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?

Let the three energy levels be E1, E2, and E3. The wavelengths λ1,λ2, and λ3 of the spectral lines corresponding to the, three energy transitions are depicted as shown in figure.E=hf=hλ or E∝1λ given λ1<λ2<λ3Thus, for the three wavelengths, we haveE3−E2=hλ3.....(i)E2−E1=hλ2..........(ii)E3−E1=hλ1..........(iii) Now, E3−E1=E3−E2+E2−E1⇒ hλ1=hλ3+hλ2 ⇒1λ1=1λ2+1λ3