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 NaI 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

NaI is a good choice for the source of iodine because it is easily soluble in water, convenient for ingestion, and can be processed by the body for thyroid activity. The Geiger counter data will look like an exponential decay curve, with the count rate decreasing as iodine-131 decays with a half-life of 8.02 days. It will take approximately 107.4 days for the radioactive iodide in the thyroid to decay to 0.01% of the original amount.

Step-by-step solution

(a) The reason NaI is a good choice for the source of iodine

Sodium iodide (NaI) is a good choice for the source of iodine because it is an ionic compound that is easily soluble in water, making it convenient for ingestion. Additionally, since iodine is present as iodide ions in NaI, the body can easily process and use it for thyroid activity, allowing for accurate monitoring of the gland. Furthermore, iodine-131 is a beta emitter, so it is less harmful when compared to alpha or gamma emitters that can cause more significant tissue damage.

(b) Geiger counter data as a function of time

Once the sodium iodide solution is taken, the radioactive iodine-131 will be absorbed by the thyroid. As time goes on, iodine-131 will undergo radioactive decay, emitting beta particles. The Geiger counter will detect these particles, and the data will represent the radioactive decay process. Initially, there will be a high number of counts per minute, corresponding to the high amount of iodine-131 present right after the solution is consumed. Over time, the count rate will decrease as iodine-131 decays according to the half-life rule of 8.02 days. The data will look like an exponential decay curve, with the activity dropping in half after each half-life cycle.

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

To solve this part, we need to find the time needed for radioactive iodide to decay to 0.01% of the original amount. We can use the radioactive decay formula: \[N = N_0 * e^{-\lambda t}\] Where \(N\) is the final amount of the radioactive substance, \(N_0\) is the initial amount, \(\lambda\) is the decay constant, and \(t\) is the decay time. We know that 0.01% of the initial amount of radioactive iodide is left, so we can write the equation as: \[0.0001 * N_0 = N_0 * e^{-\lambda t}\] Divide both sides of the equation by \(N_0\): \[0.0001 = e^{-\lambda t}\] Since we know the half-life \(\tau = 8.02\) days, we can find the decay constant using the formula: \[\lambda = \frac{ln(2)}{\tau}\] Now, we can substitute the decay constant into the equation: \[0.0001 = e^{-\frac{ln(2)}{8.02}t}\] Solve for \(t\): \[t = \frac{-8.02 * ln(0.0001)}{ln(2)}\] Calculate the value of \(t\): \[t \approx 107.4\, days\] It will take approximately 107.4 days for the radioactive iodide taken up and held by the thyroid to decay to 0.01% of the original amount.

Key concepts

Iodine-131

Iodine-131 is a radioactive isotope used in medical applications, notably for the diagnosis and treatment of thyroid conditions. It emits beta particles as it decays, which makes it suitable for therapeutic purposes since these particles can be detected and measured without causing extensive tissue damage.

Given that the thyroid is the only gland in the body that absorbs iodine, using iodine-131 in the form of sodium iodide (NaI) allows the specific targeting of this gland. This feature can be critical for the effective treatment of conditions like hyperthyroidism or for diagnostic tests that monitor thyroid function.

Beta Emission

Beta emission is a type of radioactive decay where a beta particle, which is a high-speed electron or positron, is emitted from the nucleus of an unstable atom. Iodine-131 undergoes beta-minus decay, emitting an electron and an antineutrino. This process helps to transform a neutron into a proton, altering the atom into a more stable element.

In medical imaging and treatment, the beta particles from iodine-131 can be detected externally, providing a way to visualize and assess the function of biological tissues, like the thyroid gland.

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This process occurs spontaneously and is typically modeled as an exponential decay, where the rate of decay is proportional to the amount of the radioactive substance present at any given time.

In the context of iodine-131, this decay results in the reduction of radioactive iodide over time, which can be used to determine the efficacy of the thyroid's uptake of iodine and its subsequent functioning.

Half-Life

The half-life of a radioactive isotope is the time required for half of the radioactive atoms present to decay. For iodine-131, this half-life is 8.02 days.

Understanding half-life is crucial for medical purposes, as it determines the dosing and timing for radioactive treatments. It helps to predict how long the radioactive substance will remain active in the body, allowing healthcare providers to optimize treatment and minimize potential radiation exposure to the patient.

Geiger Counter

A Geiger counter is a device used to detect and measure radiation, especially useful for tracking beta emissions from radioactive substances like iodine-131. When a person ingests NaI containing iodine-131 for thyroid monitoring, a Geiger counter placed near the thyroid can measure the beta particles emitted as the isotope decays, providing data about the gland's activity over time.

This instrument operates by registering the ionizing effect of radiation on a gas-filled tube, which results in electrical pulses that can be counted and converted into a measure of radiation intensity.

Exponential Decay Curve

An exponential decay curve is a mathematical representation of the decrease in the amount of a radioactive substance over time. It is characterized by a consistent pattern where the quantity diminishes by half with each passing half-life. The curve starts out with a steep decline, indicating a rapid loss of activity, and gradually flattens as the substance approaches complete decay.

When monitoring thyroid activity with iodine-131, the exponential decay curve provides a visual and quantitative method for understanding the rate at which the radioactive iodide is eliminated from the gland, enabling the estimation of the substance's remaining activity at any given point in the diagnostic or treatment process.