2. In the production of activated carbon, the size distribution of dust collected using a microscopic technique was measured as follows in the data below:
\begin{tabular}{|l|l|}
\hline Size range ( \( \mu \mathrm{m} \) ) & Number of particles in range (-) \\
\hline 0-2 & 2000 \\
\hline 2-4 & 600 \\
\hline 4-8 & 140 \\
\hline 8-12 & 40 \\
\hline 12-16 & 15 \\
\hline 16-20 & 5 \\
\hline 20-24 & 2 \\
\hline
\end{tabular}
i. Use the data to calculate the distributions of the mass fractions of each size range.
ii. Calculate the surface mean diameter of the distribution.
[Assume spherical particles of density \( 2650 \mathrm{~kg} / \mathrm{m}^{3} \) ]