The plutonium isotope ^239 Pu has a half-life of 24000 years and decays by the e
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The plutonium isotope ^239 Pu has a half-life of 24000 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. But the tiniest speck of plutonium can cause problems if it is inhaled and lodges deep in the lungs. Let's see why. a) Soot particles are roughly 1 micro-meter in diameter, and it is known that these particles can go deep into the lungs. How many ^239 Pu atoms are in a 1.0-micro meter-diameter particle of ^239 Pu? The density of plutonium is 19800 km/m^3. (Answer in N) b) What is the activity, in Bq, of this 1.0-micro meter-diameter particle? (Answer in Bq) c) The activity of the particle is very small, but the penetrating power of alpha particles is also very small, so the damage is concentrated. The alpha particles deposit their energy in a 50-micro meter-diameter sphere around the plutonium particle. In one year, what is the dose equivalent in mSv to this small sphere of tissue in the lungs? Assume that the tissue density is that of water. d) How does the exposure to this tissue compare to the natural background exposure? choose between=> lower than natural background? or higher than natural background? The plutonium isotope ^239 Pu has a half-life of 24000 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. But the tiniest speck of plutonium can cause problems if it is inhaled and lodges deep in the lungs. Let's see why. a) Soot particles are roughly 1 micro-meter in diameter, and it is known that these particles can go deep into the lungs. How many ^239 Pu atoms are in a 1.0-micro meter-diameter particle of ^239 Pu? The density of plutonium is 19800 km/m^3. (Answer in N) b) What is the activity, in Bq, of this 1.0-micro meter-diameter particle? (Answer in Bq) c) The activity of the particle is very small, but the penetrating power of alpha particles is also very small, so the damage is concentrated. The alpha particles deposit their energy in a 50-micro meter-diameter sphere around the plutonium particle. In one year, what is the dose equivalent in mSv to this small sphere of tissue in the lungs? Assume that the tissue density is that of water. d) How does the exposure to this tissue compare to the natural background exposure? choose between=> lower than natural background? or higher than natural background?Explanation / Answer
answer he volume of a 1-micron diameter sphere is: (4/3)*pi*(0.5*10^-6 m)^3 = 5.236*10^-19 m^3 This volume of 239Pu has a mass of: 5.236*10^-19 m^3 * 1.98*10^4 kg/m^3 = 1.037*10^-14 kg 239Pu has an atomic mass of 0.239 kg/mol, so this mass is equivalent to: (1.037*10^-14 kg)/(0.239 kg/mol) = 4.338*10^-14 mol There are 6.022*10^23 atoms/mol, so this amount of 239Pu is contains: 4.338*10^-14 mol * 6.022*10^23 atoms/mol = 2.612*10^10 atoms. ------------ (b) The activity of a sample is equal to the number of atoms in the sample multiplied by the decay constant of the material. The halflife and decay constant are related by: decay constant = (ln(2))/halflife. A halflife of 24,000 years corresponds to a decay constant of ln(2)/24000 = 2.888*10^-5 yr^-1 = 9.152*10^-13 sec^-1 The activity is then (2.612*10^10 atoms) * (9.152*10^-13 sec^-1) = 2.391*10^-2 atoms/sec = 2.391*10^-2 Bq.
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