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  • Energy levels A, B, C of a certain atom correspond to increasing values of energy i.e., <img alt="\mathrm{E_A<E_B<E_C}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7BE_A%3C

Energy levels A, B, C of a certain atom correspond to increasing values of energy i.e., \mathrm{E_A<E_B<E_C}. If \lambda_1, \lambda_2, \lambda_3  are the wavelengths of radiation corresponding to the transitions C to B, B to A and C to A respectively, which of the following relation is correct?
 

Option: 1

\lambda_3=\lambda_1+\lambda_2


Option: 2

\lambda_3=\frac{\lambda_1 \lambda_2}{\lambda_1+\lambda_2}


Option: 3

\lambda_1+\lambda_2+\lambda_3=0


Option: 4

\lambda_3^2=\lambda_1^2+\lambda_2^2


Answers (1)

best_answer

\begin{aligned} & \left(E_2-E_1\right)=h v=\frac{h c}{\lambda} \\ & \therefore \frac{h c}{\lambda_1}=\left(E_C-E_B\right) \cdot \frac{h c}{\lambda_2}=\left(E_B-E_A\right) \text { and } \frac{h c}{\lambda_3}=\left(E_C-E_A\right)\\ &\text{Now, }\left(E_C-E_A\right)=\left(E_C-E_B\right)+\left(E_B-E_A\right)\text{ or }\frac{h c}{\lambda_3}=\frac{h c}{\lambda_1}+\frac{h c}{\lambda_2} or \frac{1}{\lambda_3}=\frac{1}{\lambda_1}+\frac{1}{\lambda_2} \\ &\therefore \frac{1}{\lambda_3}=\frac{\lambda_1+\lambda_2}{\lambda_1 \lambda_2} \text { or } \frac{1}{\lambda_3}=\frac{\lambda_1 \lambda_2}{\lambda_1+\lambda_2} \end{aligned}

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