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Instructions
Determine the flux of the radioactive source you're interested in. Each bit of radioactive material puts out a specific average amount of high-energy particles. The source throws its particles out in every direction. Mathematically, this works out to be:
Flux = source strength / 4 x pi x r^2; where r is the distance from the source.
For example, you could have one milligram of manganese-54, with an activity of 8.3 curies. That source could be sitting on a table 4 feet away, which is 122 cm. So the particle flux is 8.3 / (4 x pi x 122^2) = 4.4 x 10^-5 curies/cm^2.
Convert the flux in curies to energy per second. One curie is equal to 3.7 x 10^10 disintegrations per second. Each disintegration will release a particle or photon into the environment, with a well-defined energy. Look up the data on your material in a resource such as the Table of Isotopes hosted by Lawrence Berkeley Laboratory, then multiply the energy released in each disintegration by the number of disintegrations.
For Manganese-54, each disintegration results in a gamma ray of 0.835 million electron volts (MeV). MeV is just a convenient unit with which to measure the energy of subatomic particles. So the energy flux of manganese-54 is given by
Energy flux = disintegrations per curie x energy per disintegration x particle flux.
Energy flux = 3.7 x 10^10 particles/second/curie x 0.835 MeV/particle x 4.4 x 10^-5 curies/cm^2.
Energy flux = 1.4 x 10^6 MeV/cm^2-second.
Calculate the flux incident on the object. Start by estimating the area the object exposes to the source, then multiply that by the energy flux.
For example, suppose it's you in the room 4 feet away from the source. Assume your area is roughly that of a rectangle 50 cm across and 150 cm tall. Your area will be 7500 cm^2. The amount of energy you'll intercept is the product of your area and the energy flux:
7500 cm^2 x 1.4 x 10^6 MeV/cm^2-second = 10.5 x 10^9 MeV/second.
Divide the total incident flux by the mass of the object to get the dose rate.
Assume you have a weight of 150 pounds, which is about 68,100 grams. The dose rate you receive is
10.5 x 10^9 / 68100 = 1.54 x 10^5 MeV/g-sec.
Determine the amount of time the object is exposed to the source to determine the total dose, and convert the dose to more traditional units. The total dose is the dose rate times the length of time you're exposed to the source. One of the traditional dose units is the rad, which is equal to 62.4 x 10^6 Mev per gram; so you can convert to the number of rads by dividing the dose you calculate by the definition of the rad.
For the example, assume you were exposed to the source for 5 minutes, which is 300 seconds. Your total dose would be:
1.54 x 10^5 MeV/g-sec * 300 sec = 46.3 x 10^6 MeV/g.
Converted to rads, this is:
46.3 x 10^6 MeV/g / 62.4 x 10^6 Mev/g = 0.741 rad, or 741 millirad.
Convert the dose you calculated to rems, roentgen equivalent man. That is, if your object is a human being, multiply the dose in rads by the appropriate "quality factor" to determine the dose in rems.
For the example, you are a person, so it's appropriate to convert rads to rems. The quality factor is a measure of how much damage is done by a specific type of radiation. For gamma rays, the quality factor is equal to about one, so the rad dose and the rem dose are equivalent. So the dose of 741 mrad is equivalent to a dose of 741 mrem.