Question

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 can be serious health concerns if the tiniest particles are inhaled and lodge deep in the lungs. This could happen following any kind of fire or explosion that disperses Plutonium as dust.

a) (3 pts.) Soot particles are roughly 1 μm in diameter, the density of Plutonium is 19,800 kg/m^3 , and its atomic mass is 244 amu. Determine the number of atoms in a 1 μm diameter particle of 239Pu.

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

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

(Hint: The equation involving �892 tells you how many atoms are remaining, not how many have decayed. The total energy is the number of decayed particles times the energy of an emitted alpha particle.)

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

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

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

Answer 1

(a) volume of sphere of diameter d = (1/6)d3

volume of 1 m diameter soot particle = (1/6)( 10-6 )3 = 0.524 10-18 m3

Mass of 1 m soot particle = 0.524 10-18 19800 = 1.037 10-14 kg

Number of atoms in 1 m soot particle = 6.02 1023 1.037 10-14 / 0.224 = 2.787 1010

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(b) activity in Becquerel , (dN/dt) = N = ( ln2 N ) / T1/2

(dN/dt) = ( ln2 2.787 1010 ) / ( 24000 365 24 3600 ) = 2.552 10-2 Bq

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(c) energy released by emitted particles over a period 20 years is product of number of decayed atoms and energy of particle released in each decay

If No is the initial number of atoms , then number of decayed atoms N over a period of 20 years

energy released by emitted particles over a period 20 years = 1.609 107 5.2 MeV

energy released by emitted particles over a period 20 years = 8.369 107 MeV

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Mass of lungs tissue sphere of radius 25 m = (4/3)(25)3 10-18 1000 kg

Mass of lungs tissue sphere of radius 25 m = 6.545 10-11 kg

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Radiation dose absobed in Grey = 8.369 107 1.602 10-13 J / 6.545 10-11 kg

Radiation dose absobed in Grey = 2.05 105 Gy

Radiation dose absobed in Sivert = (2.05 105 Gy 20 ) Sv= 4.1 106 Sv