question_answer

Energy levels A, B and C of a certain atom correspond to increasing values of energy i.e., \[{{E}_{A}}<{{E}_{B}}<{{E}_{C}}\]. If \[{{\lambda }_{1}},\,{{\lambda }_{2}}\] and \[{{\lambda }_{3}}\] are wavelengths of radiations corresponding to transitions C to B, B to A and C to A respectively, which of the following relations is correct?                                                                                                 [AIPMT (S) 2005]

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 :

From the energy level diagram as shown below:

\[\frac{1}{{{\lambda }_{3}}}=\frac{1}{{{\lambda }_{1}}}+\frac{1}{{{\lambda }_{2}}}\]

\[=\frac{{{\lambda }_{2}}+{{\lambda }_{1}}}{{{\lambda }_{1}}{{\lambda }_{2}}}\]

\[\Rightarrow \]   \[{{\lambda }_{3}}=\frac{{{\lambda }_{1}}{{\lambda }_{2}}}{{{\lambda }_{1}}+{{\lambda }_{2}}}\]