Question

A vial contains radioactive iodine- 131 with an activity of \(2.0 \mathrm{mCi} / \mathrm{mL}\). If the thyroid test requires \(3.0 \mathrm{mCi}\) in an "atomic cocktail," how many milliliters are used to prepare the iodine-131 solution?

Short answer

1.5 mL

Step-by-step solution

Understand the given data

You have a vial with an activity of 2.0 mCi/mL and you need a total activity of 3.0 mCi.

Set up the relationship

Use the relationship between the volume (V) and the activity (A). The formula is: \[ A = \text{concentration} \times V \]

Rearrange the formula

Rearrange the formula to solve for volume (V): \[ V = \frac{A}{\text{concentration}} \]

Substitute the values

Substitute the given values into the formula:\[ V = \frac{3.0 \text{ mCi}}{2.0 \text{ mCi/mL}} \]

Calculate the volume

Calculate the volume:\[ V = \frac{3.0}{2.0} = 1.5 \text{ mL} \]

Key concepts

radioactivity

Radioactivity is a process where unstable atomic nuclei lose energy by emitting radiation. This radiation can be in the form of particles or electromagnetic waves. There are three main types of radiation: alpha particles, beta particles, and gamma rays. Each type interacts with matter differently and has different levels of penetration power. Understanding radioactivity is crucial in various fields such as medicine, energy production, and scientific research. Its measurement and safe handling are essential for its applications.
In this exercise, we use radioactive iodine-131, a common isotope that decays by beta and gamma emission. This property makes it useful in medical diagnostics and treatments, such as thyroid function tests and cancer therapy.

unit conversion in chemistry

Unit conversion is a fundamental skill in chemistry that involves changing one unit of measurement to another. This is crucial when dealing with different systems of measurement or when preparing solutions with specific concentrations. Being comfortable with unit conversions ensures precise calculations and helps avoid costly mistakes.
In the given exercise, we are dealing with activity units measured in millicuries (mCi). The relationship between the activity concentration (mCi/mL) and the required activity (mCi) is essential. By understanding the conversion needed, we ensure the correct volume of iodine-131 solution is prepared. The basic formula used here is \(\text{Activity} = \text{Concentration} \times \text{Volume}\). Rearranging this formula helps us solve for volume.

medical applications of radioisotopes

Radioisotopes have significant medical applications due to their radioactive properties. They are used both for diagnostic and therapeutic purposes. For instance:

• **Diagnostic Imaging:** Radioisotopes like iodine-131 are used in nuclear medicine to create detailed images of internal organs. This helps in diagnosing conditions like thyroid disorders.
• **Cancer Treatment:** Radioisotopes can target and destroy cancer cells while minimizing damage to surrounding healthy tissues. Iodine-131 is used specifically for treating thyroid cancer.
• **Sterilization:** Radioisotopes can sterilize medical equipment and supplies, ensuring no harmful microorganisms are present.

In this exercise, iodine-131 is part of an 'atomic cocktail' used for thyroid function tests. This demonstrates how radioisotopes can help gather critical health information.

activity concentration

Activity concentration refers to the amount of radioactivity per unit volume of a solution. It is typically expressed in units such as mCi/mL (millicuries per milliliter). Accurate measurement of activity concentration is vital in preparing radioactive solutions for medical and industrial uses.
In the provided exercise, the activity concentration is given as 2.0 mCi/mL. Knowing this allows us to calculate the volume needed when a specific total activity is required, using the formula \(\text{Volume} = \frac{\text{Activity}}{\text{Concentration}}\). This ensures that the 'atomic cocktail' for the thyroid test has the correct amount of iodine-131. Miscalculations in activity concentration can lead to ineffective treatments or unsafe radiation levels, highlighting the importance of precise measurements.