The plutonium isotope ²³⁹Pu has a half-life of 24,000 years and decays by the emission of a 5.2 MeV alpha particle. Plutonium is not especially dangerous if handled because the activity is low and the alpha radiation doesn’t penetrate the skin. However, there are serious health concerns if even the tiniest particles of plutonium are inhaled and lodge deep in the lungs. This could happen following any kind of fire or explosion that disperses plutonium as dust. Let’s determine the level of danger.

a. Soot particles are roughly 1 mm in diameter, and it is known that these particles can go deep into the lungs. How many atoms are in a 1.0-μm-diameter particle of ²³⁹Pu? The density of plutonium is 19,800 kg/m³.

b. What is the activity, in Bq, of a 1.0-μm-diameter particle?

c. The activity of the particle is very small, but the penetrating power of alpha particles is also very small. The alpha particles are all stopped, and each deposits its energy in a 50-μm-diameter sphere around the particle. What is the dose, in mSv/year, to this small sphere of tissue in the lungs? Assume that the tissue density is that of water.

d. Is this exposure likely to be significant? How does it compare to the natural background of radiation exposure?