Long-term chronic radiation exposure

Most of what I could on the 'net about radiation sickness was about the effects of acute radiation exposure- one time or short term exposure. I was wondering just how much radiation someone could be exposed to on a daily basis, for months or years, before showing signs of clinical illness. A classic article by Cecil mentioned that the maximum nuclear workers are allowed to be exposed to is 5,000 milirems (5 rems) per year, which is ten times the limit for the general public. Wiki says that an acute dose of less than 20 rems will show no overt symptoms other than blood cell changes. I presume that at some point you’re talking about virtually guaranteeing that you’ll die of cancer before the age of 60, but just where is that line? I would suppose this has been studied in lab rats or monkeys.

Well, the usual model for carcinogens (including radiation) is that every bit of exposure increases the cancer risk by a set amount, no matter how much exposure has already happened, so there’s no lower limit below which there is no cancer risk, nor is there a particular upper limit above which cancer becomes certain, it’s all a question of what risk you’re willing to accept.
I’m not very familiar with non-cancer effects of radiation.

Cancer from radiation is at heart a random process, so you’re only going to hear things about probabilities and statistical likelihoods, not limits and lines. All it takes is for one particle to hit one piece of DNA in one cell at just the right place and time. Increasing dosages of radiation simply make this even more and more likely.