Surface of a biomaterial is placed in chamber where in noble metal would diffuse into the biomaterial to

improve its biocompatibility. When the chamber is heated to $750\backslash$deg C for $1$ hour, noble metal concentration

of $0\mathrm{.}25\%$ is obtained at a depth of $0\mathrm{.}5$ um in the biomaterial. Assume a diffusion coefficient of $10-12$

m$2$

$/$sec$.$

$($a$)$ Calculate the surface concentration of noble metal required to achieve $0\mathrm{.}25\%$ at $0\mathrm{.}5$ um depth.

$($b$)$ How long would it take to obtain $0\mathrm{.}25\%$ at a depth of $1\mathrm{.}0$ um$?$