An experiment is performed to determine the tracer diffusion coefficient of metal

$A$ in a matrix of metal $B.$ This is done by depositing a very thin film of metal $A$

onto the surface of metal $B$ and measuring the concentration profile of metal $A$

into the depth of the material at different times, which we will denote $t_1$ and $t_2.$

Estimate the ratio $\frac{t_2}{t_1}$ from the figure a given below.

Hint: the solution of Fick's $2^{nd}$ law due to a thin film of thickness $b$ with

solute concentration $c_0$ that is plated on one end of solute free material is

$c(x,t)=\frac{b{c}_0}{2\sqrt[\phantom{2}]{{}^{**}Dt}}$exp$(-\frac{x^2}{4^{**}Dt})$