Modern Physics 2 Question 10
10. Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r=\lambda _1 / \lambda _2$ is given by
(a) $r=\frac{2}{3}$
(b) $r=\frac{3}{4}$
(c) $r=\frac{1}{3}$
(d) $r=\frac{4}{3}$
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Solution:
- We have, $\lambda=\frac{h c}{\Delta E}$
$$ \begin{aligned} \therefore \quad \frac{\lambda _1}{\lambda _2} & =\frac{h c / \Delta E _1}{h c / \Delta E _2}=\frac{\Delta E _2}{\Delta E _1} \\ & =\frac{\frac{4}{3} E-E}{2 E-E}=\frac{1}{3} \end{aligned} $$
