Nuclear Chemistry Flashcards

Fundamentals of Nuclear Structure and Atomic Notation

• Atomic Components and Notation ($^A_Z X$):

  • $X$: Element Symbol.

  • $A$: Mass Number, defined as the total number of protons plus the total number of neutrons in the nucleus ($A = Z + \text{number of neutrons}$).

  • $Z$: Atomic Number, defined as the number of protons in the nucleus.

• Elementary Particles in Nuclear Chemistry:

  • Proton: Represented as $^1_1 p$ or $^1_1 H$.

  • Neutron: Represented as $^1_0 n$.

  • Electron: Represented as $^0_{-1} e$ or $^0_{-1} \beta$.

  • Positron: Represented as $^0_{+1} e$ or $^0_{+1} \beta$.

  • Alpha ($\alpha$) Particle: Represented as $^4_2 He$ or $^4_2 \alpha$.

Rules for Balancing Nuclear Equations

• Rule 1: Conservation of Mass Number ($A$):

  • The total sum of mass numbers (protons + neutrons) of the products must equal the total sum of mass numbers of the reactants.

  • Example Fission: $^{235}_{92} U + ^1_0 n \rightarrow ^{138}_{55} Cs + ^{96}_{37} Rb + 2 ^1_0 n$.

  • Calculation: $235 + 1 = 138 + 96 + 2 \times 1$.

• Rule 2: Conservation of Atomic Number ($Z$) or Nuclear Charge:

  • The total sum of nuclear charges in the products must equal the total sum of nuclear charges in the reactants.

  • Calculation for the example above: $92 + 0 = 55 + 37 + 2 \times 0$.

• Case Study: Decay of Polonium-212 ($^{212}Po$):

  • $^{212}Po$ decays by alpha emission.

  • Reaction: $^{212}_{84} Po \rightarrow ^4_2 He + ^A_Z X$.

  • Solving for $A$: $212 = 4 + A \Rightarrow A = 208$.

  • Solving for $Z$: $84 = 2 + Z \Rightarrow Z = 82$.

  • The resulting element (atomic number $82$) is Lead ($Pb$).

  • Final Equation: $^{212}_{84} Po \rightarrow ^4_2 He + ^{208}_{82} Pb$.

Chemical vs. Nuclear Reactions

• Chemical Reactions:

  • Atoms are rearranged by the breaking and forming of chemical bonds.

  • Only valence electrons in atomic or molecular orbitals are involved.

  • Accompanied by relatively small absorption or release of energy.

  • Rates are influenced by external factors: temperature, pressure, concentration, and catalysts.

• Nuclear Reactions:

  • Elements (or isotopes) are converted from one to another.

  • Involve protons, neutrons, electrons, and other elementary particles.

  • Accompanied by the absorption or release of tremendous amounts of energy.

  • Rates are generally not affected by temperature, pressure, or catalysts.

Nuclear Stability and Modes of Radioactive Decay

• Beta ($\beta$) Decay:

  • Occurs when the $n/p$ ratio is too large.

  • A neutron is converted to a proton and an electron (beta particle).

  • Equation: $^1_0 n \rightarrow ^1_1 p + ^0_{-1} \beta + \bar{\nu}$.

  • Examples: $^{14}_6 C \rightarrow ^{14}_7 N + ^0_{-1} \beta + \bar{\nu}$; $^{40}_{19} K \rightarrow ^{40}_{20} Ca + ^0_{-1} \beta + \bar{\nu}$.

  • Result: Decreases neutrons by $1$, increases protons by $1$.

• Positron Decay:

  • Occurs when the $n/p$ ratio is too small.

  • A proton is converted to a neutron and a positron.

  • Equation: $^1_1 p \rightarrow ^1_0 n + ^0_{+1} \beta + \nu$.

  • Examples: $^{11}_6 C \rightarrow ^{11}_5 B + ^0_{+1} \beta + \nu$; $^{38}_{19} K \rightarrow ^{38}_{18} Ar + ^0_{+1} \beta + \nu$.

  • Result: Increases neutrons by $1$, decreases protons by $1$.

• Electron Capture Decay:

  • An inner-shell electron is captured by the nucleus.

  • Equation: $^1_1 p + ^0_{-1} e \rightarrow ^1_0 n + \nu$.

  • Examples: $^{37}_{18} Ar + ^0_{-1} e \rightarrow ^{37}_{17} Cl + \nu$; $^{55}_{26} Fe + ^0_{-1} e \rightarrow ^{55}_{25} Mn + \nu$.

  • Result: Increases neutrons by $1$, decreases protons by $1$.

• Alpha Decay:

  • Emission of a helium nucleus.

  • Result: Decreases neutrons by $2$ and protons by $2$.

  • Example: $^{212}_{84} Po \rightarrow ^4_2 He + ^{208}_{82} Pb$.

• Spontaneous Fission:

  • Example: $^{252}_{98} Cf \rightarrow 2 ^{125}_{49} In + 2 ^1_0 n$.

Factors Influencing Nuclear Stability

• Magic Numbers: Extra stability is observed in nuclei with specific numbers of protons ($Z$) or neutrons ($N$): $2, 8, 20, 50, 82, 126$.

• Even-Odd Rules: Nuclei with even numbers of both protons and neutrons are generally more stable than those with odd numbers.

• Atomic Number Limits:

  • Every isotope of elements with Z > 83 is radioactive.

  • All isotopes of Technetium ($Tc, Z=43$) and Promethium ($Pm, Z=61$) are radioactive.

Nuclear Binding Energy

• Definition: The energy required to break up a nucleus into its constituent component protons and neutrons.

• Mass-Energy Equivalence: Calculated using Einstein's equation $E = mc^2$.

• Calculation Example (Fluorine-19):

  • Isotope: $^{19}_9 F$ (mass = $18.9984\,amu$).

  • Constituernts: $9 \times (1.007825\,amu)$ for protons + $10 \times (1.008665\,amu)$ for neutrons.

  • Binding Energy ($BE$) in amu: $0.1587\,amu$.

  • Conversion: $1\,amu = 1.49 \times 10^{-10}\,J$.

  • Final Energy: $2.37 \times 10^{-11}\,J$.

  • Binding Energy per Nucleon: $\frac{2.37 \times 10^{-11}\,J}{19\,\text{nucleons}} = 1.25 \times 10^{-12}\,J$.

• Stability Curve: Nuclear binding energy per nucleon peaks at $^{56}Fe$, making it the most stable nucleus. Elements lighter than Iron undergo fusion, while heavier elements undergo fission.

Kinetics of Radioactive Decay

• Rate Law: Radioactive decay is a first-order process.

  • $\text{rate} = - \frac{\Delta N}{\Delta t} = \lambda N$

• Integrated Rate Law:

  • $N = N_0 \exp(-\lambda t)$

  • $\ln(N) = \ln(N_0) - \lambda t$

  • Where $N$ is the number of atoms at time $t$, and $N_0$ is the number at $t = 0$.

• Half-Life ($t_{1/2}$):

  • $t_{1/2} = \frac{\ln 2}{\lambda}$ or $\frac{0.693}{\lambda}$.

Radiometric Dating

• Radiocarbon Dating:

  • Uses Carbon-14 ($^{14}C$) produced in the atmosphere: $^{14}_7 N + ^1_0 n \rightarrow ^{14}_6 C + ^1_1 H$.

  • Decay: $^{14}_6 C \rightarrow ^{14}_7 N + ^0_{-1} \beta + \bar{\nu}$.

  • Half-life ($t_{1/2}$): $5730\,\text{years}$.

• Uranium-238 Dating:

  • Used to date rocks and the Earth.

  • Decay Series: $^{238}_{92} U \rightarrow ^{206}_{82} Pb + 8 ^4_2 \alpha + 6 ^0_{-1} \beta$.

  • Half-life ($t_{1/2}$): $4.51 \times 10^9\,\text{years}$.

Nuclear Transmutation

• Definition: The conversion of one nucleus into another by bombardment with high-energy particles (using cyclotron particle accelerators).

• Historical Examples:

  • $^{14}_7 N + ^4_2 \alpha \rightarrow ^{17}_8 O + ^1_1 p$

  • $^{27}_{13} Al + ^4_2 \alpha \rightarrow ^{30}_{15} P + ^1_0 n$

  • $^{14}_7 N + ^1_1 p \rightarrow ^{11}_6 C + ^4_2 \alpha$

• Transuranium Elements: Elements with atomic numbers greater than $92$. Synthesis examples include Neptunium ($Np$), Plutonium ($Pu$), Americium ($Am$), Curium ($Cm$), and others up to Meitnerium ($Mt$).

Nuclear Fission and Reactors

• Fission Process: The splitting of a heavy nucleus into smaller nuclei.

  • Example: $^{235}_{92} U + ^1_0 n \rightarrow ^{90}_{38} Sr + ^{143}_{54} Xe + 3 ^1_0 n + \text{Energy}$.

  • Energy produced: $3.3 \times 10^{-11}\,J$ per $^{235}U$ atom ($2.0 \times 10^{13}\,J$ per mole).

  • Comparison: Burning $1\,\text{ton of coal}$ generates only $5 \times 10^7\,J$.

• Chain Reaction: Self-sustaining sequence of fission. Requires a Critical Mass—the minimum mass of fissionable material required to sustain the reaction.

• Nuclear Reactor Components:

  • Shielding (protective barrier).

  • Control Rods (absorb neutrons to regulate the rate).

  • Uranium Fuel rods.

  • Coolant/Water and Steam generation for turbines.

• Waste and Environmental Impact:

  • $1000\,MW$ Coal plant: $35,000\,\text{tons}\;SO_2$, $4.5 \times 10^6\,\text{tons}\;CO_2$.

  • $1000\,MW$ Nuclear plant: $70\,ft^3$ vitrified radioactive waste.

• Oklo Phenomenon: Natural uranium today contains $0.7202\%\;^{235}U$. Evidence at Oklo, Gabon shows a natural fission reactor operated in Earth's history ($^{235}U$ measured at $0.7171\%$).

Nuclear Fusion

• Process: Fusing light nuclei to form a heavier nucleus.

• Reactions:

  • $^2_1 H + ^2_1 H \rightarrow ^3_1 H + ^1_1 H$ (Energy: $6.3 \times 10^{-13}\,J$).

  • $^2_1 H + ^3_1 H \rightarrow ^4_2 He + ^1_0 n$ (Energy: $2.8 \times 10^{-12}\,J$/$17.5\,MeV$).

  • $^6_3 Li + ^2_1 H \rightarrow 2 ^4_2 He$ (Energy: $3.6 \times 10^{-12}\,J$).

• Confinement: Research uses the Tokamak magnetic plasma confinement system.

Radioisotopes in Medicine and Biological Effects

• Common Diagnostic Isotopes:

  • Sodium-24 ($^{24}Na$): $t_{1/2} = 14.8\,hr$; beta emitter; blood-flow tracer.

  • Iodine-131 ($^{131}I$): $t_{1/2} = 14.8\,hr$; beta emitter; thyroid activity.

  • Iodine-123 ($^{123}I$): $t_{1/2} = 13.3\,hr$; gamma emitter; brain imaging.

  • Fluorine-18 ($^{18}F$): $t_{1/2} = 1.8\,hr$; positron emitter; PET scans.

  • Technetium-99m ($^{99m}Tc$): $t_{1/2} = 6\,hr$; gamma emitter; imaging agent (bone scans).

• Production of Technetium-99m:

  • Commercial: $^{235}U$ fission yields $^{99}Mo$.

  • Decay: $^{99}Mo \rightarrow ^{99m}Tc + ^0_{-1} \beta + \bar{\nu}$.

• Detection: Geiger-Müller counter detects radiation using argon gas.

• Biological Units:

  • Rad (Radiation Absorbed Dose): $1\,rad = 1 \times 10^{-5}\,J/g$ of material.

  • Rem (Roentgen Equivalent for Man): $\text{rem} = \text{rad} \times Q$ (Quality Factor). $Q = 1$ for beta/gamma; $Q = 20$ for alpha.

• Food Irradiation:

  • Up to 100 kilorad: Inhibits sprouting; kills insects in grains/fruits.

  • 100 - 1000 kilorads: Reduces salmonella; extends shelf life of meat/fish.

  • 1000 to 10,000 kilorads: Sterilizes meat; kills microorganisms in spices.