The diagram shows-the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy.

III

In case I , energy difference is maximum but it correspond to absorption of energy.

Among photons which is emitted with maximum energy is III i.e n=2 to n=1.

Emitted energy $\Delta E=\frac{h c}{\lambda}\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$