Question

A sample of a radioactive metal used in medicine has an activity of \(3.5 \mathrm{mCi}\). What is its activity in \(\mathrm{Bq}\) and how many disintegrations/s does it give?

Short answer

The activity of the radioactive metal is 129,500,000 Bq, which is also the number of disintegrations per second.

Step-by-step solution

Understand the Conversion from mCi to Bq

One millicurie (mCi) is equal to 37 megabecquerels (MBq). Since there are a million (1,000,000) becquerels in a megabecquerel, we need to multiply 37 by 1,000,000 to get the conversion factor from mCi to Bq.

Convert the Activity from mCi to Bq

Multiply the activity in mCi by the conversion factor to get the activity in becquerels (Bq): Activity (Bq) = Activity (mCi) * 37 * 1,000,000.

Calculate the Number of Disintegrations per Second

Since 1 Bq is defined as 1 disintegration per second, the activity in Bq is equal to the number of disintegrations per second.

Key concepts

Millicurie to Becquerel Conversion

Understanding the conversion from millicuries (mCi) to becquerels (Bq) is essential for those dealing with radiopharmaceuticals or radioisotopes used in medical diagnostic and treatment procedures. A millicurie is a smaller unit of radioactivity and is widely used within the medical field. On the other hand, the becquerel is the SI (International System of Units) standard unit for radioactivity.

One millicurie is equivalent to 37 megabecquerels (MBq), and since one megabecquerel equals one million becquerels, we get the conversion factor by multiplying 37 MBq by 1,000,000. This means that one mCi is equal to 37 million Bq. To convert the activity from mCi to Bq for any given sample, you would multiply the activity in mCi by this conversion factor:
\[\begin{equation}Activity (Bq) = Activity (mCi) \times 37 \times 1,000,000.\end{equation}\]
Using this formula, we can help students understand how to translate the radioactivity levels of substances from the traditional millicurie unit to the standardized becquerel unit.

Radioactive Disintegrations Per Second

When dealing with radioactivity, one of the key concepts to grasp is the rate of radioactive decay, measured in disintegrations per second. This rate tells us how many atomic nuclei in a radioactive substance are transforming into a different nuclei or state every second as a result of radioactive decay.

The becquerel directly measures this decay rate, as 1 Bq represents one disintegration per second. Therefore, once the activity of a radioactive sample is converted to becquerels, determining the number of disintegrations per second is straightforward. For instance, an activity of 5 Bq means that there are 5 disintegrations occurring each second. In the context of our exercise:
\[\begin{equation}Activity (Bq) = Number \text{ of } Disintegrations/s,\end{equation}\]
students can easily calculate how many disintegrations are happening every second by simply observing the value expressed in becquerels. This measure is pivotal for ensuring safety and efficacy in the use of radioactive materials, particularly in medical settings where precise dosages are critical.

Activity of Radioactive Isotopes

The activity of a radioactive isotope refers to the measure of its radioactivity, or the rate at which the isotope undergoes radioactive decay. It quantifies how many atoms in a sample are expected to decay in a given time frame, which is vital in numerous applications such as nuclear medicine and radiocarbon dating.

Activity is expressed in various units, such as becquerels or curies, and is dependent upon the isotope's half-life—the time required for half of the isotope's nuclei to decay. Different isotopes have different half-lives and thus different activities. Understanding these differences is important for determining the necessary amount of a radioactive isotope for a specific application.

For example, in therapeutic procedures, knowing the activity of a radioactive isotope ensures that a sufficient dose is delivered to treat a medical condition without exposing the patient to unnecessary radiation. Equally, when dating ancient artifacts with carbon-14, scientists must consider the activity to accurately estimate their age. By mastering these calculations, students are equipped with the knowledge to safely handle and apply radioactive isotopes in various scientific and medical fields.