The splitting pattern of proton Hᵃ in the given compound is a doublet of doublet.

Introduction

The splitting pattern of proton Hᵃ in 1H NMR depends on how many magnetically non‑equivalent neighbouring protons couple with it and the corresponding coupling constants $J$. In the given benzyl dimethoxy compound, proton Hᵃ is attached to a chiral center bearing two different nonequivalent vicinal hydrogens, so its signal shows a more complex pattern than a simple doublet or triplet. Understanding this pattern is essential for interpreting multiplet structures in organic spectroscopy.​

Structure and coupling of Hᵃ

• The carbon bearing Hᵃ is attached to:

  • One vicinal hydrogen on the same carbon (the other benzylic H).

  • One vicinal hydrogen on the adjacent carbon (bearing the two OMe groups).

  • Two methoxy groups whose protons do not couple through oxygen (heteroatoms do not transmit scalar coupling efficiently in routine ¹H NMR).​

• These two neighbouring hydrogens are magnetically non‑equivalent (different chemical environments and different J values), so Hᵃ is coupled independently to each of them.​

• Coupling to one neighbour first splits the Hᵃ signal into a doublet; coupling to the second non‑equivalent neighbour then splits each line again, giving a doublet of doublets (dd) with four lines and two distinct $J$ values.​

Hence, Option (B) Doublet of doublet is correct.

Why the other options are wrong

Option (A) Doublet

• A doublet arises when a proton couples to only one set of equivalent neighbouring protons with a single coupling constant $J$.​

• Proton Hᵃ clearly has two different neighbouring hydrogens, each in a distinct environment, so there are two separate couplings, not one; therefore, the signal cannot remain a simple doublet.

Option (C) Multiplet

• The term multiplet is a generic label used when a signal cannot be described by simple patterns such as singlet, doublet, triplet, quartet, or doublet of doublets, often due to overlapped or highly complex splitting.​

• For Hᵃ the coupling pattern is well‑defined and resolvable as a doublet of doublets with two clear $J$ values, so calling it a vague multiplet would ignore the specific coupling information present.

Option (D) Triplet

• A triplet requires coupling to two equivalent neighbouring protons (n = 2 in the $n+1$ rule), giving three lines with a single $J$.​

• Hᵃ does not have two equivalent neighbours; instead, it has two non‑equivalent vicinal protons, each giving a separate coupling. This produces four lines, not three, ruling out a triplet.

Key takeaway

For the benzyl dimethoxy compound, proton Hᵃ couples with two magnetically non‑equivalent vicinal protons, so its ¹H NMR signal appears as a doublet of doublets, not as a doublet, triplet, or unresolved multiplet.​