
# Chapter 19 The Nucleus: A Chemist's View

Shaun Williams, PhD

### Review

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

• Nucleus undergoes decomposition to form a different nucleus.
• 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 $$Z$$.

• 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

• 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 $${}^{201}_{\phantom{0}80}\chem{Hg} + {}^{\phantom{-}0}_{-1}\chem{e} \rightarrow {}^{201}_{\phantom{0}79}\chem{Au} + {}^0_0\gamma$$

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

• 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 Linear Accelerator

• Geiger counter
• Scintillation counter

### Carbon-14 Dating

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

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

• 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.

### 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 Reactor Core

Depends on:

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

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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