In the Compton effect, the wavelength of the emitted photon is longer than that of the incident photon.

f the emitted photon had the same wavelength as the incident photon, it would imply that there was no change in energy or momentum, which contradicts the Compton effect.

An infinite wavelength is not a physically meaningful outcome in the context of the Compton effect. The emitted photon's wavelength is longer but not infinite.