Question

a. The dosage of technetium- \(99 \mathrm{~m}\) for a lung scan is 20\. \(\mu \mathrm{Ci} / \mathrm{kg}\) of body mass. How many millicuries of technetium- \(99 \mathrm{~m}\) should be given to a \(50.0-\mathrm{kg}\) patient? \((1 \mathrm{mCi}=1000 \mu \mathrm{Ci})\) b. A person receives 50 mrad of gamma radiation. What is that amount in grays? What would be the equivalent dose in millirems? c. Suppose a person absorbed 50 mrad of alpha radiation. What would be the equivalent dose in millirems? How does it compare with the millirems in part \(\mathbf{b}\) ?

Short answer

a: 1 mCi. b: 50 mrem. c: 1000 mrem. The alpha radiation dose is significantly higher.

Step-by-step solution

- Calculate the total dose in microcuries

The dosage of technetium-99m is 20 \(\mu \mathrm{Ci} \/ \mathrm{kg}\) of body mass. For a 50.0-kg patient, multiply the dosage by the patient's weight: \[20 \mu \mathrm{Ci} \/ \mathrm{kg} \times 50.0 \mathrm{kg} = 1000 \mu \mathrm{Ci}\]

- Convert microcuries to millicuries

Given that \(1 \mathrm{mCi} = 1000 \mu \mathrm{Ci}\), convert the total dose from microcuries to millicuries: \[1000 \mu \mathrm{Ci} \div 1000 = 1 \mathrm{mCi}\]

- Convert mrad to grays

To convert the radiation dose from mrad to grays, use the conversion factor \(1 \mathrm{Gy} = 100000 \mathrm{mrad}\). Therefore: \[50 \mathrm{mrad} \times \left( \frac{1 \mathrm{Gy}}{100000 \mathrm{mrad}} \right) = 0.0005 \mathrm{Gy}\]

- Convert grays back to millirems for gamma radiation

1 gray is equivalent to 100 rem, given that \(1 \mathrm{Gy} = 100 \mathrm{rem}\), and \(1 \mathrm{rem} = 1000 \mathrm{mrem}\), convert the gamma dose from grays to millirems: \[0.0005 \mathrm{Gy} \times 100 \mathrm{rem} \times 1000 = 50 \mathrm{mrem}\]

- Calculate equivalent dose for alpha radiation

The conversion factor from rad to rem for alpha radiation includes a quality factor of 20. Given that \(1 \mathrm{rad} = 100 \mathrm{mrem}\), calculate the equivalent dose for 50 mrad of alpha radiation: \[50 \mathrm{mrad} \times 20 \left( \mathrm{quality \ factor} \right) = 1000 \mathrm{mrem}\]

- Compare doses for parts b and c

In part b, the gamma equivalent dose was 50 mrem. In part c, the alpha equivalent dose is 1000 mrem. Therefore, the alpha radiation dose is significantly higher.

Key concepts

technetium-99m dosage

Technetium-99m is a common radioactive substance used in medical imaging. In this exercise, we calculate the dose given to a patient based on their weight. For a lung scan, the prescribed dosage is 20 microcuries (\(\text{μCi}\)) per kilogram of body mass. To find the total dose for a 50 kg patient:
Multiply 20 \( \text{μCi} / \text{kg} \) by 50 kg to get 1000 \( \text{μCi} \).
Since \(1 \text{mCi} = 1000 \text{μCi} \), simply divide 1000 \( \text{μCi} \) by 1000 to convert to millicuries (mCi).
So, the patient should receive 1 mCi of technetium-99m.

radiation dose conversion

Radiation doses can be measured in different units like grays (Gy) and millirems (mrem). Converting between these units involves specific conversion factors.
For instance, 1 gray (Gy) is equal to 100,000 millirads (mrad). To convert 50 mrad to grays:
Divide 50 mrad by 100,000 which equals 0.0005 Gy.
To convert from grays to millirems, use the fact that 1 Gy equals 100 rem and 1 rem equals 1000 millirems (mrem).
So, 0.0005 Gy converts to 50 mrem for gamma radiation.

gamma radiation

Gamma radiation is a type of electromagnetic radiation, like X-rays. It’s very penetrating and often used in medical imaging and treatment.
When dealing with radiation doses, it's important to convert units correctly to understand the impact. For gamma radiation, 1 gray (Gy) equals 100 rem and since 1 rem equals 1000 millirem (mrem), we multiply the gray value by 1000 to convert to mrem.

alpha radiation

Alpha radiation consists of heavy, positively charged particles and is less penetrating than gamma radiation. However, when absorbed by tissues, it can be much more damaging.
Because of this increased potential for harm, alpha radiation has a higher quality factor—20 compared to 1 for gamma radiation.
For example, absorbing 50 millirads (mrad) of alpha radiation equates to 50 mrad × 20 = 1000 mrem, a much higher dose than an equivalent amount of gamma radiation.

gray to millirem conversion

Converting radiation doses from grays (Gy) to millirems (mrem) involves understanding the units and their relationships.
Start with the fact that 1 gray (Gy) equals 100 rem. Since 1 rem equals 1000 millirems (mrem), multiply the gray value by 100,000 to convert to millirems.
For example, 0.0005 Gy equals 0.0005 × 100,000, giving us 50 mrem for gamma radiation.
This method helps in consistently and accurately translating exposure levels into meaningful doses.