a
\(\frac{{\text{1}}}{{{\lambda _{{{\text{K}}_{\text{a}}}}}}} \propto \left( {\frac{1}{{n_1^2}} - \frac{1}{{n_1^2}}} \right)\,\,\,\,\,\)

\(\therefore\) \(\frac{{{\lambda _{{K_\beta }}}}}{{{\lambda _{{K_\alpha }}}}} = \frac{{\left( {\frac{1}{1} - \frac{1}{4}} \right)}}{{\left( {\frac{1}{1} - \frac{1}{9}} \right)}} = \frac{{3/4}}{{8/9}} = \frac{{27}}{{32}}\)

\( \Rightarrow \,\,{\lambda _{{K_\alpha }}} = \frac{{27}}{{32}} \times 0.32\, Å\)

\(= {\text{0}}{\text{.27}}   \, Å\)