Following carbocation undergoes either methyl shift with rate constant $\left(K_2\right)$ (or) hydride shift with rate constant $\left(K_1\right)$ from same carbon at 300K. Both elementary reactions follow Arrhenius equation and have same pre-exponential factor

 

 

 

 

 

*labeled carbon represents radioactive carbon from which methyl or hydride shift occurs
If  $K_1=\frac{1}{16}{K}_2$, then find ( a – b) in units of K. cal/mol
where ‘a’ and ‘b’ represent energy of activation (k. cal/mol) for formation of

  and   from given cation respectively. 

$R=2calmo{l}^{-1}{K}^{-1}{\log }_{e}2=0.70$