c
\({\text{(i) }}{{\text{K}}_{\text{a}}} = C{\alpha ^2} = {10^{ - 3}} \times \frac{{10}}{{100}} \times \frac{{10}}{{100}} = \frac{1}{{100000}} = {10^{ - 5}}\)

\((ii)\,{\text{pH}} = \frac{{\text{1}}}{{\text{2}}}p{K_a} - \frac{1}{2}\log c\,\,\,\,\,\,\,\,\because \,\,{K_a} = {10^{ - 5}}\)

\(pH = \frac{1}{2} \times 5 - \frac{1}{2}\log \,{10^{ - 3}}\,\,\,\,\,\,\,\,\,\,\,\therefore \,p{K_a} = 5\)

\( = \frac{5}{2} + \frac{3}{2} = \frac{8}{2} = 4\)