Question

The recommended dosage of iodine- 131 is \(4.20 \mu \mathrm{Ci} / \mathrm{kg}\) of hody weight. How many microcuries of iodine- 131 are needed for a \(70.0-\mathrm{kg}\) patient with hyperthyroidism?

Short answer

294.0 \mu \mathrm{Ci} of iodine-131 is needed.

Step-by-step solution

Understand the Given Information

The recommended dosage of iodine-131 is given as \(4.20 \mu \mathrm{Ci} / \mathrm{kg}\) of body weight, and the patient's weight is 70.0 kg.

Establish the Absorption Formula

Set up the formula to calculate the required dosage: \( \text{Total Dosage} = \text{Dosage per kg} \times \text{Weight of Patient} \)

Substitute the Given Values

Insert the values into the formula: \( \text{Total Dosage} = 4.20 \mu \mathrm{Ci} / \mathrm{kg} \times 70.0 \mathrm{kg} \)

Perform the Calculation

Multiply the values: \[ 4.20 \mu \mathrm{Ci} / \mathrm{kg} \times 70.0 \mathrm{kg} = 294.0 \mu \mathrm{Ci} \]

State the Final Answer

Hence, the amount of iodine-131 needed is 294.0 microcuries.

Key concepts

Radioisotope Dosage

The calculation of radioactive doses, such as iodine-131, is critical in medical treatments. Checking the recommended dosage helps in determining an accurate and safe amount for patients.
When dealing with radioactive dosages, it's essential to understand the measurement units. In this case, iodine-131 is measured in microcuries (μCi). One curie (Ci) is a unit of radioactivity representing the decay rate of one gram of radium-226. Microcuries are one-millionth of a curie.
Radioisotopes like iodine-131 are used because of their ability to target specific tissues. It's crucial to calculate dosages precisely to avoid excessive radiation exposure. In the example, the recommended dosage is given as 4.20 μCi/kg.
The formula for calculating the total dose is:
\[ \text{Total Dosage} = \text{Dosage per kg} \times \text{Weight of Patient} \]
This ensures a personalized dosage based on the patient's body weight, optimizing treatment efficacy and safety.

Hyperthyroidism Treatment

Hyperthyroidism occurs when the thyroid gland produces too much thyroid hormone. This condition can cause symptoms like rapid heart rate, weight loss, and nervousness. One common treatment is radioactive iodine therapy using iodine-131.
Iodine-131 is taken orally, usually as a capsule or liquid. Once ingested, it is absorbed by the thyroid gland. The radioactivity destroys the overactive thyroid cells, reducing hormone production. This treatment is targeted and generally well-tolerated.
Effective hyperthyroidism treatment requires precise dosing to avoid under or over-treatment. Too little iodine-131 might not adequately reduce hormone levels, while too much can damage the thyroid excessively. Calculating the correct radioactive dose is therefore vital for successful management of hyperthyroidism.
In our example, for a 70.0 kg patient, 294.0 μCi of iodine-131 was needed. Such precision helps ensure that the treatment is effective while minimizing potential side effects.

Unit Conversion

Unit conversion plays an essential role in understanding and applying measurements in various contexts. Especially in medical fields, accurate conversions ensure patient safety and effective treatments.
Let's review our iodine-131 dosage example. The recommended dosage was in microcuries per kilogram. Understanding what microcuries (μCi) and kilograms (kg) represent helps ensure precise calculations. One microcurie is one-millionth of a curie, and one kilogram equals 1,000 grams.
When calculating drug dosages, converting units correctly avoids errors. For example, if the recommended iodine-131 dosage was given in another unit, such as millicuries (mCi), conversion would be necessary. Here is how such conversions work:
1 curie = 1,000,000 microcuries
1 curie = 1,000 millicuries
This helps in understanding how to handle different units of measurement.
Ensuring correct dosage through proper unit conversions is essential in delivering safe and effective treatment for conditions like hyperthyroidism. This process applies to various medical and scientific calculations, highlighting the importance of mastering unit conversion skills.