A) 5.41 \[\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) 4.20 \[\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) 2.70 \[\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) 1.35 \[\overset{\text{o}}{\mathop{\text{A}}}\,\]
Correct Answer: A
Solution :
The wave length of \[{{L}_{\alpha }}\]line is given by \[\frac{1}{\lambda }=R\,{{(z-7.4)}^{2}}\,\left( \frac{1}{{{2}^{2}}}-\frac{1}{{{3}^{2}}} \right)\,\Rightarrow \lambda \propto \frac{1}{{{(Z-7.4)}^{2}}}\] \[\Rightarrow \frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{{{({{z}_{2}}-7.4)}^{2}}}{{{({{z}_{1}}-7.4)}^{2}}}\]\[\Rightarrow \frac{1.30}{{{\lambda }_{2}}}=\frac{{{(42-7.4)}^{2}}}{{{(78-7.4)}^{2}}}\]\[\Rightarrow \,{{\lambda }_{2}}=5.41\,{\AA}\]
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