Energy levels $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ of a certain action corresponding to increasing…

Energy levels $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ of a certain action corresponding to increasing values of energy i.e. $E_A < E_B < E_C$. If $\lambda_1$, $\lambda_2$ and $\lambda_3$ are wavelength of radiations corresponding to transitions $\mathrm{C}$ to $\mathrm{B}, \mathrm{B}$ to $\mathrm{A}$ and $\mathrm{C}$ to $\mathrm{A}$ respectively, which of the following relations is correct?
  1. $\lambda_3=\lambda_1+\lambda_2$
  2. $\lambda_3=\frac{\lambda_1 \lambda_2}{\lambda_1+\lambda_2}$
  3. $\lambda_1+\lambda_2+\lambda_3=0$
  4. $\lambda_3^2=\lambda_1^2+\lambda_2^2$

Solution

$E_A < E_B < F_C$ $\begin{aligned} E & =\frac{h c}{\lambda} \\ E_{C A} & =E_{C B}+E_{B A} \\ \frac{h c}{\lambda_3} & =\frac{h c}{\lambda_1}+\frac{h c}{\lambda_2} \\ \frac{1}{\lambda_3} & =\frac{1}{\lambda_1}+\frac{1}{\lambda_2} \\ \Rightarrow \quad \lambda_3 & =\frac{\lambda_1 \lambda_2}{\lambda_1+\lambda_2} \end{aligned}$

Asked in: MHT CET Full Test 4

Practice more Structure of Atoms and Nuclei questions on Aicharya