===== Calculation Exercise - Mother-Daughter Equilibrium ===== ==== Tasks ==== -One kg of fresh and dry thorium nitrate, Th(NO3)4, is produced from a natural occurring thorium containing ore. *Calculate the rate 232Th and 228Th disintegrates, and explain why the rate of disintegration is approximately equal for both of the thorium isotopes. *What is the weight of 228Th in the thorium nitrate? *228Ra separated from a one year old thorium nitrate can be placed on a column to make an isotope generator. The chemical yield for this process is 90%. How much amount of thorium nitrate is required to make the column, if 228Ra disintegrates with 10000 Bq? *At which rate will 224Ra disintegrate 3 days after the column is made? *Are there any other radionuclides present at a noteworthy amount (more than 100 Bq)? -One gram of natural uranium is purified to contain no other elements than uranium at time t = 0. *Which radionuclides are present at t = 0 and what are their respective rates of disintegration? *Which radionuclides are present at t = 25.5 h and what are their respective rates of disintegration? *Which radionuclides are present at t = 24 d and what are their respective rates of disintegration? *Which radionuclides are present at t = 1.0 a and what are their respective rates of disintegration? *Which radionuclides are present at t = 10.0 a and what are their respective rates of disintegration? -A given amount of alum shale contains 10 gram naturally occurring uranium. *Calculate the amount of Ra in Bq and in grams. *Calculate the amount of Pb in grams and in Bq. *210Pb is a weak beta emitter, but is still very toxic in large amounts. Why is it so? - Some radionuclei have a major application in medicine. For practical reasons it is advantageous if these can be produced with the help of an isotope generator. *Explain how an isotope generator may impact practical conditions. *Which of the following medical radionuclides can be produced by an isotope generator?\\ 67Ga,68Ga, 64Cu, 82Br, 89Sr, 90Y, 123I, 131I, 177Lu,201Tl,211At, 212Pb,211At, 223Ra. *In heart examination 201Tl is used in amounts of 100 MBq by intravenously injection of the radionuclide. Calculate the amount in moles and in grams. *Thallium is a potent rat toxin, why do patients survive these examinations? -A daughter nuclide is eluted from a 100 MBq 44Ti source in a column *How long does it take before 50 MBq of the daughter can be eluted from the system? *How many grams are 50 MBq of the daughter? -Minerals containing thorium emits strong gamma radiation, without any of the involved thorium isotopes emitting gamma. *Explain where the gamma radiation is coming from. *Which thorium isotopes exists in natural thorium, and what is the relation between them? *As a rule of thumb, it is said equilibrium is achieved after 10 Half-Lives. How much time must pass before equilibrium is reached throughout the entire chain of natural occurring thorium and uranium? -100 grams of fresh metallic thorium is prepared from naturally occurring thorium containing minerals. *What is the rate of disintegration? *How many grams of 228Th are present? *How many grams of 229Th are present? *What is the total activity of the metallic thorium 7.2 days after it was made, and how is the branching ratio between alpha and beta radiation? -A source of 10000 Bq from the very long lived 194Hg is used to produce 194Au. Assume 100% efficiency in the production process. *How long does it take until 1000 Bq of the daughter can be extracted from the mother? *How long does it take until 7500 Bq can be extracted? -The radionuclide 211At is planned to be used for medical purposes. It has a branching of 58% EC and 42% α. *Explain why you get a long lived daughter from one of these branches. *What is the weight of At in a 50 MBq 211At sample? *What is the rate of disintegration one week after the sample was made?