In industries titanium is hardened through diffusion of carbon. The concentration of carbon at $1mm$ into the surface of the titanium slab is $0\mathrm{.}25k\frac{g}{m^3}$ and at $3mm$ the concentration is $0\mathrm{.}68k\frac{g}{m^3}.$ The rate at which the carbon is entering into its surface is $1\mathrm{.}27**10-9k\frac{g}{m^2}.$s$.$ calculate the value of diffusion coefficient of carbon.

a$)5\mathrm{.}91**{10}^{-12}$

b$)5\mathrm{.}91**{10}^{-10}$

c$)5\mathrm{.}91**{10}^{-11}$

d$)5\mathrm{.}91**{10}^{-13}$