The rate constant for a reaction at 400K and 500K are $2.60\times {10}^{-5}{s}^{-1}$ and $2.60\times {10}^{-3}{s}^{-1}$ respectively.The activation  energy of the reaction in  $Kjmo{l}^{-1}$ is

Given $k_1=2.60\times {10}^{-5}{s}^{-1},k_2=2.60\times {10}^{-1}{s}^{-1}$

$T_1=400K,T_2=500K$

According to Arrhenius equation

$\log \frac{k_2}{k_1}=\frac{E_a}{2.303R}\left[\frac{T_2-T_1}{T_1{T}_2}\right]$

$\Rightarrow \log \frac{2.60\times {10}^{-3}}{2.60\times {10}^{-5}}=\frac{E_d}{2.303\times 8.314}$
$E_a=\frac{2\times 2.303\times 8.3}{100}$

$E_a=76.6\times {10}^{3}J/mol$

$E_a=76.6Kj/mol$