A) 0.50 f
B) 1.35 f
C) 2.05 f
D) 2.70 f
Correct Answer: B
Solution :
Balmer series is the series in which the spectral lines correspond to the transition of electron from some higher energy state to the lower energy state corresponding to \[{{n}_{f}}=2\]. Therefore, for Balmer series, \[{{n}_{f}}=2\] and \[{{n}_{i}}=3,4,5,....\] Frequency, of 1st spectral line of Balmer series \[f=R{{Z}^{2}}c\left( \frac{1}{{{2}^{2}}}-\frac{1}{{{3}^{2}}} \right)\] or \[f=R{{Z}^{2}}c\times \frac{5}{36}\] ??..(i) Frequency of 2nd spectral line of Balmer series \[f=R{{Z}^{2}}c\left( \frac{1}{{{2}^{2}}}-\frac{1}{{{4}^{2}}} \right)\] or \[f=R{{Z}^{2}}c\times \frac{3}{16}\] ?..(ii) From Eqs. (i) and (ii), we have \[\frac{f}{f}=\frac{20}{27}\] \[\therefore \] \[f=\frac{27}{20}f=1.35f\]
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