At equilibrium \(\left[H^{+}=A^{-}\right]\)

\(K_{a} =\frac{\left[H^{+}\right]\left[A^{-}\right]}{[H A]}=\frac{\left[H^{+}\right]^{2}}{[H A]}\)

\(\left[H^{+}\right]=\sqrt{K_{a}[H A]} =\sqrt{1 \times 10^{-5} \times 0.1}\)

\(= \sqrt{1 \times 10^{-6}}=1 \times 10^{-3}\)

\(\alpha =\frac{A \text {ctual ionisation}}{\text {Molar concentration}}\)

\(\%\) of acid dissociated \(=10^{-2} \times 1.00\)

\(=1 \%\)