Exercises with Mother Daughter Relations and Equilibrium

Calcuation Exercises with Mother Daughter Relations and Equilibrium

1) One kg of fresh and dry thorium nitrate, Th(NO3)4, is produced from a natural occurring thorium containing ore.

    1. Calculate the rate 232Th and 228Th disintegrates, and explain why the rate of disintegration is approximately equal for both of the thorium isotopes.
    2. What is the weight of 228Th in the thorium nitrate?
    3. 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 10 000Bq?
    4. At which rate will 224Ra disintegrate 3 days after the column is made?
    5. Are there any other radionuclides present at a noteworthy amount (more than 100Bq)?

2) One gram of natural uranium is purified to contain no other elements than uranium at the time t equals 0.

    1. Which radionuclides are present at t=0?
    2. That are their respective rates of disintegration?
    3. Which radionuclides are present at t=25.5h?
    4. What are their respective rates of disintegration?
    5. Which radionuclides are present at t=24d?
    6. What are their respective rates of disintegration?
    7. Which radionuclides are present at t=1.0a?
    8. What are their respective rates of disintegration?
    9. Which radionuclides are present at t=10.0a?
    10. What are their respective rates of disintegration?

3) A given amount of alum shale contains 10 gram naturally occurring uranium.

    1. Calculate the amount of Ra in Bq and in grams.
    2. Calculate the amount of Pb in grams and in Bq.
    3. 210Pb is a weak beta emitter, but is still very toxic in large amounts. Why is it so?

4) 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.

    1. Explain how an isotope generator may impact practical conditions.
    2. 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.
    3. In heart examination 201Tl is used in amounts of 100MBq by intravenously injection of the radionuclide. Calculate the amount in mole and in grams?
    4. Thallium is a potent rat toxin, why do patients survive these examinations?

5) A daughter nuclide is eluted from a 100 MBq 44Ti source in a column.

    1. How long does it take before 50 MBq of the daughter can be eluted from the system?
    2. How many grams are 50 MBq of the daughter?

6) Minerals containing thorium emits strong gamma radiation, without any of the involved thorium isotopes emitting gamma.

    1. Explain where the gamma radiation is coming from.
    2. Which thorium isotopes exists in natural thorium, and what is the relation between them?
    3. 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?

7) 100 grams of fresh metallic thorium is prepared from naturally occurring thorium containing minerals.

    1. What is the rate of disintegration?
    2. How many grams of 228Th are present?
    3. How many grams of 229Th are present?
    4. 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?

8) A source of 10 000 Bq from the very long lived 194Hg is used to produce 194Au. Assume 100% efficiency in the production process.

    1. How long does it take until 1000 Bq of the daughter can be extracted from the mother?
    2. How long does it take until 7500 Bq can be extracted?

9) The radionuclide 211At is planned to be used for medical purposes. It has a branching of 58% EC and 42% α.

    1. Explain why you get a long lived daughter from one of these branches.
    2. What is the weight of At in a 50 MBq 211At sample?
    3. What is the rate of disintegration one week after the sample was made?


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