Health Effects of Plutonium

Plutonium atoms are unstable and decay into other elements by emitting alpha particles (two protons and two neutrons bound together). The alpha particles emitted by Plutonium are pretty massive and slow as subatomic particles go, so they are stopped by almost anything. They can travel only a few inches in air and can't even penetrate human skin.

As long as the plutonium stays outside your body it can't hurt you (unlike some other types of radiation that can slice right through you). If plutonium somehow gets inside the body however, the alpha particles emitted by that plutonium go careening about, ionizing the atoms in the body tissue and generally wrecking normal body functions as they expend their energy in collisions with the atoms of the body tissues.

The energy the alpha particles transfer to the body is measured in units called rads. One rad corresponds to one joule of energy that is absorbed by a body with a mass of 100 kilograms. Since that's an easy number to work with and is a reasonable mass for an adult human, we'll stick with the 100 kilogram figure. (That same one joule of energy would count as 2 rads if it were absorbed by someone who only weighed half as much). So a rad is one way to measure how big a radiation dose someone has absorbed.

The details of how radiation gets absorbed by different types of body tissue can get really complicated, but there are internationally recognized safety standards based upon the total amount of energy absorbed. Since an alpha particle is bigger than a small particle like an electron, it will do more damge than an electron of the same energy.

We quantify this difference by multiplying the dosage in rads by a correction factor that depends on the type of radiation and the type of body tissue.

The corrected unit is called the rem (which comes from the phrase Roentgen Equivalent Man). The correction factor for alpha particles is typically about 10 (Acosta, Cowan, & Graham, "Essentials of Modern Physics", p.409, Harper & Row, 1973)), so we have 1 rad = 10 rem.

So rads measure energy/mass, while rems measure the biological effects of that energy/mass. Since a whole rem is a bit too big for our purposes, we'll measure things in units of millirem (abbreviated mrem) which are 1/1000 rem.

Background Radiation

Now that we have the units to measure radiation, we can ask how much is too much. We are all exposed to natural background radiation every day (in fact, it's essential for the evolution of life). This natural radiation comes from the radioactive decay of atoms in the earth and atmosphere, and from cosmic rays.

Together these sources give us each an average radiation dose of about 300 mrem every year. This number varies a little from place to place. For example, you get a bit more if you live at higher altitudes where there is less air to block cosmic rays, a bit less if you live at sea level. We also get more radiation exposure from airliner flights, dental x-rays, etc...

Obviously, radiation doses that are tiny compared to the background of 300 mrem can be safely ignored - you get a bigger dose of radiation just from small changes in the background like travelling. Doses that are very large compared to background will produce obvious symptoms of damage by the radiation and are obviously dangerous. Moderate sized doses are more questionable.

The Agency for Toxic Substances and Disease Registry which is an agency of the Center for Disease Control (CDC), recommends an annual dose of no more than 500 mrem/year (including the 300 mrem or so from background).

Calculating the Radiation from Cassini -- Outline of Calculation

Here's an outline of how we'll estimate our radiation exposure from a hypothetical accident.

Ready to start?

NOTATION: To write numbers and equations in ASCII text, I'll use the following conventions:

N^2 = N squared = N x N
N^3 = N cubed = N x N x N
2.0 x 10^3 = 2000, etc...

I'll also use this notation to describe units like meter^2 for square meters, etc...

Concentration of Plutonium in the Atmosphere

Cassini carries about 33 kilograms (72 pounds) of PuO2 ceramic. That contains about 29 kilograms of plutonium. Let's assume the unlikely "worst-case" accident occurs and Cassini burns up entering the Earths atmosphere at 43,000 mph. The RTGs might rupture and release some of the plutonium. The Apollo 13 Lunar Module burned up returning from the Moon at 25,000 mph but the RTG stayed intact and didn't release any plutonium, so it might seem reasonable that the Cassini RTG would stay at least partially intact and release only a fraction of its plutonium, but we want to consider the worst possible accident so we'll assume ALL of the plutonium gets vaporized.

Burning up high in the atmosphere (say 50 km), the bits of plutonium will be distributed all over the Earth by high altitude winds and gradually settle to Earth over a period of years, just like bits of dust from meteors and volcanic eruptions. The volume of the Earth's atmosphere up to a height, h, is just V = 4 pi R^2 h where R is the radius of the Earth.

R is 6380 km (which is 6.38 x 10^6 meters) and h is 50 km, so

V = 4 (3.14) (6.38 x 10^6 meters)^2 (5.0 x 10^4 meters)

V = 2.6 x 10^19 meters^3.

Dividing this volume into the mass of the plutonium shows us the concentration in the atmosphere is 1.1 x 10^-18 kilograms per cubic meter (kg/m^3). I'll call this number "C" (for "concentration") in future equations.

How Much Gets Inhaled?

Remember, this plutonium is only dangerous if it gets inhaled and stays in the body. Only particles of plutonium close to the Earth's surface (no higher than your nose) can be inhaled. A small fraction of the plutonium in the atmosphere will settle down toward the surface over several years.

To overestimate the risk again, we'll assume that ALL the plutonium over the land area of the Earth is inhaled. Since 3/4 of the Earths surface is covered by the oceans, we'll assume that means that 1/4 of the plutonium contained in the concentration described above gets into your lungs (remember PuO2 is not soluble, so what lands in the oceans settles to the bottom of the ocean and doesn't enter the food chain).

We could ignore the plutonium that settles into uninhabited areas like Antartica, but once again we'll OVERestimate the risk and include those areas.

In reality, only a small fraction of the plutonium particles will be small enough to be inhaled. Anything larger than about 10 microns will be filtered y the nose or the cillia in the lungs and exhaled. To be safe however, we will once again OVERestimate the danger and assume ALL the particles get inhaled (Are you keeping track of how much we do this?).

A human being inhales about 0.1 liters (0.1 liter = 0.0001 meter^3) of air every second (depending upon the size of the person). Multiply by the number of seconds in one year and we find we inhale 3150 meter^3 of air per year I'll call this volume "Vyr".

Multiplying this volume by the atmospheric concentration, C, tells us how much plutonium each person breates in a year. If every cubic meter of that air contains the concentration of plutonium calculated above, every person on the surface of the Earth will inhale an amount of plutonium we'll call m, where

m = 1/4 C Vyr

m = 1/4 (1.1 x 10^-18 kilogram/meter^3) (3150 meter^3)

m = 8.7 x 10^-16 kilogram.

That's how much plutonium we would each inhale in one year. If we recall our high school chemistry, we can multiply that mass by ogadro's Number (6.02 x 10^23) and divide by the gram atomic weight of plutonium (0.238 kilogram) to see that we will each inhale about 2.2 x 10^9 plutonium atoms.

Now lets ask how much radiation we get from that plutonium.

Energy Absorbed From the Plutonium -- The Number of Alpha Particles

Remember that each atom of plutonium will emit it's alpha particle at a random time. The half-life, we'll call it "T," measures how long it takes for half the atoms in any sample to emit their alpha particles. The half-life for Pu-238 is 88 years. The mathematics of probability tells us that if we have N atoms, the number that will emit alpha particles in one year is equal to N ln(2)/T, where ln is the natural logarithm (the ln button on your calculator) and T is the half-life.

This means that the amount of radiation emitted decreases with time as the number of Pu-238 atoms decreases, but once again we'll overestimate the risk and assume N stays constant at the value N = 2.2 x 10^9 which we determined above. So the number of alpha particles emitted by the plutonium inside the body is:

Nalpha = N ln(2)/T

Nalpha = (2.2 x 10^9) ln(2) /88years

Nalpha = 1.7 x 10^7 alpha particles per year.

The Energy of Alpha Particles

An atom of plutonium emits an alpha particle with an energy of 5 MeV. The MeV is a unit of energy used in nuclear physics. For our purposes, I'll express that energy in the more common metric unit of joules (5 MeV = 8.0 x 10^-13 joule). Remember from the discussion above that a rad is defined as 1 joule absorbed in a body mass of 100 kilograms. Since each alpha particle packs an energy of 8.0 x 10^-13 joule, that means each alpha particle contributes 8.0 x 10^-13 rad to a 100 kilogram person.

If we multiply that by the number of alpha particles emitted per year, we find that the radiation dose from the Cassini plutonium is:

dose = Nalpha x 8.0 x 10^-13 rad

dose = (1.7 x 10^7) (8.0 x 10^-13) rad/year

dose = 1.4 x 10^-5 rad/year

To convert this to units of rem which measure the biological effects, we multiply by 10. So:

dose = 1.4 x 10^-4 rem/year

which is only 0.14 mrem/year! Remember that we get about 300 rem/year from natural background, so this additional 0.14 mrem from a hypothetical Cassini accident is INSIGNIFICANT! You get a lot more radiation from x-rays, airline flights, and just random changes in the background.

Let me repeat that result:

Cassini dose = 0.14 mrem/year

Background dose = 300 mrem/year

And remember this was an OVERestimate of the "worst-case" accident! If the radiation stayed constant at this rate for 50 years, it would add up to 7 mrem over that time. Of course, it actually decreases with time, so this rough estimate compares very favorably with the much more careful analysis done by NASA which predicts an exposure of about 1 mrem over 50 years.

So much for the obviously false statements of the Cassini opponents that an accident like this would "kill millions"!

SOURCE: Compliments of Proposition One Committee