Rate of ${\mathrm{S}}_{{\mathrm{N}}^2}$ reaction is :

The effect of structure on relative reactivity may be seen particularly clearly when a halogen atom is located at the bridgehead of a bicyclic system. Thus the following rates
were observed for solvolysis in 80% aqueous ethanol at 25°: 

All are tertiary halides so that attack by the S*z mode would not be expected to- occur on (16) or (17) in y more than it did on (8). ${\mathrm{S}}_{{\mathrm{N}}^2}$attack from the back' on the carbon atom carrying gr would in any case be prevent6h in (16) and (17) both sterically by their cagelike structure, and also by the impossibility of forcing the fairly rigid framework   through transition states with the required planar distribution of bonds to the bridgehead carbon atom. Solvolysis via rate- limiting formation of the ion pair (${\mathrm{S}}_{{\mathrm{N}}^1}$), as happens with (8) is also inhibited because the resultant carbocations from (16) and (17) would be unable, because of their rigid frameworks, to stabilise themselves by collapsing to the stable planar state. These cirbocation intermediates are thus of very much higher energy level titan usual, and therefore are formed only slowly and with reluctance. The very greatly reduced solvolysis rate of (17) compared with (16) reflects the greater rigidity I bout the bridgehead (cationic) carbon with a one carbon (77), than with a two- carbon (16), bridge.