Iodine-131 is often used to treat Graves' disease or hyperthyroidism. In Graves' disease the thyroid begins to overproduce thyroid hormone. If a small amount of iodine- 131 is consumed, it will concentrate in the thyroid gland and destroy its ability to function. If a tablet containing \(15.0 \mu g\) of \({ }^{131} \mathrm{I}\) is ingested by a patient, how many days will it take for the amount of iodine to decay to less than \(1 \mu \mathrm{g}\) ? (Iodine-131 has a half-life of 8 days.)

Radioactive decay is a process where an unstable atomic nucleus loses energy by emitting radiation. This happens naturally and cannot be influenced by external factors like temperature or pressure.

The elements involved release particles or electromagnetic waves. These emissions can be alpha particles, beta particles, or gamma rays.

In the context of iodine-131, a radioactive isotope of iodine, the emission helps treat medical conditions like Graves' disease. When iodine-131 decays, it transforms into a stable element, releasing radiation that affects surrounding tissues.

Understanding radioactive decay is crucial for calculating the amount of a substance over time and determining the necessary dosage for medical treatments.

The exponential decay formula is essential for understanding how the quantity of a radioactive substance decreases over time. The general formula is:

\[ A_t = A_0 \times \frac{1}{2}^{\frac{t}{T_{1/2}}} \]

Here,

• \(A_t\) represents the amount of substance remaining after time \(t\).
• \(A_0\) is the initial amount.
• \(T_{1/2}\) is the half-life period.

Half-life is the time it takes for half of the radioactive atoms to decay.

In our problem, we started with 15 micrograms and needed the amount to decay to less than 1 microgram. The half-life of iodine-131 is 8 days. By using the exponential decay formula, we can find out how many days it takes to reach the desired amount. The result from calculation shows it takes about 31.2 days for iodine-131 to decay from 15 micrograms to less than 1 microgram.

Graves' disease is an autoimmune disorder where the thyroid gland overproduces thyroid hormones. Too much thyroid hormone can cause symptoms like rapid heartbeat, weight loss, and irritability.

Iodine-131 is often used to treat this condition. When iodine-131 is ingested, it concentrates in the thyroid gland. The radiation emitted by iodine-131 during radioactive decay destroys the overactive thyroid cells. This helps in reducing the symptoms and normalizing hormone levels.

The treatment is non-invasive and usually involves taking a small dose of radioactive iodine in liquid or capsule form. Over time, the radioactive iodine decays and leaves the body, making it a relatively safe and effective treatment.

The half-life of a radioactive substance is crucial in understanding how long the substance remains active. For iodine-131, the half-life is 8 days. This means that every 8 days, half of the iodine-131 present will decay into a stable element.

Given this half-life, we can predict how long it will take for a specific amount of iodine-131 to reduce to a desired level. In our problem, we needed 15 micrograms to decay to less than 1 microgram. Using the half-life of 8 days and the exponential decay formula, we found it takes about 31.2 days.

Knowing the half-life is also important for safety and medical protocols, ensuring precise dosage and timing for treatments like those for Graves' disease.