${K_a} = \frac{{{\alpha ^2}C}}{{1 - \alpha }} = \frac{{{{(0.1)}^2} \times (0.01)}}{{(1 - 0.1)}} = 1.11 \times {10^{ - 4}}$
Now $p{K_a} = - \log \,1.11 \times {10^{ - 4}} = 3.9542$
$pH = p{K_a} + \log \frac{{[salt]}}{{[acid]}}$
$ = 3.9542 + \log \,\left[ {\frac{{0.05}}{{0.10}}} \right] = 3.653$