A) \[{{\lambda }_{1}}={{\lambda }_{2}}=4{{\lambda }_{3}}=9{{\lambda }_{4}}\]
B) \[4{{\lambda }_{1}}=2{{\lambda }_{2}}=2{{\lambda }_{3}}={{\lambda }_{4}}\]
C) \[{{\lambda }_{1}}=2{{\lambda }_{2}}=2\sqrt{2}{{\lambda }_{3}}=3\sqrt{2}{{\lambda }_{4}}\]
D) \[{{\lambda }_{1}}={{\lambda }_{2}}=2{{\lambda }_{3}}=3\sqrt{2}{{\lambda }_{4}}\]
Correct Answer: A
Solution :
Using \[\Delta E\propto {{Z}^{2}}\] (∵ \[{{n}_{1}}\] and \[{{n}_{2}}\] are same) Þ \[\frac{hc}{\lambda }\propto {{Z}^{2}}\] Þ \[\lambda {{Z}^{2}}=\text{constant}\] Þ \[{{\lambda }_{1}}Z_{1}^{2}={{\lambda }_{2}}Z_{2}^{2}={{\lambda }_{3}}Z_{3}^{2}={{\lambda }_{4}}Z_{^{4}}^{2}\] Þ \[{{\lambda }_{1}}\times 1={{\lambda }_{2}}\times {{1}^{2}}={{\lambda }_{3}}\times {{2}^{2}}={{\lambda }_{4}}\times {{3}^{3}}\] Þ \[{{\lambda }_{1}}={{\lambda }_{2}}=4{{\lambda }_{3}}=9{{\lambda }_{4}}\].You need to login to perform this action.
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