A) \[\frac{5}{27}\]
B) \[\frac{3}{23}\]
C) \[\frac{7}{29}\]
D) \[\frac{9}{31}\]
Correct Answer: A
Solution :
Wavelength for Lyman series \[{{\lambda }_{L}}=\frac{1}{R\left( 1-\frac{1}{4} \right)}=\frac{4}{3R}\] and wavelength for Balmer series \[{{\lambda }_{B}}=\frac{1}{R\left( \frac{1}{4}-\frac{1}{9} \right)}=\frac{1}{R\left( \frac{5}{36} \right)}=\frac{36}{5R}\] \[\therefore \] \[\frac{{{\lambda }_{L}}}{{{\lambda }_{B}}}=\frac{4}{3R}\times \frac{5R}{36}=\frac{5}{27}\] \[\Rightarrow \] \[{{\lambda }_{L}}:{{\lambda }_{B}}=5:27\]
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