CALC -- integrals!

Iodine-131 is used to treat hypo-thyroidism since it is preferentially absorbed by the thyroid and typically involves a total radiation dosage of 10,000,000 millirem. Iodine-131 has a half-life of eight days.

1. Set up the appropriate integral to represent the radiation dosage delivered by the absorbed iodine in eight days.

2. Use the fact that eight days is the half-life of the isotope to find the initial radiation intensity in millrems/hour.

3. To the nearest 10 millirems, how much of the total radiation is delivered in six weeks?

  1. 👍
  2. 👎
  3. 👁
  1. well, we know the intensity is exponential in time.
    I = Io e^-kt
    the half life is 8 days
    I/Io = .5 = e^-8k
    ln .5 = -8k
    -.693147=-8k
    k = .0866
    so
    I = Io e^-.0866 t
    now total over 8 days, call it D for dose
    D = int I dt
    D = int dt Io e^-.0866 t from t=0 to t = 8
    D = (Io/-.0866) [ e^-.0866(8)-e^0]
    e^0 = 1 of course
    e^-.6931 = .5 of course
    so
    D = .5 Io/.0866
    or
    Io = 5.77 D
    D is given of course so you are there in millirems /24 hours
    I will leave the doing it in hours and the six weeks thing for you

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. chemistry

    A sample of 131 I was purified and then analyzed for iodine content. It was found that the sample was 99.8% pure. 25 hours later the sample was tested again and it was found that the sample was now just 78.2% pure. What is the

  2. Chemistry

    Iodine 131 is a radioactive isotope. After 4.00 days, 70.8% of a sample of 131I remains.What is the half life of 131I?

  3. Math with science

    Radioactive iodine treatment is so successful at treating hyperthyroidism that it has virtually replaced thyroid surgery. To the nearest full day, determine how long it will take for 400 millicuries of I-131, which has a half-life

  4. chem

    Iodine-131 has a half-life of 8 days. How many days would it take for a sample of Iodine -131 to go from 50 grams to 3.125 grams?

  1. chemistry

    Iodine-131 has a half life of 2.2 × 10-2 year. How long will it take to reduce a 130 g sample of 131I to 74 g 131I?

  2. Math please help!

    Nuclear medicine technologists use the Iodine isotope I-131, with a half-life of 8 days,to check thyroid function of patients. After ingesting a tablet containing the iodine, the isotopes collect in a patient's thyroid, and a

  3. Chemistry

    A solution of iodine (I2) in carbon tetra-chloride(CCl4) is used when iodine is needed for certain chemical tests. how much iodine must be added to prepare a 0.480 m solution of iodine in CCl4 if 100.0g of carbon tetra-chloride is

  4. chemistry

    80.0 g of iodine (v) oxide reacts with 28.0 g of carbon monoxide determine the mass of iodine

  1. Radioactivity

    Iodine-131 is a radioactive isotope. After 8.00 days, 50.2% of the sample remains. What is the half life of 131-I?

  2. Statistics

    4. The data below are from an independent-measures experiment comparing three different treatment conditions. Treat. 1 Treat 2 Treat 3 0 1 4 0 4 3 G=24 0 1 6 2 1 3 Ó X² = 92 T=2 T=6 T=16 SS=3 SS=9 SS=6 Use an analysis of

  3. MATH

    A paper bag contains a mixture of three types of treats: 12 granola bars, 10 fruit bars, and 8 cheese strips. Suppose that you play a game in which a treat is randomly taken from the bag and replaced, and then a second treat is

  4. Chemistry!

    1. Write balanced equations for each of the following processes. a. Chromium- 51, which targets the spleen and is used as a tracer in studies of red blood cells, decays by electron capture. b. Iodine-131, used to treat hyperactive

You can view more similar questions or ask a new question.