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Chapter 24: Problem 35

What is the specific activity (in \(\mathrm{Bq} / \mathrm{g}\) ) if \(8.58 \mu \mathrm{g}\) of an isotope emits \(7.4 \times 10^{4} \alpha\) particles per minute?

Short Answer

Expert verified
The specific activity is \( 1.44 \times 10^{8} \text{ Bq/g}. \)

Step by step solution

01

- Convert Micrograms to Grams

First, convert the mass from micrograms to grams. Recall that 1 microgram (\textmu g) is equal to \(10^{-6}\) grams. Thus, \( 8.58 \textmu \text{g} \) is equivalent to \( 8.58 \times 10^{-6} \text{ g} \).
02

- Convert Particles per Minute to Becquerels

Becquerels (\text{Bq}) represent decays per second. Given that \( 7.4 \times 10^{4} \) \textalpha\text{ particles are emitted per minute, we need to convert this to particles per second: \( 7.4 \times 10^{4} \text{ particles/minute} \times \frac{1 \text{ minute}}{60 \text{ seconds}} = \approx 1233.33 \text{ particles/second} \text{ (Bq)}. \)
03

- Calculate the Specific Activity

Specific activity is defined as the activity per unit mass. Use the values from the previous steps to find specific activity: \( \text{Specific Activity} = \frac{1233.33 \text{ Bq}}{8.58 \times 10^{-6} \text{ g}} \approx 1.44 \times 10^{8} \text{ Bq/g}. \)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Radioactivity
Radioactivity is the process by which unstable atomic nuclei lose energy by emitting radiation. This emission can take the form of alpha particles, beta particles, or gamma rays. Understanding radioactivity is crucial in fields such as nuclear medicine, radiography, and environmental science. This process is inherently random, but we can measure overall rates of decay using units called Becquerels (Bq), which represent one decay per second.
Isotope Decay
Isotope decay refers to the transformation of an unstable isotope into a more stable form, often resulting in the emission of radiation. Each isotope has a characteristic decay rate, which can be quantified using its half-life - the time it takes for half of a given sample to decay. In this problem, alpha particles are emitted, indicating alpha decay, where the nucleus releases an alpha particle (2 protons and 2 neutrons). This kind of decay is common in heavy elements.
Unit Conversion
Unit conversion is essential for performing precise scientific calculations. In this problem, we convert micrograms to grams and decay rates from particles per minute to Becquerels. Here's a quick breakdown:
  • 1 microgram (μg) is equivalent to 10^{-6} grams (g).
  • To convert particles per minute to particles per second, divide by 60 since there are 60 seconds in a minute.
This careful conversion ensures that all units are consistent, allowing us to accurately calculate specific activity in Bq/g.

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Most popular questions from this chapter

What are the expected advantages of fusion reactors over fission reactors?

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Determine the age of a rock containing \(0.065 \mathrm{~g}\) of uranium-238 \(\left(t_{1 / 2}=4.5 \times 10^{9} \mathrm{yr}\right)\) and \(0.023 \mathrm{~g}\) of lead-206. (Assume that all the lead- 206 came from \({ }^{238} \mathrm{U}\) decay.

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