5. Iodine 53131I is used in diagnostic and therapeutic techniques in the treatme

Question

5. Iodine 53131I is used in diagnostic and therapeutic techniques in the treatment of thyroid disorders. This isotope has a half-life of 8.04 days. What percentage of an initial sample of 131I remains after 37.0 days? % 5. Iodine 53131I is used in diagnostic and therapeutic techniques in the treatment of thyroid disorders. This isotope has a half-life of 8.04 days. What percentage of an initial sample of 131I remains after 37.0 days? % 5. Iodine 53131I is used in diagnostic and therapeutic techniques in the treatment of thyroid disorders. This isotope has a half-life of 8.04 days. What percentage of an initial sample of 131I remains after 37.0 days? %

Explanation / Answer

According to the question

We know that

Decay constant k = ln(2)/half life

= 0.6931/8.04 = 0.08621 day^-1

A/Ao = exp(-kt) where A is the amount remaining after time t, and Ao is the initial amount

= exp(-0.08621 x 37.0) = 0.0411

Then,

Percentage remaining = A/Ao x 100

That's

= 0.0411 x 100 = 4.11%

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