A) \[1215.4\overset{o}{\mathop{\text{A}}}\,\]
B) \[2500\overset{o}{\mathop{\text{A}}}\,\]
C) \[7500\overset{o}{\mathop{\text{A}}}\,\]
D) \[600\overset{o}{\mathop{\text{A}}}\,\]
Correct Answer: A
Solution :
\[\frac{{{\lambda }_{Lymen}}}{{{\lambda }_{Balmer}}}=\frac{\left( \frac{1}{{{2}^{2}}}-\frac{1}{{{3}^{2}}} \right)}{\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}} \right)}=\frac{5}{27}\] \[\left[ \because \frac{1}{\lambda }=R\left( \frac{1}{n_{f}^{2}}-\frac{1}{n_{i}^{2}} \right) \right]\] \[{{\lambda }_{Lymen}}=\frac{5}{27}\times {{\lambda }_{Balmer}}\] \[=\frac{5}{27}\times 6563\] \[=1215.4\overset{o}{\mathop{\text{A}}}\,\]
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