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The number of signals in a proton NMR (\({}^{\bf{1}}{\bf{H}}\)NMR) spectroscopy depends on the number of protons and their chemical environment.

Chemically equivalent protons resonate at the same frequency and exhibit a single signal.

The hydrogen atoms attached to heteroatoms give only a single signal.

The splitting of the \({}^1H\)NMR signal of a particular proton/hydrogen depends on the number of hydrogens present on the adjacent carbon atoms.

The splitting and multiplicity of a hydrogen atom are predicted using the n+1 rule, where n represents the number of hydrogens present on the carbon atoms adjacent to the hydrogen atom under consideration.

a. Since the compound consists of three chemically distinct groups, it exhibits three signals.

Non-equivalent protons in compound a

The a, b, and c hydrogen atoms exhibit a singlet each, as, in the case of a and b, there are no hydrogen atoms on the carbon adjacent to it. In c, the hydrogen is attached to a heteroatom.

b. The given compound exhibits four NMR signals.

Non-equivalent protons in compound b

The multiplicity of a is \(2 + 1\; = 3\) (triplet).

The multiplicity of b is \(5 + 1\; = 6\) (multiplet)

The multiplicity of c is \(2 + 1\; = 3\) (triplet).

The multiplicity of d is a singlet.

c. The given compound exhibits three NMR signals.

Non-equivalent protons in compound c

The multiplicity of a is \(1 + 1\; = 2\) (doublet).

The multiplicity of b is \(6 + 1\; = 7\) (multiplet)

The multiplicity of c is a singlet.