Question

If a radioactive sample has an activity of \(65 \mu \mathrm{Ci}\), how many disintegrations per second are occurring?

Short answer

Approximately 2.405 million disintegrations per second occur.

Step-by-step solution

Understand Units

The activity of a radioactive sample is given as 65 microcuries (\(\mu \mathrm{Ci}\)), where 1 microcurie is equal to \(3.7 \times 10^4\) disintegrations per second.

Convert Microcuries to Curie

To find the activity in curies, note that 1 curie = \(10^6 \mu \mathrm{Ci}\). Thus, convert 65 \(\mu \mathrm{Ci}\) to curies:\[65 \mu \mathrm{Ci} \times \frac{1}{10^6} = 6.5 \times 10^{-5} \mathrm{Ci}\]

Calculate Disintegrations Per Second

Multiply the curie value by the conversion factor for curies to disintegrations per second (\(3.7 \times 10^{10}\) disintegrations per second per curie):\[6.5 \times 10^{-5} \mathrm{Ci} \times 3.7 \times 10^{10} \frac{\text{disintegrations}}{\text{s}\cdot\mathrm{Ci}} = 2.405 \times 10^{6} \text{ disintegrations per second}\]

Key concepts

Activity Measurement

Activity measurement in the context of radioactive decay refers to determining how many atomic disintegrations occur in a given amount of radioactive material over a specific period of time. It's a crucial property that helps us understand the potency or intensity of a radioactive source.
Activity is commonly expressed in units of curie (Ci) or becquerel (Bq). The curie is traditionally utilized in many nuclear engineering and physics fields, primarily in the United States. One curie equals the activity of a material wherein 3.7 x 10^10 disintegrations occur per second. On the other hand, the becquerel is the SI unit of activity and is defined as one disintegration per second.
When measuring the activity of a radioactive sample, radiologists and scientists often use these measurements for practical purposes:

• To calculate dosages for medical treatments.
• To understand the decay rates of radioactive materials in nuclear power plants and during scientific research.
• To manage and assess safety regulations by tracking radioactive emissions.

Understanding these measurements is vital for assessing the safety levels of radioactive exposure and for numerous scientific applications.

Microcurie to Disintegrations Per Second Conversion

Converting microcurie (\(\mu Ci\)) measurements to the disintegrations per second is an essential process in the world of radioactivity. The microcurie is a smaller unit, convenient for measuring lower activity levels. The need to convert arises from practical situations, such as when a precise understanding of the exact number of atomic disintegrations is required.
The general conversion strategy follows these straightforward steps:

• Recognize that one microcurie equals 3.7 x 10^4 disintegrations per second.
• To convert, multiply the number of microcuries by this conversion factor.

For instance, if you start with 65 µCi, multiplying by 3.7 x 10^4 gives you the disintegrations per second:\[65 \mu \mathrm{Ci} \times 3.7 \times 10^4 = 2,405,000\]This indicates that 2,405,000 atoms in the sample decay every second. This conversion is highly helpful to simplify and tell us how active a radioactive material is in producing radiation.

Units of Radioactivity

Radioactivity, the process through which unstable atomic nuclei release energy, is measured in specific units that standardize these measurements and make them interoperable between various fields of use. There are primary units used to express the activity of a radioactive substance, offering different levels of precision and context suitability.
The most common units are:

• Curie (Ci): Mostly used in the United States. One curie equals the activity of a radioactive substance in which 3.7 x 10^10 disintegrations occur per second. This unit is named after the pioneering scientist Marie Curie.
  
• Becquerel (Bq): The SI unit of activity. It is more commonly used worldwide and defined as one disintegration per second.
  
• Microcurie (\(\mu Ci\)): A smaller subdivision of the curie, where one microcurie is equal to 3.7 x 10^4 disintegrations per second. This unit is useful for lab-scale experiments and medical applications where radioactive materials may have lower activity.
  

Understanding these units is crucial for fields such as healthcare, nuclear power, and scientific research, where precise and accurate measurement of radioactivity is needed to ensure safety, compliance, and effectiveness of applications.