b
\(\frac{\text{1}}{{{\lambda }_{\text{L}\alpha }}}=R{{(Z-b)}^{2}}\left( \frac{1}{{{2}^{2}}}-\frac{1}{{{3}^{2}}} \right)\)

\(\Rightarrow \,\frac{{{({{\lambda }_{L\alpha }})}_{1}}}{{{({{\lambda }_{L\alpha }})}_{2}}}={{\left( \frac{{{Z}_{2}}-b}{{{Z}_{1}}-b} \right)}^{2}}\)

\(\frac{{1.32{\text{Å}}}}{{4.17{\text{Å}}}}\) 

\(={{\left( \frac{Z-7.4}{78-7.4} \right)}^{2}}\,\)

\(\Rightarrow \,\,\,0.56=\frac{Z-7.4}{70.6}\)

\(\Rightarrow \,\,\,0.56=\frac{Z-7.4}{70.6}\)

\(\Rightarrow \,\,Z-7.4\,\,=\,\,0.56\,\,\times \,\,70.6\)

\(\text{Z = 39}\text{.72 + 7}\text{.4 ;    Z = 47}\)