A) 5 : 9
B) 5 : 36
C) 1 : 4
D) 3 : 4
Correct Answer: A
Solution :
For Balmer series \[\frac{1}{\lambda }=R\left( \frac{1}{{{2}^{2}}}-\frac{1}{{{n}^{2}}} \right)\] R = Rydbergs constant for, \[{{\lambda }_{\min ,}}\]put \[n=\infty \] \[\therefore \] \[\frac{1}{{{\lambda }_{\min }}}=R\left( \frac{1}{4}-0 \right)\] or \[{{\lambda }_{\min }}=\frac{4}{R}\] For \[{{\lambda }_{\max ,}}\]put \[n=3\] \[\frac{1}{{{\lambda }_{\max }}}=R\left( \frac{1}{4}-\frac{1}{9} \right)=\frac{5R}{36}\] \[\Rightarrow \] \[{{\lambda }_{\max }}=\frac{36}{5R}\] Hence, \[{{\lambda }_{\min }}:{{\lambda }_{\max }}=5:9\]
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