Transitions between three energy levels in a particular atom give rise to three spectral lines of wavelengths, in increasing magnitudes, λ$$1$$,λ$$2$$, and λ$$3$$. Which one of the following equations correctly relates λ$$1$$,λ$$2$$, and λ$$3$$?

Question

Transitions between three energy levels in a particular atom give rise to three spectral lines of wavelengths, in increasing magnitudes, λ$$1$$,λ$$2$$, and λ$$3$$. Which one of the following equations correctly relates λ$$1$$,λ$$2$$, and λ$$3$$?

Infinity Learn · Accepted Answer

Let the three energy levels be $$E1$$, $$E2$$, and $$E3$$. The wavelengths λ$$1$$,λ$$2$$, and λ$$3$$ of the spectral lines corresponding to the, three energy transitions are depicted as shown in figure.$$E=hf=h$$λ or E∝$$1$$λ given λ$$1$$<λ$$2$$<λ$$3Thus$$, for the three wavelengths, we $$haveE3$$−$$E2=h$$λ$$3$$.....(i)E2$$−$$E1=h$$λ$$2$$..........$$(ii)E3$$−$$E1=h$$λ$$1$$..........$$(iii) Now, $$E3$$−$$E1=E3$$−$$E2+E2$$−$$E1$$⇒ hλ$$1=h$$λ$$3+h$$λ$$2$$ ⇒$$1$$λ$$1=1$$λ$$2+1$$λ$$3$$

Transitions between three energy levels in a particular atom give rise to three spectral lines of wavelengths, in increasing magnitudes, $λ_{1}, λ_{2}, and λ_{3}$ . Which one of the following equations correctly relates $λ_{1}, λ_{2}, and λ_{3} ?$

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Transitions between three energy levels in a particular atom give rise to three spectral lines of wavelengths, in increasing magnitudes, λ1,λ2, and λ3. Which one of the following equations correctly relates λ1,λ2, and λ3?

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Transitions between three energy levels in a particular atom give rise to three spectral lines of wavelengths, in increasing magnitudes, $λ_{1}, λ_{2}, and λ_{3}$ . Which one of the following equations correctly relates $λ_{1}, λ_{2}, and λ_{3} ?$