A nine$-$tray multi$-$tray settling chamber that includes the bottom surface can accommodate $7\frac{m^3}{s}$ of air at $200C.$ The chamber must be $1m$ wide and $4m$ long, with the trays placed $0\mathrm{.}25m$ apart.

$($i$)$ What is the minimum particle size of density $2000k\frac{g}{m^3}$ that can be collected with $100\%$ efficiency?

$($ii$)$ What will be the efficiency of the settling chamber if $50m$ particles are to be removed