The Plutonium isotope 239Pu has a half-life of 24,000 years anddecays by the emission of a 5.2 MeV alpha particle. Plutonium isnot especially dangerous if handled because the activity is low,and the alpha radiation doesn’t penetrate the skin. However, therecan be serious health concerns if the tiniest particles are inhaledand lodge deep in the lungs. This could happen following any kindof fire or explosion that disperses Plutonium as dust.

a) (3 pts.) Soot particles are roughly 1 μm in diameter, thedensity of Plutonium is 19,800 kg/m^3 , and its atomic mass is 244amu. Determine the number of atoms in a 1 μm diameter particle of239Pu.

b) (1 pt.) Determine the activity (in Bq) of this particle.

c) (2 pts.) Suppose the particle stays lodged in the lungs for20 years. How much energy is released by emitted alpha particlesover this 20-year period?

(Hint: The equation involving �892 tells you how many atoms areremaining, not how many have decayed. The total energy is thenumber of decayed particles times the energy of an emitted alphaparticle.)

We want to determine the dose delivered to the lungs by thisparticle, averaged over this 20-year period. You can assume all thealpha particles are stopped within a 25 µm-radius sphere around theparticle.

d) (2 pts.) What is the mass of the sphere in which the alphaparticles deliver all their energy? Assume the tissue density isthe same as water, 1000 kg/m^3.

e) (2 pts.) Determine the dose (in Sv) delivered to the lungs bythis particle, averaged over this 20-year period. The RBE for alphaparticles is 20.