A $5c{m}^2$ Ge solar cell with a dark reverse saturation current of $2$ nA has solar radiation incident upon it$,$ producing $4{10}^{17}$ electron$-$hole pairs per second. The electron and hole diffusion lengths are given to be $5m$ and $2m,$ respectively. Calculate for the cell of the following :

$($i$)$ The short$-$circuit current

$($ii$)$ The open$-$circuit voltage