The debate started in the late 1950s and early 1960s when people began to call for the cessation of above ground nuclear weapons tests.
Some junk science was used to convince people that the trivial amount of radioactive contamination released from the tests were causing increased infant mortality, increased cancers, and increased death rates from cancer.
As a result Congress halted above ground testing in 1962.
In the same year, popular comic book heroes such as the Incredible Hulk, Spiderman, and the Fantastic Four (late 1961) were developed by Stan Lee at Marvel Comics.
Each hero was created as the result of radiation or other nuclear related phenomena.
(Hulk created by gamma radiation, Spiderman by a radioactive spider, and the Fantastic Four by cosmic radiation.) At the same time, motion pictures were being made showing various monsters like Godzilla resulting from nuclear weapons tests in the South Pacific.
In other words it started to seep into the pop culture that anything nuclear related was bound to turn out badly.
Through the 1960s and 1970s, this pop culture influence was muted, but still present.
Then in April of 1979, the Three Mile Island accident occurred at virtually the same time the movie the "China Syndrome" was released.
The combination of these two events had the public up in arms about nuclear power and the resulting increase in regulations and influence of anti-nuclear fear mongers gradually made building nuclear power plants so expensive, it resulted in dozens of projects being cancelled and others being completed only to have the parent company declare bankruptcy due to cost over-runs.
Seven years after Three Mile Island, the Chernobyl plant in soviet Ukraine exploded and killed a few dozen workers and fire fighters.
Despite the USSR's effort to keep the information secret, the presence of radioactive particles in air samples in various laboratories in Europe let scientists and their governments aware that something had gone very wrong behind the iron curtain.
Soon the whole world knew that a nuclear power plant could explode and burn and Reactor #4 at the Chernobyl plant burned for 10 or 11 days.
Due to the Russian designed RBMK reactor not having a containment building, the burning core spread huge amounts of radioactive contamination across thousands of square miles of the Ukrainian forest forcing hundreds of thousands of people to be relocated.
However, because the Soviet government didn't tell anyone about the contamination for days or weeks, the foods (especially cow's milk) consumed in these contaminated areas caused radioactive iodine to concentrate in people's thyroid gland ultimately resulting in thousands of cases of thyroid cancer (which is easily treatable and rarely fatal).
The main stream media's coverage of these accidents and incidents only leads to exaggerated claims of health impacts from radiation (whether or not any had actually be released to the environment).
This is due to the linear no threshold concept of radiation exposure.
This concept was developed by plotting radiation exposure of atomic bombing victims against the number of deaths at that exposure.
By drawing a straight line through these points and extrapolating all the way back to zero exposure means zero deaths (without any evidence to support it, and huge amounts of evidence against it) the radiation regulations were written to assume that any amount of radiation had a very small but non-zero probability to cause a fatal cancer.
This is complete hogwash, of course, because we are exposed to radiation every single second of our lives, but it was written into law due to an over abundance of caution on the part of politicians who know nothing about science or technology, just how to get votes.
The latest tragedy at the Fukushima power plant in Japan as a result of the earthquake and tsunami last year has only given the anti-nuclear crowd fresh ammunition to convince the gullible public that every nuclear power plant is just a ticking time bomb ready to fail and kill them in their sleep.
No matter how loudly scientists and engineers try to refute the absurd claims of the anti-nuclear crowd, people (and especially the mainstream media) seem to prefer to listen to somebody who tells them they or their children are going to get cancer and die as a result of any exposure to radiation.
So, the debate continues on many fronts but truly began in the 1950s when the horror of the Hiroshima and Nagasaki attacks were still fresh in the public's mind and above ground nuclear tests were being pursued by the U.S. and several other nations.