A diffusion couple of two metals, A and $B,$ was fashioned as shown:

After a $670$ hour heat treatment at $1150C$ the concentration of A is $2\mathrm{.}5wt\%$ at the $3\mathrm{.}5$ mm position within Metal B $.$ At what temperature $($in Kelvin$)$ must the diffusion couple need to be heated to produce this same concentration at a $1\mathrm{.}9$ mm position after $670$ h $?$ The preexponential and activation energy values for the diffusion of $A$ in $B$ are $2\mathrm{.}4{10}^{-4}\frac{m^2}{s}$ and $260k\frac{J}{m}ol,$ respectively.

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