• # question_answer Energy levels A, B, C of a certain atom corresponds to increasing value 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 the transitions C to B, B to A and C to A respectively. Which of the following statement 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 :

${{E}_{3}}={{E}_{1}}+{{E}_{2}}$ $\frac{hc}{{{\lambda }_{3}}}=\frac{hc}{{{\lambda }_{1}}}+\frac{hc}{{{\lambda }_{2}}}\,\,\,\Rightarrow \,\,\,\frac{1}{{{\lambda }_{3}}}=\frac{1}{{{\lambda }_{1}}}+\frac{1}{{{\lambda }_{2}}}$

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