a
આપેલ  \({{\lambda }_{{{\text{K}}_{^{\alpha }}}}}-\lambda _{\min }^{'}=\left( {{\lambda }_{{{K}_{\alpha }}}}-{{\lambda }_{\min }} \right)\)

\(\Rightarrow \,\,{{\lambda }_{{{K}_{\alpha }}}}-\lambda _{\min }^{'}=3{{\lambda }_{K}}_{\alpha }-3{{\lambda }_{\min }}\)

\(\Rightarrow \,{{2}_{{{\lambda }_{{{K}_{\alpha }}}}}}=3{{\lambda }_{\min }}-\lambda _{\min }^{'}\)

\(\,\,2\left[ \frac{4}{3R{{(Z-1)}^{2}}} \right]=3{{\lambda }_{\min }}-\lambda _{\min }^{'}\,\)

[\(\because\)  \(\frac{1}{R}=912\,  Å\)]

\( \Rightarrow \,\frac{{8 \times 912{\text{Å}}}}{{{\text{3(Z - 1}}{{\text{)}}^{\text{2}}}}} = 3\left( {\frac{{12400}}{{10000}}{\text{Å}}} \right) - \left( {\frac{{12400}}{{20000}}{\text{Å}}} \right)\)

\( \Rightarrow \,\frac{{8 \times 912{\text{Å}}}}{{{\text{3(Z - 1)}}}} = \frac{{372}}{{100}}{\text{Å - }}\frac{{{\text{62}}}}{{{\text{100}}}}{\text{Å}} = \frac{{{\text{310}}}}{{{\text{100}}}}{\text{Å}}\)

\( \Rightarrow \,\frac{{{\text{8}} \times {\text{304}}}}{{{{{\text{(Z - 1)}}}^{\text{2}}}}}{\text{Å}} = \frac{{{\text{310}}}}{{{\text{100}}}}{\text{Å}}\)

\( \Rightarrow \,{{\text{(Z - 1)}}^{\text{2}}} = \frac{{8 \times 304 \times 100}}{{310}}\,\,\,\,\,Z - 1 = \sqrt {784.51613}  = 28\)

\( \Rightarrow \,Z = 29\)