemic mixture
D.
$x=1$ , $z=0$ , $y=50\%$ , Diastereomeric mixture

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Exception_Exposure

Learn to identify edge cases and boundary exceptions that JEE examiners hide in math problems.

Concepts Behind This Question

Angular Nodes and Planar Nodes|Optical Isomerism Logic|Stereochemical Outcome of Halogenation

Why This Question Is Tricky

Common Mistakes

The question tests the student's ability to link quantum mechanical orbital properties (nodes) with macroscopic stereochemical outcomes.

The 'Chemical Exception/Trap' lies in the assumption of asymmetric induction.

Students often assume that starting with an optically pure compound will yield an optically active product (or a diastereomeric mixture).

However, because the only stereocenter is the reactive site, the intermediate passes through a planar $sp^2$ state with a $p$ -orbital (1 planar node).

The loss of the chiral center makes the faces enantiotopic, leading to a perfectly racemic mixture (0% optical purity).

Distractors exploit misconceptions about radical hybridization ( $sp^3$ vs $sp^2$ ), orbital nodes, and residual chirality.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Structure of Atom - Class 11 Part 1
Concept	Angular Nodes and Planar Nodes
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free