A catalyst slab of half-thickness $L$ (the width and length of the slab $>>\:L$) is used to conduct the
first order reaction $A{\rightarrow} B$. At $450\: K$, the Thiele modulus for this system is $0.5$. The activation energy for the first order rate constant is $100\: kJ$/mol. The effective diffusivity of the reactant in the slab can be assumed to be independent of temperature, and external mass transfer resistance can be neglected. If the temperature of the reaction is increased to $470\:K$, then the effectiveness factor at $470 \:K$ (up to two decimal places) will be _____________.
Value of universal gas constant $8.314 \:J$/mol. $K$.