Question

Short answer

(a) Splitting pattern for \({\rm{s}}{{\rm{p}}^{\rm{2}}}\) hybridized carbon:Doublet

Splitting pattern for proton \({{\rm{H}}_{\rm{a}}}\): Doublet

Splitting pattern for proton \({{\rm{H}}_{\rm{b}}}\): triplet of doublet

(b) \({{\rm{H}}_{\rm{b}}}\) signal comes at the downfield region because of the carbon-carbon double bond conjugation with a carbonyl group.

Step-by-step solution

Spin-spin coupling

The magnetic interaction between the spins of neighboring, non-equivalent NMR-active nuclei causes splitting of the NMR spectrum which is known as spin-spin coupling.

The splitting pattern is due to the equivalent H-atom at the nearby nuclei.

Splitting pattern of protons

(a) Splitting pattern for proton \({{\rm{H}}_{\rm{a}}}\): Proton \({{\rm{H}}_{\rm{a}}}\) is surrounded by a single proton \({{\rm{H}}_{\rm{b}}}\). Hence it couples with \({{\rm{H}}_{\rm{b}}}\) to give a doublet of 11Hz.

Splitting pattern for proton \({{\rm{H}}_{\rm{a}}}\)

(b) Splitting pattern for proton\({{\rm{H}}_{\rm{b}}}\): Protons\({{\rm{H}}_{\rm{b}}}\)are surrounded by two kinds of proton which include one proton\({{\rm{H}}_{\rm{a}}}\)and two protons\({{\rm{H}}_{\rm{c}}}\).

\({{\rm{H}}_{\rm{b}}}\)couples with\({{\rm{H}}_{\rm{a}}}\)to give a doublet of 11Hz, then each signal couples with one\({{\rm{H}}_{\rm{c}}}\)which further splits each signal into 2 signals with coupling constant 4Hz.

Finally, each signal couples with a second\({{\rm{H}}_{\rm{c}}}\)and furthersplits each signal into 2 signals with a coupling constant 4Hz.

Therefore, \({{\rm{H}}_{\rm{b}}}\) protons give a triplet of the doublet.