Question

Iodine-131 is a convenient radioisotope to monitor thyroid activity in humans. It is a beta emitter with a half-life of 8.02 days. The thyroid is the only gland in the body that uses iodine. A person undergoing a test of thyroid activity drinks a solution of Nal, in which only a small fraction of the iodide is radioactive. (a) Why is Nal a good choice for the source of iodine? (b) If a Geiger counter is placed near the person's thyroid (which is near the neck) right after the sodium iodide solution is taken, what will the data look like as a function of time? (c) A normal thyroid will take up about 12\(\%\) of the ingested iodide in a few hours. How long will it take for the radioactive iodide taken up and held by the thyroid to decay to 0.01\(\%\) of the original amount?

Short answer

Nal is a good choice for the source of iodine because it is water-soluble, easily absorbed by the body, and iodine selectively targets the thyroid gland, making it a specific and effective monitoring tool for thyroid activity. The data from the Geiger counter placed near the thyroid will indicate an initial high count that decreases exponentially over time, following a decay curve. To find the time required for radioactive iodide to decay to 0.01% of the original amount, we use the decay formula and solve for t, resulting in approximately 53.69 days.

Step-by-step solution

(a) Why is Nal a good choice for the source of iodine?

Sodium iodide (Nal) is a good choice for the source of iodine because it is water-soluble, allowing easy absorption by the body. Moreover, as iodine is selective to the thyroid gland, it ensures that the radioactive element (iodine-131) is primarily absorbed by the thyroid, making it a highly specific and effective monitoring tool for thyroid activity.

(b) Data from the Geiger counter

The data obtained from the Geiger counter placed near the person's thyroid right after taking the sodium iodide solution will show an initial high count, indicating the presence of radioactive iodine. As time passes, the count will decrease exponentially, following a decay curve. This is because the half-life of iodine-131 is 8.02 days, and with each passing half-life, the amount of radioactive material present around the thyroid will reduce by half.

(c) Time required for radioactive iodide to decay to 0.01% of the original amount

We are given that a normal thyroid will take up about 12% of the ingested iodide. We are supposed to find the time it takes for this radioactive iodide to decay to 0.01% of the original amount. The decay of radioactive isotopes can be described by the formula: \[ N_t = N_0 * (1/2)^{t/T} \] where: - \(N_t\) is the remaining amount of the substance at a given time \(t\) - \(N_0\) is the initial amount of the substance - \(T\) is the half-life of the substance Let's assume the initial radioactive iodide ingested was 100 units. Therefore, the thyroid would take up 12 units (12% of 100 units). To find the time it takes for this amount to decay to 0.01% of the original amount (which is 0.01 units), we can set up the equation: \[ 0.01 = 12 * (1/2)^{t/8.02} \] We can then solve for \(t\): 1. Divide both sides by 12: \[ 0.0008333 = (1/2)^{t/8.02} \] 2. Take the logarithm base 2 of both sides: \[ \log_2{0.0008333} = \frac{t}{8.02} \] 3. Multiply both sides by 8.02 to isolate \(t\): \[ t = 8.02 * \log_2{0.0008333} \] 4. Calculate the value of \(t\): \[ t \approx 53.69\; \text{days} \] Hence, it takes approximately 53.69 days for the radioactive iodide taken up and held by the thyroid to decay to 0.01% of the original amount.

Key concepts

Radioactive Decay

Radioactive decay is a process where unstable atomic nuclei lose energy by emitting radiation, such as beta particles, alpha particles, or gamma rays. In the case of Iodine-131, it is a beta emitter, meaning it emits beta particles during its decay. This decay process transforms the radioactive element into a more stable form. It's a random process at the level of single atoms, meaning it's impossible to predict when a particular atom will decay. However, for a large number of atoms, the overall decay rate can be mathematically described using decay laws, like the exponential decay formula.
Radioactive decay is critical in many fields:

• Medical: Helping in diagnostics, like thyroid tests with Iodine-131.
• Archaeology: Carbon-14 dating to estimate the age of artifacts.
• Energy: Nuclear power generation involves the decay of radioactive fuels.

For students, understanding radioactive decay involves appreciating the unpredictable nature of atomic behavior while being able to apply deterministic statistical methods to predict outcomes over time. This foundational insight into atomic physics is key for parsing more complex concepts such as nuclear reactions and radiation health impacts.

Thyroid Monitoring

The thyroid gland is pivotal for regulating metabolism, and monitoring its function is crucial for diagnosing and managing various health conditions. Since the thyroid is the only gland that uses iodine, radioactive iodine, such as Iodine-131, is a valuable diagnostic tool. When a patient ingests sodium iodide ( (NaI)), the iodine is absorbed by the thyroid and the radioactivity can be measured to monitor gland activity.

Benefits of Using Iodine-131:

• Specificity: Targets the thyroid, since it's the only ion-used gland.
• Safety: Allows for non-invasive monitoring with minimal radiation dose due to its short half-life.
• Information: Allows for real-time data collection on thyroid uptake and activity.

A common method is using a Geiger counter to detect beta emissions from Iodine-131 around the neck area. The readings help doctors determine if the thyroid is working within normal ranges or exhibiting signs of hypo- or hyperactivity. With Iodine-131, thyroid function is tracked over time, assisting in the diagnosis and treatment of disorders like hyperthyroidism or thyroid cancer.

Half-Life Calculation

The half-life of a radioactive substance is the time required for half of the substance to decay. This concept helps predict how quickly a substance will lose its radioactivity. For Iodine-131, the half-life is 8.02 days. Understanding half-life is essential in scenarios like medical diagnostics or radioactive waste management.
To calculate how long it takes for a substance to decay to a certain level, you can use the formula: \[ N_t = N_0 \left( \frac{1}{2} \right)^{t/T} \]where

• \( N_t \) is the amount remaining,
• \( N_0 \) is the initial amount,
• \( T \) is the half-life,
• \( t \) is time elapsed.

Breaking down the decay of an initial 12% uptake of Iodine-131 to 0.01%, the calculation results in roughly 53.69 days, as solved in the exercise. Such calculations are imperative in determining safe levels for medical treatments and understanding environmental impacts of radioactive materials.