A) \[{{v}_{1}}-{{v}_{2}}={{v}_{3}}\]
B) \[{{v}_{2}}-{{v}_{1}}={{v}_{3}}\]
C) \[{{v}_{3}}=\frac{1}{2}({{v}_{1}}+{{v}_{2}})\]
D) \[{{v}_{2}}+{{v}_{1}}={{v}_{3}}\]
Correct Answer: A
Solution :
[a] Series limit means, the shortest possible wavelength (maximum photon energy) and first line means the largest possible wavelength (minimum photon energy) in the series \[v=C\left[ \frac{1}{{{n}^{2}}}-\frac{1}{{{m}^{2}}} \right]\] (Where C is a constant) For series limit of Lyman series: \[n=1,m=\infty ,\]\[\therefore {{v}_{1}}=C\] For first line of Lyman series: \[n=1,m=2,\]\[\therefore {{v}_{2}}=3C/4\] For series limit of Balmer series: \[n=2,\]\[m=\infty \], \[\therefore {{v}_{3}}=C/4\]
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