Question

Draw a splitting diagram for the ${\mathrm{H}}_{\mathrm{b}}$proton and give its multiplicity if

a.${\mathbf{J}}_{\mathrm{ba}}\mathbf{=}{\mathbf{J}}_{\mathrm{bc}}$ b.${\mathbf{J}}_{\mathbf{ba}}\mathbf{=}\mathbf{2}{\mathbf{J}}_{\mathbf{bc}}$

Short answer

a.

This has five peaks, called quintet.

b.

This has eight peaks i.e., double of quartet.

Step-by-step solution

Step-by-Step SolutionStep 1: Splitting diagram for Hbproton

a.

This shows five peaks i.e., a quintet.

b.

This shows eight peaks i.e., double of quartet.

Multiplicity

a. Here,${\mathbf{H}}_{\mathbf{b}}$proton is split into four peaks initially by the${\mathbf{H}}_{\mathbf{a}}$ protons and further to five peaks, i.e. a quintet.

b. Here,${\mathbf{H}}_{\mathbf{b}}$proton is split into doublet of quartet, i.e. eight peaks by the ${\mathbf{H}}_{\mathbf{c}}$protons.

So${\mathrm{J}}_{\mathrm{ba}}={\mathrm{J}}_{\mathrm{bc}}$ and${\mathrm{J}}_{\mathrm{ba}}=2{\mathrm{J}}_{\mathrm{bc}}$.