We have to compare the basicity of the following compounds:
While comparing compound I and II:
Since there is no conjugated system, there is no resonance at play and we only have to discuss hyperconjucation and inductive effect.
The conjucate acid of compound I has 1 $\ce \alpha$ hydrogen while the conjugate acid of compound II has 4 $\ce \alpha$ hydrogens. So according to hyperconjugation,the conjugate acid of compound II is more stable than the conjugate acid of compound I and hence the basicity of compound is more than that of compound I.
Further the conjucate acid of compound I has 1 $\ce \alpha$ carbon, 2$\ce \beta$ carbons, 2 $\ce \gamma$ carbons and 1 $\ce \delta$ carbon. While the conjugate acid of compound II has 2 $\ce \alpha$ carbons, 2$\ce \beta$ carbons and 1 $\ce \gamma$ carbon.
Alkyl groups are electron releasing groups and since the conjugate acid of compound II has its carbon atoms closer to the amine than in the case of compound I, it is further stabilised and hence compound II is more basic.
I don't know how to compare I and III, so instead I tried to compare II and III:
The conjugate acid of compound III has an ether group attached to the amine while that of compound II has an alkyl group to the amine. Since ether is an electron withdrawing group and alkyl is an electron releasing group, the former will destabilise the conjugate acid compound III while the latter will stabilise the compound II and hence compound II is more basic than compound III.
So I know that compound II is the most basic but I still don't know how to compare compound I and III.
Can anyone help?