The ionization constant of HF is $3.2\times {10}^{-4}.$ Which of the following is the correct value of degree of dissociation if concentration is 0.02 M?

$\frac{{\mathrm{C\alpha }}^2}{1-\mathrm{\alpha }}={\mathrm{K}}_{\mathrm{a}} \left(\mathrm{The} \mathrm{solution} \mathrm{is} \mathrm{not} \mathrm{very} \mathrm{dilute}\right)$

$\frac{0.02\times {\mathrm{\alpha }}^2}{1-\mathrm{\alpha }}=3.2\times {10}^{-4} \left(\mathrm{given}\right)$

$\frac{{\mathrm{\alpha }}^2}{1-\mathrm{\alpha }}=1.6\times {10}^{-2}$

${\mathrm{\alpha }}^2+\left(1.6\times {10}^{-2}\right)\mathrm{\alpha }-1.6\times {10}^{-2}=0$

$\mathrm{\alpha }=\frac{-\left(1.6\times {10}^{-2}\right)\pm \sqrt{{\left(1.6\times {10}^{-2}\right)}^2+4\times 1.6\times {10}^{-2}}}{2}$

$=\frac{-1.6\times {10}^{-2}+\sqrt{6.4\times {10}^{-2}}}{2}$                                   $\left[{\left(1.6\times {10}^{-2}\right)}^2 \mathrm{neglected}\right]$

$=\frac{-0.016+0.253}{2}0.12$

Alternatively,

For dilute weak acid, $\mathrm{\alpha }=\sqrt{\frac{\mathrm{K}}{\mathrm{C}}}$

                                   $\mathrm{\alpha }=\sqrt{\frac{3.2\times {10}^{-4}}{0.02}}=\sqrt{1.6\times {10}^{-2}}=0.126$