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(A) The energy of an emitted photon is given by the difference in energy between the two levels involved in the transition: $E = E_{initial} - E_{fina

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$III$

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(A) The energy of an emitted photon is given by the difference in energy between the two levels involved in the transition: $E = E_{initial} - E_{final} = h
u$.For emission to occur,the electron must transition from a higher energy level to a lower energy level.Transitions $II$ and $III$ are emission transitions (downward arrows).Transition $I$ is an absorption transition (upward arrow).Transition $IV$ is also an emission transition.Comparing the energy gaps:Transition $II$ is from $n=4$ to $n=3$.Transition $III$ is from $n=2$ to $n=1$.Transition $IV$ is from $n=4$ to $n=2$.The energy difference is proportional to the gap between the levels. The gap between $n=2$ and $n=1$ is significantly larger than the gap between $n=4$ and $n=3$ or $n=4$ and $n=2$.Therefore,transition $III$ corresponds to the largest energy change and thus emits the photon with the highest energy.

The energy levels for an electron in a certain atom are shown in the figure. Which of the following transitions will emit a photon with the highest energy?

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