Why obtain a CT?
CT is most useful when the injury is complex (multiple fractures / fracture dislocation) and / or when the fracture morphology is difficult to determine on plain films.
Wrist fractures are common. Is the radiation does form CT a concern?
Well yes and no. As a general principle radiation dose should be minimized (as low as reasonably achievable (ALARA) principle), however in many instances CT of the extremities can be performed without irradiating the head or trunk (superman position for the wrist works well). Musculoskeletal tissues are quite resistant to radiation, and they are small in cross-section. The end result is that effective doses to the patient from scanning the wrist are very low.
Single image from a CT of the wrist demonstrates the fracture to extend from the articular sufrace of the radiocarpal joint, down to the volar aspect of the distal radius. The carpus remains aligned to the fracture fragment, and is thus subluxed with respect to the intact part of the radius.