A) \[\frac{5}{27}\upsilon \]
B) \[\frac{5}{36}\upsilon \]
C) \[\frac{3}{4}\upsilon \]
D) none of the above
Correct Answer: A
Solution :
: According to Bohrs theory of hydrogen spectrum, \[\frac{1}{{{\lambda }_{1}}}=R\left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right)\]for Lyman series\[=\frac{3R}{4}\] \[\frac{1}{{{\lambda }_{2}}}=R\left( \frac{1}{n_{2}^{2}}-\frac{1}{n_{3}^{2}} \right)\]for Balmer series\[\frac{2R}{36}\] \[\therefore \]\[\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{5R}{36}\times \frac{4}{3R}=\frac{5}{27}\] Or \[\frac{{{\upsilon }_{2}}}{{{\upsilon }_{1}}}=\frac{5}{27}\]or\[{{\upsilon }_{2}}=\frac{5}{27}{{\upsilon }_{1}}=\frac{5\upsilon }{27}\] \[\therefore \]Frequency emitted\[=\frac{5}{27}\upsilon \].
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