To solve this problem, we need to understand the effect of temperature on the equilibrium constant for an exothermic reaction.$\\$For an exothermic reaction, the equilibrium constant $K_p$ decreases with an increase in temperature.$\\$This behavior is explained by Le Chatelier's principle, which states that if a system at equilibrium is subjected to a change in temperature,$\\$the system will adjust itself to counteract the effect of the change.$\\$In the case of an exothermic reaction, increasing the temperature shifts the equilibrium position to the left (towards the reactants),$\\$thereby decreasing the equilibrium constant $K_p. \\$Mathematically, this can be understood using the van 't Hoff equation:$\\ \frac{d \ln K}{dT} = \frac{\Delta H}{RT^2} \\$For an exothermic reaction, $\Delta H < 0.$ Therefore, $\frac{d \ln K}{dT} < 0,$ indicating that $K$ decreases as $T$ increases.$\\$Given that $T_1 < T_2,$ and since the reaction is exothermic, we have:$\\ K_p > K_p' \\$Thus, the correct option is Option 1: $K_p > K_p'.$