The radioactive 131 I isotope decays by gamma emission following first order kin

Question

The radioactive 131I isotope decays by gamma emission following first order kinetics. The half life for this decay is 8.025 days. Because of its short half life, this isotope has found extensive use in medicine. In very small doses, it is used to measure how effectively the thyroid gland is taking up iodine from food sources. Iodine is essential for the production of many thyroid hormones and tests such as the RAUI (radioactive uptake of iodine test) check to see if the patient has a healthy, functioning thyroid. In the test, the patient is given a small oral dose of 131I and then 24 hours later, the thyroid is scanned to see what percent of the isotope is now located in the gland. A normal test will show 8-25% uptake after approximately 24 hours.

Taken into account in these tests is the natural loss of 131I due to radioactive decay. If the test were run 21.8 hours after the patient injested the 131I isotope, what percent of the isotope has been lost due to radioactive decay?

Explanation / Answer

The half-life of iodine-131 is 8.025 days.

What percentage of an iodine-131 lost after 21.8 hours?

percentage of an iodine-131 remain = (1/2)^(number of half-lives)

number of half-lives=   (21.8 hours / 24 hours/day) / 8.025 days = 0.113

percentage of an iodine-131 remaining = (1/2)^0.113 = 0.925

percent remaining = 92.5 %
  
  
Therefore, percent of iodine-131 lost due to radioactive decay = 100 - 92.5 = 7.5%

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