Why do larger alkyl groups show a greater inductive (+I) effect?

I have been taught that an alkyl group shows a +I (positive inductive) effect. Why do they do so? I know that hyperconjugation can explain how alkyl groups could stabilize a carbocation (better than a hydrogen). But, how does a longer chain alkyl group (or a bulkier alkyl group) show more +I effect than a smaller one?

Qualitatively:

If a methyl group is more electron donating than a hydrogen, then an ethyl group would be more donating that a methyl group by the same reason.

The effect drops off with distance, and generally a pentyl group is considered no more donating than a butyl group.

As for why a methyl group is more electron donating than a hydrogen, the carbon has a higher electronegativity than hydrogen (slightly), polarizing the bond (slightly). This increased electron density near the carbon, which increases (slightly) its electron donation (I+) ability.

• How can the reason be same? A methyl group should (in my opinion) show less +I than a hydrogen as carbon's electronegativity is higher. So its greater stabilization (compared to hydrogen) of a carbocation may be explained by hyperconugation. How can we apply same reason to ethyl group's more donating capacity than a methyl group? – FreezingFire Feb 27 '16 at 5:48
• One thing still remains unclear (after your recent edit), in an ethyl group, one hydrogen is replaced by a methyl group, thus we replace an atom of lower electronegativity with an atom of equal electronegativity, reducing the electron density which would have otherwise been available to the central carbon of methyl group. How then is ethyl more +I than methyl group? – FreezingFire Feb 27 '16 at 16:15
• Electronegativity is not explicitly related to inductive effect. The inductive effect is the ability to donate electrons, which requires an electron presence. The methyl 'carbon' of an ethyl group owns more of the electron density from its hydrogens and is able to donate it to the ipso carbon slightly. I appreciate the depth to which you want this resolved, but anything more than this begins to require QM math. Hammet correlations may provide some insight, but they are empirical. – Lighthart Feb 28 '16 at 16:48
• Oh! I used to naturally correlate electronegativity with +I effect... well my doubt is as good as cleared. Thank you for explaining this to me so patiently! – FreezingFire Mar 3 '16 at 13:27
• @Lighthart Can we say that the electron density at alpha-carbon is more in ethyl group than that in methyl group? Considering the $\ce{+I}$ effect of methyl in ethyl group. – Apurvium Sep 5 '20 at 6:52

It is because the methyl group has a positive inductive effect; this effect is due to the higher electronagetivity of carbon than hydrogen, which attracts the electron from hydrogen and becomes slightly negative and push the electrons towards other groups.