Under critical states for one mole of a gas, compressibility factor is

we know that compressibility factor,  

$$\begin{gathered} \mathrm{Z}=\frac{{\mathrm{P}}_{\mathrm{c}}{\mathrm{V}}_{\mathrm{c}}}{{\mathrm{RT}}_{\mathrm{c}}} \\ {\mathrm{P}}_{\mathrm{c}}=\frac{\mathrm{a}}{27{\mathrm{b}}^2} \\ {\mathrm{V}}_{\mathrm{c}}=3\mathrm{b} \\ {\mathrm{T}}_{\mathrm{c}}=\frac{8\mathrm{a}}{27\mathrm{Rb}} \end{gathered}$$

Substituting the values of critical constants in the above equation of compressibility factor (Z), we get,

$\mathrm{Z}=\left(\frac{\mathrm{a}}{27{\mathrm{b}}^2}\right)\left(\frac{27\mathrm{Rb}}{8\mathrm{a}}\right)=\frac{3}{8}$

Hence, option(A) is the answer.