When considering the potential for radiation spreading out from the severely damaged Fukushima Daiichi nuclear power plant, it is very important to understand the ‘inverse-square law‘, which helps to put in context the potential intensity of radioactive Fallout as it relates to distance.

What is the inverse-square law?
It is a physical law (Newton) stating that a specified physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity.

Translation:
For every doubling of distance away from the source that is emitting an ‘intensity’ (in this case, radiation), the radiation will be diluted to one-fourth the original quantity as it disperses into three-dimensional space to a point representing a doubling of distance.

If you double the distance between you and the source of radiation, you will theoretically be exposed to one-fourth the amount. There are variables of course, like the wind carrying concentrated amounts of radioactive particles in a particular direction, but the concept of the inverse-square law is helpful when putting distance versus dosage into perspective.

The Math – Inverse-Square Law

The Inverse-Square Law formula is as follows:

I1/I2 = (D2*D2)/(D1*D1)

I1 = Intensity at D1
I2 = Intensity at D2
D1 = Distance 1
D2 = Distance 2

To solve for the intensity at a location where an original set of measurements are known, we can solve for ‘I2′ by using the following version of the formula:

I2 = (I1*(D1*D1))/(D2*D2)

Average Radiation Dosage for Americans

First, lets put it in terms relating to the average dose per day that Americans get from natural and man-made radiation…

600 milliRem per year
6 milliSieverts per year

0.016438 mSv per day (milli Sieverts)
16.438 uSv per day (micro Sieverts)

0.000684932 mSv per hour (milli Sieverts)
0.684931507 uSv per hour (micro Sieverts)

Real world radiation examples relating to the Fukushima nuclear plant

Some recent reporting that appears valid, indicates that the radiation level at and around the immediate vicinity of the plant is around 500 uSv/h (micro Sieverts per hour). This is equivalent to 730 times the average radiation per hour that Americans receive!

The highest number I had read about earlier during the crisis was around 3,000 uSv/h. This is equivalent to 4,380 times the average radiation per hour that Americans receive!

The situation is obviously quite terrible nearby the plant and at least out to the current evacuation perimeter that has been recommended, 20 miles (the U.S. has recommended 50 miles).

To anyone that doubts the formula that Ken shared with us should put in numbers that reflect the absolute worst case scenario with that plant in Japan and see that even with those outrageous numbers that long distance disperses anything to much, much, much lower safer levels. Math is one of the perfect constants and does not lie. As Ken mentioned there are of course variables and this is a good ballpark estimate and helps to show people that unnecessary panic at thousands of miles from Japan is not realistic. Just look at how much the oil was dispersed last year from the Deepwater Horizon disaster. When oil finally was moving out of the Gulf of Mexico it never tarred European beaches, never destroyed northern Atlantic coasts, it did not even mar the Caribbean like all the hype that we heard about. Distance dissipated the oil to near to nothing.

The ONLY scenario in which I could think of there being a problem with radiation thousands of miles away would be if the contaminates somehow clumped together and stayed together and somehow deposited it over very isolated hot spots. This type of event would be quite rare and would have to have very unusual weather and climate patterns. I would also not eat anything from the area that has been polluted. Common sense.

I would worry much more about the nuclear reactors over in this country and the fact that the United States is one of the most hated countries by the Muslim world and there are millions of those that are radical gunning for the suffering of the US. With all the news about the Japanese disaster with the nuclear reactors, what better way for these haters to make the US hurt than go after the nuclear industry. Countries with large oil reserves have the money to do a lot of damage to just about anything they want to. A lot of money will unfortunately buy the most skilled mercenaries in the world, like from Russia for example. I would personally be more worried about this than getting sick from an event that is really local and thousands of miles away.

It should be noted that particles, radioactive or not, normally go through what is called a hydrological cycle. It takes an extremely unusual set of atmospheric conditions for lower attitude mass of particles to “surf” their way across thousands of miles, fluidlike or not. Most of these radioactive particles are going to go up and become hygroscopic nuclei, this is the seed that raindrops form around, and come down locally as toxic rain on areas around the affected nuclear plants, 200 miles or so. Yes, water molecules do form around anything that is foreign, including anything that comes out of a nuclear reactor. Also Japan has one of the higher areas of evapotranspiration, the amount of evaporation that occurs. So most of these deadly particles are going to up and come back down quicker as rain or snow locally.

For those of you concerned about contaminated rain clouds coming all the way acrosss the Pacific and raining poison down on the west coast, the life cycle of clouds is quite short. Storms go through many cycles of evaporation and condensation and raining out what it originally started with. This can be shown by looking at raindrops from storms that come fresh off the Pacific under the microscope and most of the time you will find very tiny salt crystals as the seed that started the raindrops. This is because their are few particles other than salt spray out in the middle of the ocean. The exception to this is very high attitude particles that are from volcanic material, even meteoritic dust, something that got those particles up there. The nuclear plants in Japan have fortunately not had anything to push the particles up very far.

Particles that do get up that high in the atmosphere go through tremendous shearing and cross winds even in the jet stream. They are going to be greatly dispersed before reaching the west coast just like Ken demonstrated with the inverse square law. For those that still are afraid of glowing vegetables, water and milk you should get a good college atmospheric science book or even a meteorological book and read about particle air flow in all three dimensions and see how the inverse square law works above us.

The inverse square law applies to volume of radioactive particles going a certain distance, inhaled or not. During the 1950′s and 1960′s five countries, United States, the Russians, France, England and China, did above ground testing of nuclear weapons and there was a lot more inhaled radiation then from nuclear bombs tested that threw fine blasted dust and soil particles miles into atmosphere, some cases over 20 miles up. Those particles were dispersed over distance just like the inverse square law showed and really only some those within 1000 miles or less were those that ended up with cancer. The higher rates of cancer that showed up from these inhaled particles showed up in states within only about 500 miles downwind of the test sites in Nevada; Utah, Wyoming, Arizona, Idaho, Colorado. The east coast did not show any higher rates due to testing. WHY? Distance makes all the difference. There is nothing over in Japan to lift most of these particles high enough in attitude to mass amounts anyway. Even if a volcano erupted directly below the Fukushima reactors, distance would still dissipate those particles a great deal over the large distance.

My suggestion to anyone that is concerned about radioactive fallout particles being inhaled from a disaster that is several thousand miles, you should be much more worried about the inhaled radioactive particles that could be in your own home or workplace, it is called RADON. The distance from you and radon could be a few feet as opposed to thousands of miles from the Japanese radiation. The inverse square law would sure work with this. With the tiny minute amount of particles that have gotten over here you are likely to be exposed in the outdoor air to it. With radon you are exposed to it in a closed concentrated environment. If you live west of the Rockies your home or workplace is especially prone to radon in certain areas. Radon is one of the leading causes of lung cancer in the United States.

Those of you worried about inhaled radiation should go to a hardware store and get a radon test kit for your home, workplace, and homes of family and friends. You are way more likely to receive enough lung cancer causing radon in the inside air or from the radon in steam from hot water in your pipes than from the infinitesimal tiny amounts of inhaled contamination from Japan. These tiny amounts “might” make 1 in 100 million sick as opposed to 1 in 100 sick closer to the source. The inverse square law also shows the exponentially reduced risk to anything harmful with distance. Thank you again Ken for showing us this valuable formula.