Monday, June 27, 2005

Math Problem VIII / Physics Problem I

The Bush Administration is renewing production of Plutonium-238, a radioactive substance not found naturally on the Earth. 94Pu238 has a half-life of 86 years and decays by ejecting an alpha particle. It has a high spontaneous fission rate and a very high heat output. It is not normally used for weapons, nor is it normally produced in pure form. It is typically a minor constituent of plutonium produced by neutron bombardment of 92U238.

Plutonium can be used as a power source in space probes, espionage devices, etc., owing to its intrinsic heat, as well as in nuclear weapons. The Bush plan calls for 330 pounds of Plutonium to be produced over a 30-year period. The program would cost $1.5 billion over that period; no specific information has been released about the intended use of the material, but powering espionage devices is the assumed purpose for most of it.

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Plutonium will cause death in a few days to a few weeks if swallowed as 500 mg of a soluble salt or a finely divided powder. Inhalation effects depend on the size of the particles inhaled, but 20-100 mg is sufficient to cause death within one month if the particles are retained.

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Physics:

Into what isotope does 94Pu239 decay?

Math:

(1 kg = 2.205 lb)

1) If all the plutonium about to be produced according to the Bush Administration's plans were converted to soluble plutonium and ingested by human beings, how many human beings could it kill?

2) If all the plutonium about to be produced were converted to finely divided airborne particles and inhaled by human beings, what is the maximum number of people it could kill?

3) If the overall estimate of the program's cost at $1.5b is correct, what would be the cost per person of killing the people in 2)? Can you think of other ways to kill that many people which would be cheaper?

Answers in comments.

2 comments:

Jessi Guilford said...

Physics:

plutonium-238 would decay into uranium-234:

94-Pu-238 --> 2-He-4 (alpha particle) + 92-U-234.

Math:

1)(330 lb)(1 kg/2.205 lb)(1000 g/kg)(1000mg/g)(1 person killed / 500 mg) = 299,000 people killed via ingestion. (This is approximately the population of Toledo, Ohio, St. Paul, Minnesota, or Buffalo, New York.)

2)(330 lb)(1 kg/2.205 lb)(1000 g/kg)(1000mg/g)(1 person killed / 20 mg) = 7,480,000 people killed by inhalation. (This is slightly less than the population of New York City, New York.)

3)$1,500,000,000 / 7,480,000 people = $201 per person. This is relatively expensive, as mass murder goes, and there would be a number of less expensive ways to do it. We can therefore conclude that the intent of the program is not to kill a large number of people, at least not with the plutonium directly.

Lauren said...

wow. nicely met.