$($a$)$ Integrate the rate equation

$-\frac{dC}{dt}=k{C}^{\frac{1}{2}}$

$($b$)$ Athow could a group of data be checked grophically to see if they describe a half order

$($c$)$ Derive an expression for the half life $t_{\frac{1}{2}}$ in terms of $k$ and $C_0$

$($d$)$ What is the unit of $k?$