A) \[\sqrt{\frac{\lambda R}{\lambda R-1}}\]
B) \[\sqrt{\frac{\lambda }{\lambda R-1}}\]
C) \[\sqrt{\frac{\lambda {{R}^{2}}}{\lambda R-1}}\]
D) \[\sqrt{\frac{\lambda R}{\lambda -1}}\]
Correct Answer: A
Solution :
Here, \[{{n}_{f}}=1,{{n}_{i}}=n\] \[\therefore \]\[\frac{1}{\lambda }=R\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{n}^{2}}} \right)\Rightarrow \frac{1}{\lambda }=R\left( 1-\frac{1}{{{n}^{2}}} \right)\]?(i) or\[\frac{1}{\lambda R}=1-\frac{1}{{{n}^{2}}}or\frac{1}{{{n}^{2}}}=1-\frac{1}{\lambda R}\]or\[n=\sqrt{\frac{\lambda R}{\lambda R-1}}\]
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