Rank each group of protons in order of increasing chemical shift.

a.

b.

The difference in the absorption position of a particular proton due to variation in its chemical environment from that of an isolated proton is the chemical shift of that proton. It is usually represented by $\delta$-scale and $\tau$-scale.

A chemical shift in terms of frequency can be represented by the equation:

$\delta =\frac{{\nu }_{sample}-{\nu }_{reference}}{{\nu }_{sample}}\times {10}^6$

Representation of different protons in a.

Since H_c is bonded to the sp³ CH_c , the protons are highly shielded, and this gives them the lowest chemical shift value. H_a is bonded to an sp C , so they are shielded, giving them a chemical shift value higher than that of Hc . And the Hb protons are deshielded as they are bonded to the sp2 C , which gives them a higher chemical shift value. So, the order of increasing chemical shift value is, Hc < Ha < Hb .

Representation of different protons in b.

Since Hc is bonded to the sp3 CHc , the protons are highly shielded and this gives them the lowest chemical shift value. Ha is slightly deshielded as the CH3 group is bonded to a C=O, and this gives them a chemical shift value higher than that of Hc . And the Hb protons are deshielded as the CH2 group is bonded to an O atom, which gives them a higher chemical shift value. So, the order of increasing chemical shift value is, Hc<Ha<Hb.