Answer
Judging solely by the criterion of energy loss in a single photon–electron encounter:
It would not be feasible to detect the Compton shift in the microwave and visible regions of the electromagnetic spectrum.
It would be feasible to detect the Compton shift in the x-ray and gamma regions of the electromagnetic spectrum.
Work Step by Step
The energy loss is negligible in the microwave range and the visible range.
Therefore, it would not be feasible to detect the Compton shift in the microwave and visible regions of the electromagnetic spectrum, judging solely by the criterion of energy loss in a single photon–electron encounter.
The energy loss is significant in the x-ray range and the gamma range.
Therefore, it would be feasible to detect the Compton shift in the x-ray and gamma regions of the electromagnetic spectrum, judging solely by the criterion of energy loss in a single photon–electron encounter.
