A) \[\frac{16}{25}{{\lambda }_{0}}\]
B) \[\frac{20}{27}{{\lambda }_{0}}\]
C) \[\frac{27}{20}{{\lambda }_{0}}\]
D) \[\frac{25}{16}{{\lambda }_{0}}\]
Correct Answer: B
Solution :
\[\frac{1}{\lambda }=R\left( \frac{1}{{{2}^{2}}}-\frac{1}{{{3}^{2}}} \right)=\frac{5}{36}R\] \[\frac{1}{{{\lambda }_{0}}}=R\left( \frac{1}{{{2}^{2}}}-\frac{1}{{{4}^{2}}} \right)=\frac{3}{16}R\] \[\Rightarrow \] \[\frac{\lambda }{{{\lambda }_{0}}}=\frac{16\times 5}{36\times 3}=\frac{20}{27}\] \[\Rightarrow \] \[\lambda =\frac{20}{27}{{\lambda }_{0}}\]
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