A) \[\frac{4RC{{Z}^{2}}}{{{n}^{2}}}\]
B) \[\frac{2RC{{Z}^{2}}}{{{n}^{3}}}\]
C) \[\frac{2RC{{Z}^{3}}}{{{n}^{3}}}\]
D) \[\frac{4RC{{Z}^{3}}}{{{n}^{3}}}\]
Correct Answer: B
Solution :
According to Rydberg's equation, \[\frac{1}{\lambda }=R{{Z}^{2}}\left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right)\] \[{{n}_{1}}=n,{{n}_{2}}=n+1\] \[\frac{1}{\lambda }=R{{Z}^{2}}\left( \frac{1}{{{n}^{2}}}-\frac{1}{{{(n+1)}^{2}}} \right)\] \[\frac{1}{\lambda }=\left( \frac{2n+1}{{{n}^{2}}(n+1)} \right)R{{Z}^{2}}\] Since, n >>1 We can write \[2n+1\approx 2n\] and \[{{(n+1)}^{2}}\approx {{n}^{2}}\]
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