That is a very good question and not easy to answer. This will depend on the individual, the risk they are taking and the benefit that they will receive from it. As pointed out in the Radiation and Us page, we receive approximately 360 mrem of radiation every year. The legal limit imposed by the federal government in this country for an occupationally exposed worker is 5,000 mrem per year. If we look first at doses received in a short amount of time, (acute doses), the first biological effect begins to be able to be detected by laboratory analysis at 10,000 to 25,000 mrem. Actual immediate life threatening doses are limited to levels of 100,000 mrem and above. The life shortening doses may be lower than that, and are approximated by taking the data at higher doses where the effects are apparent and extrapolating the risk down to lower doses. Being conservative, the regulators use a model of a straight line from high doses down through the zero dose/zero risk point, so that any dose presents some small risk. Also you need to know that doses received over a longer period of time allows for repair of cells by the body, and presents less of a risk. See the Radiation and Risk page for more information. So to answer the question, the doses receive by the workers in nuclear power, an extra 100 to 5,000 mrem per year (average about 500 mrem), are seen by most scientific organizations as presenting a low risk compared to normal occupational hazards encountered during a working lifetime. Children, fetuses and embryos are more sensitive and have a longer expression time than adults, and so have smaller allowable doses. It is really a personal choice how much is too much. In some situations, such as to save someone's life, I personally would accept around 100 rem, but in the normal course of my work, I would rather keep my dose to less than 5 rem per year.
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