A) \[{{\lambda }_{3}}={{\lambda }_{1}}+{{\lambda }_{2}}\]
B) \[{{\lambda }_{3}}=\frac{{{\lambda }_{1}}{{\lambda }_{2}}}{{{\lambda }_{1}}+{{\lambda }_{2}}}\]
C) \[{{\lambda }_{1}}+{{\lambda }_{2}}+{{\lambda }_{3}}=0\]
D) \[\lambda _{3}^{2}=\lambda _{1}^{2}+\lambda _{2}^{2}\]
Correct Answer: B
Solution :
Idea This question is based on the energy levels of an atom and the transition of the electrons between them. From the figure, \[({{E}_{A}}-{{E}_{B}})+({{E}_{B}}-{{E}_{C}})=({{E}_{C}}-{{E}_{A}})\] \[\Rightarrow \]\[\frac{hc}{{{\lambda }_{1}}}+\frac{hc}{{{\lambda }_{2}}}=\frac{hc}{{{\lambda }_{3}}}\] \[\Rightarrow \]\[{{\lambda }_{3}}=\frac{{{\lambda }_{1}}{{\lambda }_{2}}}{{{\lambda }_{1}}+{{\lambda }_{2}}}\] TEST Edge Similar questions based on the energy levels of hydrogen atom are normally asked in JEE Main.You need to login to perform this action.
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