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Generally, the unit in which exposure to ionizing radiation is being measured is "Gray" (Gy) which is absorbed energy (Measured in Joules, equal to one Watt-Second) per kg of absorbing material. That's called the "Dose". If you account for the amount of damage that this Dose can do to humans, you'll call this weighted Dose "Sievert" (Sv). Generally the weighting is not that important for X-Rays or gamma-radiation (the "normal radioactivity" people are concerned about), but will be important when dealing with neutrons.

The Wikipedia article on Sievert has a few examples: http://en.wikipedia.org/wiki/Sievert#Dose_examples

If a person is subjected to 5-10 Sv instantaneously, so many cells will be damaged that this person will die, not of cancer but of multiple organs ceasing to function properly over the course of a few days.

But, as you already have written, that's about 2000 years of background radiation (3mSv/year) in a very short time (documented accidents: probably few or less than one second). -> http://en.wikipedia.org/wiki/Background_radiation

There's data from survivors of the Hiroshima and Nagasaki bombs, and this data corresponds to exposure to about 50mSv to 2Sv. There are also other studies, including people living in areas with hither (or lower) natural radiation levels, working in former Soviet-Union closed-off nuclera-research areas, and so on... (http://www.nap.edu/openbook.php?record_id=11340) All these "cohorts" (as they are called: a number of test subjects) have been studied for health effects. And a lot of people that got high doses died of cancer. Unfortunately everyone of us has a high high probability of getting cancer at some point in his life. And it turns out that you need a lot of radiation to double the risk of getting this disease:

http://en.wikipedia.org/wiki/File:Increased_risk_with_dose.s...

The straight line in this plot represents the "linear model" which assumes that the additional chance of getting malignant tumors rises just the same as the amount of radioactivity. But then, if you go down to the very-low-end, which is very, very, very difficult to analyze, because you are looking at only miniscule differences in cancer-rates, sometimes people find that it appears that a small amount of radiation might even be beneficial and reduce the risk of acquiring cancer in a lifetime.

http://en.wikipedia.org/wiki/Radiation_hormesis



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