Answer
The frequency of every photon is related to its energy by E = hf.
Work Step by Step
If two frequencies add up to a third frequency:
$$f_{1} + f_{2} = f_{3}$$
then the photon energies associated with those frequencies obey a similar relationship:
$$h f_{1} + h f_{2} = h f_{3}$$
$$E_{1} + E_{2} = E_{3}$$
In a transition that skips an energy level, such as the one from n = 3 to n = 1 shown in Figure 32.9, energy conservation requires that the emitted energy be the same as the sum of the emitted energies if it made 2 transitions, from n = 3 to n = 2 and then from n = 2 down to n = 1.
Therefore the emitted photon frequency for the large transition will be the sum of the photon frequencies emitted during the two other transitions. This is the Ritz combination principle.
