A block of FCC iron has nitrogen $(N)$ atmospheres on one side at $1000C$ and is permitted to achieve a steady$-$state diffusion condition. The diffusion flux is found to be $1\mathrm{.}35{10}^{-7}k\frac{g}{m^2}-s.$ Also, it is known that the concentration of $N$ at the high$-$pressure surface is $45\mathrm{.}0k\frac{g}{m^3}.$

How far below the high pressure surface can $N$ diffused into the Fe sheet when the diffusion coefficient of $N$ through $Fe$ under these conditions is equal to $1\mathrm{.}16{10}^{-11}\frac{m^2}{s}?$ Assume a linear concentration profile.

$1\mathrm{.}25cm$

$0\mathrm{.}39cm$

$11\mathrm{.}59cm$

$7\mathrm{.}34cm$

$8\mathrm{.}40cm$

$2\mathrm{.}83cm$