The answer is A (tertiary > secondary > primary; alkyl groups are electron-donating).
Basic strength depends on how available the lone pair on N is for donation to \(\text{H}^+\).
In the gas phase there are no solvent molecules, so there is no solvation (hydrogen bonding with water) to stabilise the protonated ion. The order is controlled only by the electron-donating (positive inductive) effect of the alkyl groups.
Each alkyl group donates electron density to N, making the lone pair more available and also dispersing the positive charge on \(\text{R}_3\text{NH}^+\), so the more alkyl groups on N, the stronger the base:
tertiary (3 R groups) > secondary (2 R groups) > primary (1 R group).
• B is wrong: the order is correct, but a greater steric effect of the alkyl groups would hinder the approach of \(\text{H}^+\) to the lone pair and make the amine a weaker base, so it cannot explain why the tertiary amine is the strongest.
• C is wrong: the reason is correct, but electron-donating alkyl groups make the amine with the most alkyl groups the strongest base, so the order must be tertiary > secondary > primary, not the reverse.
• D is wrong: the order is reversed. \(\text{H}^+\) is very small, so steric effects do not control gas-phase basicity; the electron-donating effect of the alkyl groups does.
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