Finely divided spherical particle of activated carbon $(1500gm)$ is used as an adsorbent for the removal of emerging pollutants from aqueous solutions. The adsorbent particle has a density of $2\mathrm{.}1\frac{g}{c}c$ and the screen analysis data is given below. Assume that the volume shape factor is $1\mathrm{.}992.$ Calculate the specific surface area of adsorbent particles in $c{m}^2$ per $gm$ and a specific number of particles present in the sample mixture using the differential analysis method. The screen analysis data is given below $(5)$

$\backslash$table$[[$A$,4,8,14,28,48,65,100,150,200],[$B$,4\mathrm{.}699,2\mathrm{.}362,1\mathrm{.}168,0\mathrm{.}589,0\mathrm{.}295,0\mathrm{.}208,0\mathrm{.}147,0\mathrm{.}104,0\mathrm{.}074],[$C$,0,168,444,411,258,90,57,42,30]]$

Where $A=$ Mesh no; $B=$ Screen opening $(mm)$;$C=$ Mass of particle retained $(gm)$