Radioactive Decay Chapter 4

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Questions and Answers

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?

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?

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?

It will be higher due to a shorter half-life Signup and view all the answers

What is the specific activity of 226 Ra defined as in terms of Ci?

1 Ci g–1 Signup and view all the answers

To calculate specific activity, which value is used in place of atomic weight for more accuracy?

Mass number A Signup and view all the answers

How does the specific activity of a nuclide relate to its atomic mass number?

Lower atomic mass number contributes to higher specific activity Signup and view all the answers

What is the correct equation to compute the specific activity of a nuclide given its half-life T and atomic mass number A?

$SA = \frac{1600 A}{T} Ci g^{-1}$ Signup and view all the answers

What happens to the activity A1 of the parent radionuclide over time, given T1 ≫ T2?

It remains constant. Signup and view all the answers

In the equation dN2/dt = A1 - λ2 N2, what does A1 represent?

The constant activity of the parent radionuclide. Signup and view all the answers

What is the purpose of the substitution u = A1 - λ2 N2 in the equations?

To simplify the variable separation process. Signup and view all the answers

What does the equation A1 - λ2 N2 = (A1 - λ2 N20)e^{-λ2 t} imply regarding the daughter nuclide?

It demonstrates how the daughter activity builds up over time. Signup and view all the answers

When considering a pure sample of nuclide (1) at time t = 0, what is the initial activity A20 of nuclide (2)?

Equal to zero. Signup and view all the answers

After approximately seven half-lives of the daughter radionuclide, e^{-λ2 t} behaves how?

It approaches zero. Signup and view all the answers

In the context of radioactive decay, what does λ2 signify?

The rate of decay of the daughter radionuclide. Signup and view all the answers

The equation A2 = A1(1 - e^{-λ2 t}) + A20e^{-λ2 t} ultimately describes what phenomenon?

Increase and stabilization of daughter activity over time. Signup and view all the answers

What is the specific activity of a sample of 14C produced by the 14N(n,p)14C reaction?

4.51 Ci g–1 Signup and view all the answers

Which equation is used to calculate specific activity based on the decay of a long-lived parent to a short-lived daughter?

Eq. (4.24) Signup and view all the answers

In the context of specific activity, what does the term ‘carrier-free’ radionuclide signify?

It is produced without the presence of nonradioactive isotopes Signup and view all the answers

What does specific activity express in terms of solutions?

Concentration of activity in terms of volume Signup and view all the answers

What factor primarily influences the specific activity of 60Co produced by neutron absorption in 59Co?

The history of radiation exposure Signup and view all the answers

When does secular equilibrium occur in a decay chain?

When the parent decays much slower than the daughter Signup and view all the answers

How is specific activity defined mathematically?

Total decay rate over the mass of the sample Signup and view all the answers

Which of the following units is NOT commonly used for expressing specific activity?

Atoms per gram Signup and view all the answers

What condition must be met for secular equilibrium to exist between a parent and daughter radionuclide?

A1 = A2 Signup and view all the answers

In the case of secular equilibrium, what is the total activity if the parent activity is A1?

2A1 Signup and view all the answers

When do you say a chain of short-lived radionuclides is in secular equilibrium with a long-lived parent?

When each member's activity equals the parent's activity. Signup and view all the answers

What is the general condition described by the equation dN2/dt = λ1 N1 – λ2 N2?

It describes the transient equilibrium situation. Signup and view all the answers

If the half-life of the parent is greatly greater than that of the daughter, what happens to the activity A2 of the daughter?

It eventually equals A1. Signup and view all the answers

What does the equation N2 = (λ1 N10 e^(-λ1 t) - λ2 t e^(-λ2 t)) / (λ2 - λ1) model under specific conditions?

The daughter build-up when the half-life is not greatly different. Signup and view all the answers

Which variable combination indicates that the daughter radionuclide is more stable than the parent in transient equilibrium?

T1 > T2 Signup and view all the answers

What happens to the ratio e^(-λ2 t) as time increases in a transient equilibrium situation?

It becomes negligible. Signup and view all the answers

What occurs to the daughter activity A2 over time according to the derived equations?

It reaches a maximum and then decreases. Signup and view all the answers

What condition describes transient equilibrium?

When all activities decay with the half-life T1 of the parent. Signup and view all the answers

What does the equation (4.43) define?

The time at which the daughter activity A2 is maximized. Signup and view all the answers

When is secular equilibrium typically observed?

When λ2 is significantly greater than λ1. Signup and view all the answers

The maximum activity for the total activity A1 + A2 occurs at which point, according to equation (4.44)?

An earlier time in relation to A1's maximum. Signup and view all the answers

What relationship is indicated by the term λ2 A1 in equation (4.42)?

It defines the activity of the daughter as a function of time. Signup and view all the answers

How is the time at which transient equilibrium is established influenced?

By the relative values of T1 and T2. Signup and view all the answers

Which variable significantly impacts the peak of the daughter activity curve?

The decay constant of the parent, λ1. Signup and view all the answers

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.

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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.