Nuclear Chemistry Lecture Notes

Nuclear Chemistry Lecture Notes

Introduction

• Source: Blackman, Bottle, Schmid, Mocerino and Wille, Chemistry 5th Ed., 2023 (John Wiley & Sons) ISBN: 9780730396673.
• Focus Areas of Lectures:
  • Lecture 2: Atomic symbols, Isotopes, Nucleogenesis
  • Lecture 3: Radioactivity and nuclear decay, Half-life and carbon dating
  • Lecture 4: Nuclear stability, Predicting radioactive modes of decay

Radioactivity

• Definition: Atomic nuclei can be classified into two categories: stable and radioactive.
  • Stable nuclei do not undergo decay.
  • Radioactive nuclei undergo spontaneous decay transitioning to stable forms over time.
• Each radioactive nuclide has its unique mode of decay and characteristic half-life.

Half-life

• Definition: The half-life of a radioactive nuclide is the time required for half of the nuclei in a sample to decay.
• Example: The half-life of Iodine-131 (I-131) is 8 days. For an initial sample of 160 nuclei, the decay progression is as follows:
  • After 8 days: 80 nuclei remaining
  • After 16 days: 40 nuclei remaining
  • After 24 days: 20 nuclei remaining
  • After 32 days: 10 nuclei remaining
  • After 40 days: 5 nuclei remaining
• Exponential Decay Function:
  • The decay process can be described with the equation:
    $N = N_0 e^{-kt}$
  • Where:
  • $N$ = Number of nuclei remaining
  • $N_0$ = Initial number of nuclei
  • $k$ = Decay constant
  • $t$ = Time elapsed

Decay Constant and Rate of Decay

• Decay Constant (k): This is a unique property of a particular radioactive nuclide and remains constant regardless of the sample size.
• Rate of Decay: The rate of decay $\frac{ riangle N}{ riangle t}$ depends directly on the number of remaining nuclei in a sample.

Activity

• Definition: Activity (A) measures the rate of decay of a radioactive sample, specifically defined as the number of disintegrations or decay events per second.
• Unit of Measurement:
  • Activity is measured in Becquerel (Bq).
  • 1 Becquerel = 1 disintegration per second.
• Relationship with Nuclei: The activity is proportional to the number of radioactive nuclei present in the sample.
• For the relationship involving activity and decay constant:
  $A = k N$
• Exponential decay also connects final and initial activity:
  $A(t) = A_0 e^{-kt}$
• Key scientist in nuclear research: Marie Sklodowska-Curie.

Specific Activity and Molar Activity

• Specific Activity: This refers to the activity per gram of a radioactive nuclide.
• Molar Activity: This is the activity per mole of a radioactive nuclide.
  • Example: 117 g of Uranium-234 (U-234) has an activity of $1.45 imes 10^6$ Bq:
  • $ext{Specific Activity} = \frac{1.45 imes 10^6 ext{ Bq}}{117 ext{ g}} \ ext{Molar Activity} = \frac{1.45 imes 10^6 ext{ Bq}}{234 ext{ g/mol}} \ = 2.90 imes 10^6 ext{ Bq/mol}$

Activity and Half-life Relationship

• Connection between activity and half-life:
  • A low activity correlates with a small decay constant and a larger half-life.
  • A high activity correlates with a large decay constant and a shorter half-life.
  • The absolute values of half-lives and corresponding activities of radioactive nuclides can vary enormously.

Equations for Half-life

• The equations for determining half-life are also based on population decay dynamics:
  • $N(t) = N_0 e^{-kt}$
  • For specific half-life time ($t=t<em>{1/2}$): $N(t</em>{1/2}) = \frac{N_0}{2}$
  • This understanding reveals that larger half-lives correspond with softer decay constants and lower activity levels.

Radiocarbon Dating

• C-14 Decay Process:
  • C-14 is a radioactive nuclide with a half-life of 5730 years produced in the atmosphere by neutron interaction with Nitrogen-14 (N-14).
  • In living organisms, the ratio of Carbon-12 (C-12) to C-14 remains constant (approximately 1:1 trillion). After the organism dies:
  • C-14 continues to decay.
  • The C-12:C-14 ratio increases.
  • The decline of C-14 activity in the sample allows for estimates of the time of death.
  • Decay Reaction:
    ^{14}{6}C ightarrow^{14}{7}N + e^{-}

Carbon Dating Equation

• Using the half-life of C-14, the equation manipulations lead to:
  • By replacing the decay constant $k$ with $\frac{ ext{ln} 2}{t<em>{1/2}}$, and recognizing $t</em>{1/2}$ as known (5730 y), the method is experimentally validated.

Carbon Dating Process

1. Measure C-14 activity in the archaeological sample (denote as $A_t$).
2. Measure C-14 activity in an equivalent modern sample (denote as $A_0$).
3. Insert values into the C-14 age calculation formula.

• Note: Carbon dating is valid for samples younger than 60,000 years.

Learning Outcomes

• After this lecture, you should be able to:
  • Recall the unique rates of decay for all radioactive nuclides.
  • Manipulate exponential decay equations accordingly.
  • Calculate activity, molar activity, specific activity, and half-life effectively.
• Further Reading: Reference section 27.2, 27.4 in Blackman et al.