question_answer

Energy levels A, B and C of a certain atom corresponding to increase values of energy i.e., \[{{E}_{A}}<{{E}_{B}}<{{E}_{C}}\]If\[{{\lambda }_{1}},{{\lambda }_{2}}\]and\[{{\lambda }_{3}}\]are the wavelengths of radiations corresponding to transition C to B, B to A and C to A respectively. Then, which of the following statements/relations is correct?

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.