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Chapter 19

The Nucleus: A Chemist's View

Shaun Williams, PhD

Review

Radioactive

Radioactive Stability

The Zone of Stability

Plot of stable and unstable isotopes. When the isotope has less than twenty protons, the isotope is stable when the ratio of protons to neutrons is about 1:1. As the number of protons get a lot higher, more neutrons are needed per proton to make the isotope stable.

Types of Radioactive Decay

Decay Series (Series of Alpha and Beta Decays)

A plot of mass number versus atomic number showing the steps in the path from uranium-238 to lead-206. Each step is showing how the atomic number and mass number are changing with different alpha and beta decay. These steps are in the following tables.

The Half-Lives of Nuclides in the \({}^{238}_{\phantom{0}92}\chem{U}\) Decay Series

Decay Half-Life
\( {}^{238}_{\phantom{0}92}\chem{U} \rightarrow {}^{234}_{\phantom{0}90}\chem{Th} + \alpha \) \( 4.51 \times 10^9\,\mathrm{years} \)
\( {}^{234}_{\phantom{0}90}\chem{Th} \rightarrow {}^{234}_{\phantom{0}91}\chem{Pa} + \beta \) \( 24.1\,\mathrm{years} \)
\( {}^{234}_{\phantom{0}91}\chem{Pa} \rightarrow {}^{234}_{\phantom{0}92}\chem{U} + \beta \) \( 6.75\,\mathrm{hours} \)
\( {}^{234}_{\phantom{0}92}\chem{U} \rightarrow {}^{230}_{\phantom{0}90}\chem{Th} + \alpha \) \( 2.48 \times 10^5\,\mathrm{years} \)
\( {}^{230}_{\phantom{0}90}\chem{Th} \rightarrow {}^{226}_{\phantom{0}88}\chem{Ra} + \alpha \) \( 8.0 \times 10^4\,\mathrm{years} \)
\( {}^{226}_{\phantom{0}88}\chem{Ra} \rightarrow {}^{222}_{\phantom{0}86}\chem{Rn} + \alpha \) \( 1.62 \times 10^3\,\mathrm{years} \)
\( {}^{222}_{\phantom{0}86}\chem{U} \rightarrow {}^{218}_{\phantom{0}84}\chem{Po} + \alpha \) \( 3.82\,\mathrm{days} \)
\( {}^{218}_{\phantom{0}84}\chem{Po} \rightarrow {}^{214}_{\phantom{0}82}\chem{Pb} + \alpha \) \( 3.1\,\mathrm{minutes} \)

The Half-Lives of Nuclides in the \({}^{238}_{\phantom{0}92}\chem{U}\) Decay Series Continued

Decay Half-Life
\( {}^{214}_{\phantom{0}82}\chem{Pb} \rightarrow {}^{214}_{\phantom{0}83}\chem{Bi} + \beta \) \( 26.8\,\mathrm{minutes} \)
\( {}^{214}_{\phantom{0}83}\chem{Bi} \rightarrow {}^{214}_{\phantom{0}84}\chem{Po} + \beta \) \( 19.7\,\mathrm{minutes} \)
\( {}^{214}_{\phantom{0}84}\chem{Po} \rightarrow {}^{210}_{\phantom{0}82}\chem{Pb} + \alpha \) \( 1.6 \times 10^{-4}\,\mathrm{seconds} \)
\( {}^{210}_{\phantom{0}82}\chem{Pb} \rightarrow {}^{210}_{\phantom{0}83}\chem{Bi} + \beta \) \( 20.4\,\mathrm{years} \)
\( {}^{210}_{\phantom{0}83}\chem{Bi} \rightarrow {}^{210}_{\phantom{0}84}\chem{Po} + \beta \) \( 5.0\,\mathrm{days} \)
\( {}^{210}_{\phantom{0}84}\chem{Po} \rightarrow {}^{206}_{\phantom{0}82}\chem{Pb} + \alpha \) \( 138.4\,\mathrm{days} \)

Radioactive Decay Kinetics

Exercise

A first order reaction is 35% complete at the end of 55 minutes. What is the value of \(k\)?

\( k = 7.8 \times 10^{-3}\,\mathrm{min}^{-1} \)

Nuclear Transformation

A Schematic Diagram of a Cyclotron

Photo of an actual cyclotron showing the outer steel casing and the copper electrodes that are used to accelerate the ions.

Diagram of a cyclotron. Two hollow D-shaped electrode forming a circle with a gap between them. This arrangement in placed in a vertical magnetic field. Introduction of ions at the center while oscillating the voltage on two D-shaped electrodes. The ions accelerate in an ever widening circular path outward from the center to an exit port. Outside the exit port is either a target or collection container for the ions.

A Schematic Diagram of a Linear Accelerator

An ion source is exposed to a sequence of metal tubes of alternating charges. At the end of the tubes is a target or collection container.

Measuring Radioactivity Levels

Geiger-Muller Counter

A steel chamber with a small window has an electrode inside it. Radiation entering the chamber ionizes the argon ions contained in the chamber. The ionized argon atoms are attracted to the electrode causing a current to flow which is detected on a counter.

Carbon-14 Dating

Radiotracers

Nuclide Half-Life Area of the Body Studied
\( {}^{131}\chem{I} \) 8.0 days Thyroid
\( {}^{59}\chem{Fe} \) 44.5 days Red blood cells
\( {}^{99}\chem{Mo} \) 66 hours Metabolism
\( {}^{32}\chem{P} \) 14.3 days Eyes, liver, tumors
\( {}^{51}\chem{Cr} \) 27.7 days Red blood cells
\( {}^{87}\chem{Sr} \) 2.8 hours Bones
\( {}^{99m}\chem{Tc} \) 6.0 hours Heart, bones, liver, and lungs
\( {}^{133}\chem{Xe} \) 5.2 days Lungs
\( {}^{24}\chem{Na} \) 15.0 hours Circulatory system

Energy and Mass

Mass Defect (\( \Delta m\))

Binding Energy

Binding Energy per Nucleon vs. Mass Number

The binding energy start off low with hydrogen and rises rapidly up to a maximum at iron-56 before slowly falling.

Nuclear Fission and Fusion

Fission Processes

Schematic Diagram of a Nuclear Power Plant

Within the containment shell of the power plant, a closed loop of water is pumped between the reactor core and a heat exchanger. A second water loop is pumped through the containment shell between the heat exchanger and second heat exchanger through a turbine. A third water loop is pumped between from a large body of water into the second heat exchanger and then back into the body of water. The turbine generates the electricity.

Schematic Diagram of a Reactor Core

Within the reactor core are uranium fuel rods. Between the fuel rods are neutron-absorbing control rods that can be inserted or withdrawn from the core. Through the entire system, hot coolant is pumped.

Biological Effects of Radiation

Depends on:

  1. Energy of the radiation
  2. Penetrating ability of the radiation
  3. Ionizing ability of the radiation
  4. Chemical properties of the radiation source

rem (roentgen equivalent for man)

Effects of Short-Term Exposure to Radiation

Dose (rem) Clinical Effect
0-25 Nondetectable
25-50 Temporary decrease in white blood cell counts
100-200 Strong decrease in white blood cell counts
500 Death of half the exposed population within 30 days after exposure

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