Podcast
Questions and Answers
What does specific activity measure in a radionuclide sample?
What does specific activity measure in a radionuclide sample?
- Volume of the sample
- Decay rate of the sample only
- Activity per unit mass (correct)
- Total mass of the sample
How is the specific activity of a pure radionuclide calculated?
How is the specific activity of a pure radionuclide calculated?
- By multiplying its half-life and atomic mass
- By dividing the number of atoms by the mass
- Dividing the decay constant by the atomic weight (correct)
- Using its density and total decay time
What units can specific activity be expressed in?
What units can specific activity be expressed in?
- Decibels per gram
- Joules per gram
- Becquerels per gram (correct)
- Grams per liter
If a nuclide has a shorter half-life than 226 Ra, what can be concluded about its specific activity?
If a nuclide has a shorter half-life than 226 Ra, what can be concluded about its specific activity?
What is the specific activity of 226 Ra defined as in terms of Ci?
What is the specific activity of 226 Ra defined as in terms of Ci?
To calculate specific activity, which value is used in place of atomic weight for more accuracy?
To calculate specific activity, which value is used in place of atomic weight for more accuracy?
How does the specific activity of a nuclide relate to its atomic mass number?
How does the specific activity of a nuclide relate to its atomic mass number?
What is the correct equation to compute the specific activity of a nuclide given its half-life T and atomic mass number A?
What is the correct equation to compute the specific activity of a nuclide given its half-life T and atomic mass number A?
What happens to the activity A1 of the parent radionuclide over time, given T1 ≫ T2?
What happens to the activity A1 of the parent radionuclide over time, given T1 ≫ T2?
In the equation dN2/dt = A1 - λ2 N2, what does A1 represent?
In the equation dN2/dt = A1 - λ2 N2, what does A1 represent?
What is the purpose of the substitution u = A1 - λ2 N2 in the equations?
What is the purpose of the substitution u = A1 - λ2 N2 in the equations?
What does the equation A1 - λ2 N2 = (A1 - λ2 N20)e^{-λ2 t} imply regarding the daughter nuclide?
What does the equation A1 - λ2 N2 = (A1 - λ2 N20)e^{-λ2 t} imply regarding the daughter nuclide?
When considering a pure sample of nuclide (1) at time t = 0, what is the initial activity A20 of nuclide (2)?
When considering a pure sample of nuclide (1) at time t = 0, what is the initial activity A20 of nuclide (2)?
After approximately seven half-lives of the daughter radionuclide, e^{-λ2 t} behaves how?
After approximately seven half-lives of the daughter radionuclide, e^{-λ2 t} behaves how?
In the context of radioactive decay, what does λ2 signify?
In the context of radioactive decay, what does λ2 signify?
The equation A2 = A1(1 - e^{-λ2 t}) + A20e^{-λ2 t} ultimately describes what phenomenon?
The equation A2 = A1(1 - e^{-λ2 t}) + A20e^{-λ2 t} ultimately describes what phenomenon?
What is the specific activity of a sample of 14C produced by the 14N(n,p)14C reaction?
What is the specific activity of a sample of 14C produced by the 14N(n,p)14C reaction?
Which equation is used to calculate specific activity based on the decay of a long-lived parent to a short-lived daughter?
Which equation is used to calculate specific activity based on the decay of a long-lived parent to a short-lived daughter?
In the context of specific activity, what does the term ‘carrier-free’ radionuclide signify?
In the context of specific activity, what does the term ‘carrier-free’ radionuclide signify?
What does specific activity express in terms of solutions?
What does specific activity express in terms of solutions?
What factor primarily influences the specific activity of 60Co produced by neutron absorption in 59Co?
What factor primarily influences the specific activity of 60Co produced by neutron absorption in 59Co?
When does secular equilibrium occur in a decay chain?
When does secular equilibrium occur in a decay chain?
How is specific activity defined mathematically?
How is specific activity defined mathematically?
Which of the following units is NOT commonly used for expressing specific activity?
Which of the following units is NOT commonly used for expressing specific activity?
What condition must be met for secular equilibrium to exist between a parent and daughter radionuclide?
What condition must be met for secular equilibrium to exist between a parent and daughter radionuclide?
In the case of secular equilibrium, what is the total activity if the parent activity is A1?
In the case of secular equilibrium, what is the total activity if the parent activity is A1?
When do you say a chain of short-lived radionuclides is in secular equilibrium with a long-lived parent?
When do you say a chain of short-lived radionuclides is in secular equilibrium with a long-lived parent?
What is the general condition described by the equation dN2/dt = λ1 N1 – λ2 N2?
What is the general condition described by the equation dN2/dt = λ1 N1 – λ2 N2?
If the half-life of the parent is greatly greater than that of the daughter, what happens to the activity A2 of the daughter?
If the half-life of the parent is greatly greater than that of the daughter, what happens to the activity A2 of the daughter?
What does the equation N2 = (λ1 N10 e^(-λ1 t) - λ2 t e^(-λ2 t)) / (λ2 - λ1) model under specific conditions?
What does the equation N2 = (λ1 N10 e^(-λ1 t) - λ2 t e^(-λ2 t)) / (λ2 - λ1) model under specific conditions?
Which variable combination indicates that the daughter radionuclide is more stable than the parent in transient equilibrium?
Which variable combination indicates that the daughter radionuclide is more stable than the parent in transient equilibrium?
What happens to the ratio e^(-λ2 t) as time increases in a transient equilibrium situation?
What happens to the ratio e^(-λ2 t) as time increases in a transient equilibrium situation?
What occurs to the daughter activity A2 over time according to the derived equations?
What occurs to the daughter activity A2 over time according to the derived equations?
What condition describes transient equilibrium?
What condition describes transient equilibrium?
What does the equation (4.43) define?
What does the equation (4.43) define?
When is secular equilibrium typically observed?
When is secular equilibrium typically observed?
The maximum activity for the total activity A1 + A2 occurs at which point, according to equation (4.44)?
The maximum activity for the total activity A1 + A2 occurs at which point, according to equation (4.44)?
What relationship is indicated by the term λ2 A1 in equation (4.42)?
What relationship is indicated by the term λ2 A1 in equation (4.42)?
How is the time at which transient equilibrium is established influenced?
How is the time at which transient equilibrium is established influenced?
Which variable significantly impacts the peak of the daughter activity curve?
Which variable significantly impacts the peak of the daughter activity curve?
Study Notes
Specific Activity
- Specific activity (SA) is the activity of a radionuclide per unit mass, expressed in Bq g–1 or Ci g–1.
- For pure radionuclides, SA is derived from the decay constant (λ) or half-life (T) and atomic weight (M) using the formula:
SA = (6.02 × 10²³ λ) / M - When T is in seconds, SA is measured in Bq g–1; atomic mass number (A) can be used for sufficient accuracy.
- Example of 226 Ra:
- Half-life (T) = 1600 years; Atomic mass (A) = 226.
- SA calculation yields 3.66 × 10¹⁰ s⁻¹ g⁻¹ or 3.7 × 10¹⁰ Bq g–1 (equivalent to 1 Ci).
- For other radionuclides, the specific activity can be expressed as:
SA = (1600 × 226) / (T × A) using T in years.
Examples of Specific Activity Calculations
- Specific activity of 14 C:
- T = 5730 years; A = 14.
- Results in SA = 4.51 Ci g–1 (or 4.46 Ci g–1 using alternative units).
- Specific activity can also apply to non-pure radionuclides, such as 14 C produced from the 14 N(n,p)14 C reaction, indicating a carrier-free state.
- The specific activity is relevant in solutions too, commonly represented in µCi mL⁻¹ or Bq L⁻¹.
Serial Radioactive Decay
- Activity can involve one radionuclide decaying into radioactive progeny.
- In secular equilibrium (T1 ≫ T2), the activity of the parent nuclide remains constant while the daughter nuclide's activity changes.
- The rate of daughter atom changes is given by:
dN2/dt = A1 - λ2 N2. - Eventually, after approximately seven half-lives, daughter activity (A2) equals parent activity (A1) leading to secular equilibrium where total activity is 2A1.
General Case of Decay
- When decay rates are comparable, the equation changes to:
dN2/dt = λ1 N1 - λ2 N2. - The derived relation for daughter nuclide:
N2 = (λ1 N10 / (λ2 - λ1)) * (e^(-λ1 t) - e^(-λ2 t)).
Transient Equilibrium
- Occurs when the parent radionuclide’s half-life is greater than the daughter’s but not vastly different.
- Daughter activity initially increases, then peaks and declines as it mirrors parent activity.
- The time to maximize daughter activity is given by:
t = (1 / (λ2 - λ1)) * ln(λ2 / λ1).
Key Concepts
- Secular and transient equilibrium can be mathematically described, with secular being a special case where the parent decay is negligible.
- Understanding these dynamics is crucial for applications in nuclear medicine, radiochemical analysis, and environmental monitoring.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Explore the concepts of radioactive decay in Chapter 4. This quiz focuses on specific activity, decay constants, and the relationships between atomic weight and the activity per unit mass. Test your understanding of these crucial concepts in nuclear physics.
