We wish to purify \(99.78 \mathrm{wt} \%\) anthracene to \(\mathrm{x}_{\text {anthracene,avg }}=99.99^{+} \mathrm{wt} \%\) by zone melting. The only impurity is fluorene. Determine the smallest number of passes that will give the desired average mass fraction anthracene or higher if \(\mathrm{L} / l=10\) and \(\mathrm{z}_{\text {cut }}=0.80(20 \%\) of the final ingot is removed). Use a figure showing the solution for \(\mathrm{k}=0.1\) from Ezheiyan and Sadeghi (2017), Pfann (1966), Wankat (1990), or other sources.