a. The relative rates of hydroxide ion-catalyzed deuterium exchange at $\mathrm{C}(3)$ have been measured for bicyclo[2.1.1]hexan-2-one, bicyclo[2.2.1]heptan-2one, and bicyclo[2.2.2]octan-2-one. What factor(s) could account for the much smaller rate of exchange for bicyclo[2.1.1]hexan-2-one?
b. Treatment of $(+)$-camphenilone with $\mathrm{K}^{+.-}-\mathrm{O}-t$-Bu in $t$-BuOD at $185^{\circ} \mathrm{C}$ results in incorporation of D, as indicated below. Racemization occurs at the same rate. Suggest a mechanism that could account for these observations.