Podcast
Questions and Answers
What does the equation N/N0 = e–λt represent in the context of radioactive decay?
What does the equation N/N0 = e–λt represent in the context of radioactive decay?
- The total number of radioactive particles at time t
- The fractional quantity of radionuclide remaining after time t (correct)
- The rate of increase in activity over time
- The initial mass of a radionuclide
How is the half-life T related to the decay constant λ?
How is the half-life T related to the decay constant λ?
- T = 0.693 / λ (correct)
- T = ln 2 / λ (correct)
- T = e–λ/2
- T = λ / ln 2
During the half-life period T, how does the activity A of a radionuclide behave?
During the half-life period T, how does the activity A of a radionuclide behave?
- It increases exponentially
- It doubles
- It remains constant
- It decreases by a factor of one-half (correct)
What mathematical operation is used to derive the equation for half-life from the exponential decay law?
What mathematical operation is used to derive the equation for half-life from the exponential decay law?
Which equation represents the activity of a radionuclide over time?
Which equation represents the activity of a radionuclide over time?
What happens to the dose rate at a fixed radionuclide source over time?
What happens to the dose rate at a fixed radionuclide source over time?
In the equation A/A0 = e–λt, what does the term A0 represent?
In the equation A/A0 = e–λt, what does the term A0 represent?
Which factor influences the rate of radioactive decay in the equations provided?
Which factor influences the rate of radioactive decay in the equations provided?
What is the decay constant λ of the nuclide with a half-life of 15.0 hours?
What is the decay constant λ of the nuclide with a half-life of 15.0 hours?
After 2.5 days, what is the activity of a 30-MBq source of the radionuclide mentioned?
After 2.5 days, what is the activity of a 30-MBq source of the radionuclide mentioned?
What is the total beta activity in a solution containing 0.10 µCi of 198Au and 0.04 µCi of 131I after 21 days?
What is the total beta activity in a solution containing 0.10 µCi of 198Au and 0.04 µCi of 131I after 21 days?
At what time will the total beta activity of the isotopes decay to half of its original value?
At what time will the total beta activity of the isotopes decay to half of its original value?
What is the exponent used in the equations to calculate decay from the half-life?
What is the exponent used in the equations to calculate decay from the half-life?
Which of the following statements is true regarding the isotopes mentioned?
Which of the following statements is true regarding the isotopes mentioned?
What is the required condition for the exponential decay equation to be dimensionless?
What is the required condition for the exponential decay equation to be dimensionless?
Which formula correctly relates the activity and decay constant?
Which formula correctly relates the activity and decay constant?
What is the unit of activity for radionuclides?
What is the unit of activity for radionuclides?
What relationship does the decay constant λ have with the number of atoms N in a sample?
What relationship does the decay constant λ have with the number of atoms N in a sample?
What does the equation dN = –λN dt represent in radioactive decay?
What does the equation dN = –λN dt represent in radioactive decay?
How is the activity (A) of a radionuclide expressed mathematically?
How is the activity (A) of a radionuclide expressed mathematically?
What does the negative sign in the equation dN = –λN dt indicate?
What does the negative sign in the equation dN = –λN dt indicate?
What is the significance of the constant c in the integrated equation ln N = –λt + c?
What is the significance of the constant c in the integrated equation ln N = –λt + c?
What does the integration of both sides of the equation dN/dt = –λN yield?
What does the integration of both sides of the equation dN/dt = –λN yield?
What transformation does the unit curie (Ci) represent in terms of becquerels (Bq)?
What transformation does the unit curie (Ci) represent in terms of becquerels (Bq)?
Flashcards are hidden until you start studying
Study Notes
Activity
- Activity measures the decay rate of a radionuclide, indicating the number of atoms decaying per unit time.
- The unit of measurement for activity is the becquerel (Bq), defined as one disintegration per second (1 Bq = 1 s⁻¹).
- The curie (Ci) is a traditional unit of activity, equivalent to 3.7 × 10¹⁰ Bq, based on 1 gram of 226Ra.
Exponential Decay
- The quantity N represents the number of atoms of a radionuclide at a given time.
- The change in atom number (dN) over time (dt) is proportional to the current quantity of atoms (N) multiplied by a decay constant (λ), expressed as dN = –λN dt.
- The decay constant (λ) has units of inverse time (s⁻¹) and indicates the rate of decay of radionuclides.
- The activity (A) of a sample relates to the decay:
- A = –(dN/dt) = λN.
Mathematical Foundations
- Integration of the decay equation leads to ln N = –λt + c, with c determined by initial conditions, particularly if N0 atoms are present at t=0.
- The exponential decay law can be expressed as:
- N/N0 = e⁻λt, indicating that the number of atoms decreases exponentially over time.
Activity and Half-Life
- The relationship between activity at a specific time (A) and initial activity (A0) is given by A/A0 = e⁻λt.
- The half-life (T) represents the time taken for the activity to reduce to half its original value, defined mathematically as:
- 1/2 = e⁻λT, leading to T = ln 2/λ (approximately T = 0.693/λ).
Examples of Decay Calculations
- To calculate the activity of a radionuclide after a specified time using its decay constant:
- Activity (A) after time t can be calculated using A = A0 e⁻λt, ensuring time units are consistent.
- Example given for a 30-MBq source of Na-24 after 2.5 days shows:
- λ calculated as 0.0462 h⁻¹ and resulting activity A = 1.88 MBq after time t.
Total Activity Calculation
- For solutions containing multiple radionuclides, the total beta activity is the sum of individual activities at a given time.
- Example calculation provided for a solution with 0.10 µCi of Au-198 and 0.04 µCi of I-131 at time t = 0:
- Activity calculated for both isotopes at t = 21 days gives a total beta activity of 7.02 × 10⁻³ µCi.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
