A) \[\lambda =\frac{36}{5R}\]
B) \[\lambda =\frac{5R}{36}\]
C) \[\lambda =\frac{5}{R}\]
D) \[\lambda =\frac{R}{6}\]
Correct Answer: A
Solution :
From Bohr's model of atom, the wave number is given by \[\frac{1}{\lambda }=R\left( \frac{1}{{{n}_{1}}^{2}}-\frac{1}{{{n}_{2}}^{2}} \right)\] where R is Rydberg's constant and \[{{n}_{1}}\] and \[{{n}_{2}}\] the energy levels. Given, \[{{n}_{1}}=2,\,\,\,\,{{n}_{2}}=3\] \[\therefore \] \[\frac{1}{\lambda }=R\left( \frac{1}{{{2}^{2}}}-\frac{1}{{{3}^{2}}} \right)\] \[\frac{1}{\lambda }=R\left[ \frac{5}{36} \right]\] \[\Rightarrow \] \[\lambda =\frac{36}{5R}\] This gives the corresponding wavelength of Balmer series.
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