The acceptable level depends on who you are, where you are, your age, and a judgment on whether that level can readily be reduced. There are maximum permissible exposure levels which have been promulgated by the International Commission on Radiological Protection and in the USA by the National Council on Radiation Protection and Measurements. These recommended levels have been endorsed by various federal agencies such as the Nuclear Regulatory Commission, by State governments and by numerous employers. There are dose limits for the whole body and for specific organs of the body. The limits are different for persons who are occupationally exposed and persons who are not occupationally exposed but are in the vicinity of radiation sources; for the whole body these limits are 5 rem per year and 0.1 rem per year, respectively. The limit to persons younger than 18 and the fetus in occupationally exposed pregnant women is 0.5 rem per year.
Very few occupationally exposed persons receive the 5 rem limit per year. The national average for occupationally exposed persons is less than 0.5 rem per year. All such persons carry a radiation monitor. It is a requirement of the Nuclear Regulatory Commission that radiation doses received occupationally must be reviewed periodically by radiation safety personnel and that efforts be made to maintain such doses at levels which are "as low as reasonably achievable."
These maximum levels were arrived at by considering combined cancer and genetic risk from radiation and choosing a dose level such that radiation work would carry a risk comparable with the less hazardous occupations in our society. The general public limit has been set somewhat arbitrarily at 50 times less than the occupational limit with an average to the whole population not to exceed 170 millirem per year which is somewhat less than an additional background dose.