Assignment:
The only radiogenic lead isotope that is not either stable (Pb-206, 207, 208) or with a halflife of less than one day is Pb-210, which is found in nature in secular equilibrium with U-238/U-234. Suppose that we can treat a minor selenium deficiency problem by giving the patient a cocktail of polonium-210, which binds to the appropriate organ permanently. We decide to make an isotope generator which willl bind lead to it, but which releases any polonium when we pour water through it. We load the generator with Pb-210 and then we will remove the Po-210 at 8 AM everyday. We wish to have enough Po-210 to treat 10 patients per day.
The targeted organ has an effective mass of one gram, and we wish to deposit a total of 1000 rads to it when all of the 138 day Po-210 has decayed. The alpha decay of Po-210 is essentially 100% to the Pb-206 ground state.
A) What is the miniumum amount of Po-210 that must be administred to a patient to provide a lifetime dose of 1000 Rad to the 1 gram organ? This needs to be in atoms, in grams, and in activity units.
1.177x10^10 atoms, 4.103x10^-12 g, 683.837 Bq, 1.84x10^-13
B) How much Pb-210 must be loaded onto the column in order to provide enough Po-210 for ten patients per day? This needs to be in atoms, in grams, and in activity units.
3.315x10^16 atoms, 1.156x10^-5 g, 3.27x10^7 Bq, 8.84x10^-10 micro curie
C) How much Pb-210 is there per mole of U-238 in secular equilibrium with it's daughters? How much uranium oxide (UO2) must be mined to provide the Pb-210 for one elution column in part B?
D) We could also produce Po-210 by irradiating bismuth with thermal neutrons, and letting the 5-day Bi-210 bproduced beta decay to Po-210. The polonium will spontaneously electroplate onto a clean silver foil once the bismuth is disoolved, to provide very pure Po-210. How long would you need to irradiate one gram of bismuth in a neutron flux of 1 E13 n/cm^2/second to provide enough Po-210 for ten patients?