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 :
[a] Using \[\Delta E\propto {{Z}^{2}}\](\[\therefore \]\[{{n}_{1}}\]and \[{{n}_{2}}\] are same) \[\Rightarrow \frac{hc}{\lambda }\propto {{Z}^{2}}\Rightarrow \lambda {{Z}^{2}}=\text{constant}\] \[\Rightarrow {{\lambda }_{1}}{{Z}^{2}}_{1}={{\lambda }_{2}}{{Z}^{2}}_{2}={{\lambda }_{3}}{{Z}^{2}}_{3}={{\lambda }_{4}}{{Z}^{2}}_{4}\] \[\Rightarrow {{\lambda }_{1}}\times 1={{\lambda }_{2}}\times {{1}^{2}}={{\lambda }_{3}}\times {{2}^{2}}={{\lambda }_{4}}\times {{3}^{3}}\] \[\Rightarrow {{\lambda }_{1}}={{\lambda }_{2}}=4{{\lambda }_{3}}=9{{\lambda }_{4}}\]You need to login to perform this action.
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