A) \[\left( 27/5 \right)\lambda \]
B) \[\left( 5/27 \right)\lambda \]
C) \[\left( 32/27 \right)\lambda \]
D) \[\left( 27/32 \right)\lambda \]
Correct Answer: B
Solution :
[b] For first line of Balmer series \[\frac{1}{\lambda }=R\left( \frac{1}{4}-\frac{1}{9} \right)\Rightarrow R=\frac{36}{5\lambda }\] \[\therefore \] Wavelength of the first line, \[{{\lambda }_{L}}\] of the Lyman series is given by \[\frac{1}{{{\lambda }_{L}}}=R\left( 1-\frac{1}{4} \right)=\frac{36}{5\lambda }\times \frac{3}{4}=\frac{27}{5\lambda }\] \[\Rightarrow {{\lambda }_{L}}=\frac{5\lambda }{27}\]
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