Chapter 21

Nuclear Chemistry

Shaun Williams, PhD

Review

• Atomic Number (Z) – number of protons
• Mass Number (A) – sum of protons and neutrons
$$ {}^A_Z\mathrm{X} $$

Radioactive

• Radioactivity Decay
• Nucleus undergoes decomposition to form a different nucleus.
• Radioactive Stability
• Nuclides with 84 or more protons are unstable.
• Light nuclides are stable when \(Z\) equals \(A – Z\) (neutron/proton ratio is 1).
• For heavier elements the neutron/proton ratio required for stability is greater than 1 and increases with \(Z\).

Radioactive Stability

• Certain combinations of protons and neutrons seem to confer special stability.
• Even numbers of protons and neutrons are more often stable than those with odd numbers.
• Certain specific numbers of protons or neutrons produce especially stable nuclides.
• 2, 8, 20, 28, 50, 82, and 126

The Zone of Stability

Types of Radioactive Decay

• Alpha production (\(\alpha\)) $$ {}^{238}_{\phantom{0}92}\chem{U} \rightarrow {}^{4}_{2}\chem{He} + {}^{234}_{\phantom{0}90}\chem{Th} $$
• Beta production (\(\beta\)) $$ {}^{234}_{\phantom{0}90}\chem{Th} \rightarrow {}^{234}_{\phantom{0}91}\chem{Pa} + {}^{\phantom{-}0}_{-1}\chem{e} $$
• Gamma ray production (\(\gamma\)) $$ {}^{238}_{\phantom{0}92}\chem{U} \rightarrow {}^4_2\chem{He} + {}^{234}_{\phantom{0}90}\chem{Th} + 2{}^0_0\gamma $$
• Positron production $$ {}^{22}_{11}\chem{Na} \rightarrow {}^0_1\chem{e} + {}^{22}_{10}\chem{Ne} $$
• Electron capture $$ {}^{201}_{\phantom{0}80}\chem{Hg} + {}^{\phantom{-}0}_{-1}\chem{e} \rightarrow {}^{201}_{\phantom{0}79}\chem{Au} + {}^0_0\gamma $$

Decay Series (Series of Alpha and Beta Decays)

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

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

Radioactive Decay Kinetics

• Decay rate $$ \mathrm{Rate}=kN $$
• The rate of decay is proportional to the number of nuclides.
• Half-Life - Time required for the number of nuclides to reach half the original value. $$ t_\bfrac{1}{2} = \frac{\ln(2)}{k} = \frac{0.693}{k} $$

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

• The change of one element into another. $$ \begin{align} {}^{27}_{13}\chem{Al} + {}^4_2\chem{He} &\rightarrow {}^{30}_{15}\chem{P} + {}^1_0\chem{n} \\ {}^{249}_{\phantom{0}98}\chem{Cf} + {}^{18}_{\phantom{0}8}\chem{O} &\rightarrow {}^{263}_{106}\chem{Sg} + 4{}^1_0\chem{n} \end{align} $$

A Schematic Diagram of a Cyclotron

A Schematic Diagram of a Linear Accelerator

Measuring Radioactivity Levels

• Geiger counter
• Scintillation counter

Geiger-Muller Counter

Carbon-14 Dating

• Used to date wood and cloth artifacts.
• Based on carbon–14 to carbon–12 ratio.

Radiotracers

• Radioactive nuclides that are introduced into organisms in food or drugs and whose pathways can be traced by monitoring their radioactivity.

Energy and Mass

• When a system gains or loses energy it also gains or loses a quantity of mass. $$ \begin{align} \Delta E &= \Delta mc^2 \\ \Delta m &= \text{mass defect} \\ \Delta E &= \text{change in energy} \end{align} $$
• If \(\Delta E\) is negative (exothermic), mass is lost from the system.

Mass Defect (\( \Delta m\))

• Calculating the mass defect for \( {}^4_2\chem{He} \):
• Since atomic masses include the masses of the electrons, we must account for the electron mass.
$$ \begin{align} 4.0026 &= \text{mass of }{}^4_2\chem{He} \text{ atom} = \text{mass of }{}^4_2\chem{He} \text{ nucleus} + 2m_e \\ 1.0078 &= \text{mass of }{}^1_1\chem{H} \text{ atom} = \text{mass of }{}^1_1\chem{H} \text{ nucleus} + m_e \end{align} $$
• \( {}^4_2\chem{He} \) nucleus is “synthesized” from 2 protons and two neutrons.
$$ \begin{align} \Delta m &= \left( 4.0026 - 2m_e \right) - \left[ 2\left( 1.0078-m_e \right) +2\left( 1.0087 \right) \right] \\ \Delta m &= -0.0304\,\mathrm{amu} \end{align} $$

Binding Energy

• The energy required to decompose the nucleus into its components.
• Iron-56 is the most stable nucleus and has a binding energy of 8.79 MeV.

Binding Energy per Nucleon vs. Mass Number

Nuclear Fission and Fusion

• Fusion – Combining two light nuclei to form a heavier, more stable nucleus.
$$ \chem{{}^3_2He + {}^1_1H \rightarrow {}^4_2He + {}^0_1e} $$
• Fission – Splitting a heavy nucleus into two nuclei with smaller mass numbers.
$$ \chem{{}^1_0n + {}^{235}_{\phantom{0}92}U \rightarrow {}^{142}_{\phantom{0}56}Ba + {}^{91}_{36}Kr + 3{}^1_0n} $$

Fission Processes

• A self-sustaining fission process is called a chain reaction.

Event	Neutron Causing Fission Event	Result
subscritical	\(<1\)	reaction stops
critical	\(=1\)	sustained reaction
supercritical	\(>1\)	violet explosion

Schematic Diagram of a Nuclear Power Plant

Schematic Diagram of a Reactor Core

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)

• The energy dose of the radiation and its effectiveness in causing biologic damage must be taken into account.
$$ \begin{align} \text{Number of rems} =& \left( \text{number of rads} \right) \times \mathrm{RBE} \\ \mathrm{rads} =& \text{radiation absorbed dose} \\ \mathrm{RBE} =& \text{relative effectiveness of the} \\ & \text{radiation in causing biologic damage} \end{align} $$

Effects of Short-Term Exposure to Radiation