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Each radionuclide represents a somewhat different health risk.  However, health physicists currently estimate that overall, if each person in a group of 10,000 people exposed to 1 rem of ionizing radiation, in small doses over a life time, we would expect 5 or 6 more people to die of cancer than would otherwise. 

In this group of 10,000 people, we can expect about 2,000 to die of cancer from all non-radiation causes. The accumulated exposure to 1 rem of radiation, would increase that number to about 2005 or 2006.  

To give you an idea of the usual rate of exposure, most people receive about 3 tenths of a rem (300 mrem) every year from natural background sources of radiation (mostly radon).