Diffusion of particles across a plane surface


> 
> A relatively viscous material is coated with a thin film consisting of gold nanoparticles that can diffuse into the material. We can assume that all particles have a diameter of $\pu{25 nm}.$ Coating can be seen as a completely flat surface.
> 
> 
> In an experiment performed at $\pu{30 °C},$ the nanoparticle concentration $c$ was determined at different distances $d$ from the coating after 60 days. The following data were obtained:
> $$
> \begin{array}{rr}
> \hline
> d/\pu{mm} & c/\pu{mol dm^-3} \\
> \hline
> 1 & \pu{8.7E-12} \\
> 2 & \pu{5.8E-12} \\
> 4 & \pu{1.1E-12} \\
> 6 & \pu{7.5E-14} \\
> 8 & \pu{1.7E-15} \\
> \hline
> \end{array}
> $$
> 
> 
> In the same viscous material, equal number of latex nanoparticles with radii of $5$ and $\pu{10 nm}$ are added. How far from the point source do we have to go for the ratio (in concentration) between the small and the large latex particles to be $2$ or higher after $1,$ $10$ and $100$ days, respectively? The temperature is the same as in the first attempt.
> 
> 
> 


I began by plotting $\ln c$ against $x^2$ to determine the diffusivity constant $D$ using the equation


$$c = \frac{n\_0}{A\sqrt{\pi Dt}}\exp\left(\frac{-x^2}{4Dt}\right).$$


From this I got that the slope $-0.135$ and $D = \pu{3.57E-7}.$


However, I am unsure how to continue. At first I thought that I could use the same equation by finding the ratio $c(\pu{5 nm})/c(\pu{10 nm})$ and then solving for $x$ since both $A$ and $n\_0$ would cancel out as they are equal.


But I think that there should be some other way in which I use *both* the radii and the temperature given as I don't see any other reason as to why they are provided.


