Final answer:
The technologist should dispose of the vial according to radioactive waste protocols due to the level of decay indicated by the radiation measurement.
Step-by-step explanation:
The technologist should dispose of the vial according to radioactive waste protocols. The fact that the radiation level is twice the background radiation level after 53 days suggests that the radioactive decay of Xe-133 has reached a point where it may no longer be useful or safe to use, especially considering that medical radioisotopes like Xe-133 typically have short half-lives. Furthermore, hospital or laboratory safety guidelines usually dictate the proper procedures for handling and disposing of radioactive materials, which tend to be stringent to ensure safety. Consulting the radiation safety officer can also provide further guidance, but given the context, disposal seems to be the logical step.