Suppose a patient is given 1.55 mg of I-131, a beta emitter with a half-life of 8.0 days. Assuming that none of the I-131 is eliminated from the person's body in the first 4.0 hours of treatment, what is the exposure (in Ci) during those first four hours?

Verified step by step guidance

1. Convert the mass of I-131 from milligrams to grams by using the conversion factor: 1 mg = 0.001 g.
2. Calculate the number of moles of I-131 using its molar mass (approximately 130.91 g/mol).
3. Determine the number of atoms of I-131 using Avogadro's number (6.022 x 10^23 atoms/mol).
4. Use the decay constant formula, \( \lambda = \frac{0.693}{t_{1/2}} \), where \( t_{1/2} \) is the half-life in days, to find the decay constant in terms of hours.
5. Calculate the activity in curies (Ci) using the formula \( A = \lambda N \), where \( N \) is the number of atoms, and convert the result from disintegrations per second to curies using the conversion factor: 1 Ci = 3.7 x 10^10 disintegrations per second.

Key Concepts

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. This decay occurs at a predictable rate characterized by the half-life, which is the time required for half of the radioactive substance to decay. Understanding this concept is crucial for calculating the remaining quantity of a radioactive isotope over time.

Half-Life

Half-life is a specific time period in which half of a given amount of a radioactive substance will decay. For I-131, the half-life is 8.0 days, meaning that after 8.0 days, only 50% of the original amount will remain. This concept is essential for determining how much of the substance is present at any given time, especially in the context of medical treatments.

Curie (Ci)

The Curie (Ci) is a unit of radioactivity that measures the rate of decay of radioactive material. One Curie is defined as 3.7 x 10^10 disintegrations per second. In the context of medical treatments, understanding the exposure in Ci helps quantify the amount of radiation a patient is receiving, which is critical for assessing safety and efficacy.