Comprehensive Notes on Nuclear Chemistry

Nuclear Chemistry

Introduction to Nuclear Chemistry

• Nuclear chemistry involves the study of reactions involving the nucleus of an atom.
• Key symbols and notations:
  • X: Element symbol
  • A: Mass number (number of protons + number of neutrons)
  • Z: Atomic number (number of protons)

Particles

• Proton: {1}^{1}p or {1}^{1}H
• Neutron: _{0}^{1}n
• Electron: {-1}^{0}e or {-1}^{0}\beta
• Positron: {+1}^{0}e or {+1}^{0}\beta
• Alpha particle: {2}^{4}He or {2}^{4}\alpha

Balancing Nuclear Equations

• Two main rules for balancing nuclear equations:

  1. Conserve mass number (A): The sum of mass numbers (protons + neutrons) must be the same on both sides of the equation (reactants and products).
  2. Conserve atomic number (Z) or nuclear charge: The sum of atomic numbers (nuclear charges) must be the same on both sides of the equation.

• Example:

  • _{92}^{235}U + _{0}^{1}n \rightarrow _{55}^{138}Cs + _{37}^{96}Rb + 2_{0}^{1}n
  • Mass number conservation: 235 + 1 = 138 + 96 + 2(1)
  • Atomic number conservation: 92 + 0 = 55 + 37 + 2(0)

Example Problem

• Problem: {84}^{212}Po decays by alpha emission. Write the balanced nuclear equation for the decay of {84}^{212}Po.
• Alpha particle: {2}^{4}He or {2}^{4}\alpha
• Solution:
  • _{84}^{212}Po \rightarrow _{2}^{4}He + _{Z}^{A}X
  • 212 = 4 + A \Rightarrow A = 208
  • 84 = 2 + Z \Rightarrow Z = 82
  • Therefore, the balanced nuclear equation is: _{84}^{212}Po \rightarrow _{2}^{4}He + _{82}^{208}Pb

Comparison of Chemical Reactions and Nuclear Reactions

Nuclear Stability and Radioactive Decay

Types of Radioactive Decay

• Beta decay: A neutron is converted into a proton, emitting a beta particle (_{−1}^{0}\beta) and a neutrino (\nu).
  • Decreases the number of neutrons by 1.
  • Increases the number of protons by 1.
  • Example:
    • _{6}^{14}C \rightarrow _{7}^{14}N + _{-1}^{0}\beta + \nu
    • _{19}^{40}K \rightarrow _{20}^{40}Ca + _{-1}^{0}\beta + \nu
    • _{0}^{1}n \rightarrow _{1}^{1}p + _{-1}^{0}\beta + \nu
• Positron decay: A proton is converted into a neutron, emitting a positron (_{+1}^{0}\beta) and a neutrino (\nu).
  • Increases the number of neutrons by 1.
  • Decreases the number of protons by 1.
  • Example:
    • _{6}^{11}C \rightarrow _{5}^{11}B + _{+1}^{0}\beta + \nu
    • _{19}^{38}K \rightarrow _{18}^{38}Ar + _{+1}^{0}\beta + \nu
    • _{1}^{1}p \rightarrow _{0}^{1}n + _{+1}^{0}\beta + \nu
• Electron capture decay: An inner orbital electron is captured by the nucleus, converting a proton into a neutron and emitting a neutrino (\nu).
  • Increases the number of neutrons by 1.
  • Decreases the number of protons by 1.
  • Example:
    • _{18}^{37}Ar + _{-1}^{0}e \rightarrow _{17}^{37}Cl + \nu
    • _{26}^{55}Fe + _{-1}^{0}e \rightarrow _{25}^{55}Mn + \nu
    • _{1}^{1}p + _{-1}^{0}e \rightarrow _{0}^{1}n + \nu
• Alpha decay: The nucleus emits an alpha particle (_{2}^{4}He).
  • Decreases the number of neutrons by 2.
  • Decreases the number of protons by 2.
  • Example:
    • _{84}^{212}Po \rightarrow _{2}^{4}He + _{82}^{208}Pb
• Spontaneous fission: The nucleus spontaneously splits into two smaller nuclei and several neutrons.
  • Example:
    • _{98}^{252}Cf \rightarrow _{49}^{125}In + _{49}^{125}In + _{0}^{1}n

Neutron-Proton Ratio and Nuclear Stability

• Belt of stability: A region on a plot of number of neutrons vs. number of protons, representing stable nuclei.
• n/p ratio too large: Nuclei above the belt of stability tend to undergo beta decay to decrease the n/p ratio.
• n/p ratio too small: Nuclei below the belt of stability tend to undergo positron decay or electron capture to increase the n/p ratio.

Magic Numbers

• Certain numbers of neutrons or protons result in extra stable nuclei.
• n or p = 2, 8, 20, 50, 82, and 126
• Analogous to stable electron configurations in noble gases (e- = 2, 10, 18, 36, 54, and 86)
• Nuclei with even numbers of both protons and neutrons are generally more stable than those with odd numbers.
• All isotopes of elements with atomic numbers higher than 83 are radioactive.
• All isotopes of Technetium (Tc) and Promethium (Pm) are radioactive.

Nuclear Binding Energy

Definition

• Nuclear binding energy (BE) is the energy required to break up a nucleus into its component protons and neutrons.

Calculation

• BE + _{9}^{19}F \rightarrow 9 _{1}^{1}p + 10 _{0}^{1}n
• BE = 9 \times (p \text{ mass}) + 10 \times (n \text{ mass}) - ^{19}F \text{ mass}
• E = mc^2
• BE (amu) = 9 \times 1.007825 + 10 \times 1.008665 - 18.9984
• BE = 0.1587 \text{ amu}
• 1 \text{ amu} = 1.49 \times 10^{-10} J
• BE = 2.37 \times 10^{-11} J

Binding Energy per Nucleon

• \text{Binding energy per nucleon} = \frac{\text{Binding energy}}{\text{Number of nucleons}}
• \text{Binding energy per nucleon} = \frac{2.37 \times 10^{-11} J}{19 \text{ nucleons}} = 1.25 \times 10^{-12} J

Nuclear Binding Energy per Nucleon vs Mass Number

• A plot of nuclear binding energy per nucleon against mass number shows that ^{56}Fe has the highest binding energy per nucleon, indicating its exceptional nuclear stability.
• Lighter nuclei like ^{4}He and ^{2}H have relatively high binding energy per nucleon.
• The curve illustrates the relationship between nuclear binding energy, nucleon number, and nuclear stability.
• Heavier nuclei like ^{238}U have lower binding energies per nucleon compared to medium-sized nuclei, implying they are less stable.

Kinetics of Radioactive Decay

Rate of Decay

• Rate of decay is proportional to the number of radioactive nuclei present.
  • Rate = - \frac{dN}{dt} = \lambda N
  • Where:
    • N is the number of atoms at time t
    • N_0 is the number of atoms at time t = 0
    • \lambda is the decay constant
• Integrated rate law:
  • N = N_0 \exp(-\lambda t)
  • \ln{N} = \ln{N_0} - \lambda t

Half-Life

• Half-life (t_{1/2}) is the time required for half of the radioactive nuclei in a sample to decay.
  • t_{1/2} = \frac{\ln{2}}{\lambda}
• Kinetics of Radioactive Decay
• $[N] = [N]_0exp(-λt)$
• $In[N] = In[N]_0 - λt$

Radiocarbon Dating

• Radiocarbon dating uses the decay of carbon-14 (_{6}^{14}C) to estimate the age of organic materials.
• Carbon-14 is produced in the atmosphere by neutron capture:
  • _{7}^{14}N + _{0}^{1}n \rightarrow _{6}^{14}C + _{1}^{1}H
• Carbon-14 decays through beta emission:
  • _{6}^{14}C \rightarrow _{7}^{14}N + _{-1}^{0}\beta + \nu
• Half-life of carbon-14: t_{1/2} = 5730 \text{ years}

Uranium-238 Dating

• Uranium-238 decays to Lead-206 with a half-life of 4.51 \times 10^{9} \text{ years}.
  • _{92}^{238}U \rightarrow _{82}^{206}Pb + 8 _{2}^{4}\alpha + 6 _{-1}^{0}\beta

Nuclear Transmutation

• Nuclear transmutation is the conversion of one element into another through nuclear reactions.

Examples of Nuclear Transmutation

• _{7}^{14}N + _{2}^{4}\alpha \rightarrow _{8}^{17}O + _{1}^{1}p
• _{13}^{27}Al + _{2}^{4}\alpha \rightarrow _{15}^{30}P + _{0}^{1}n
• _{7}^{14}N + _{1}^{1}p \rightarrow _{6}^{11}C + _{2}^{4}\alpha

Particle Accelerators

• Cyclotrons are used to accelerate charged particles to high energies for nuclear transmutation.

Transuranium Elements

• Transuranium elements are elements with atomic numbers greater than 92 (Uranium).
• These elements are artificially produced through nuclear transmutation.

Preparation of Transuranium Elements

• Examples:
  • Neptunium (Np): _{92}^{238}U + _{0}^{1}n \rightarrow _{93}^{239}Np + _{-1}^{0}\beta
  • Plutonium (Pu): _{93}^{239}Np + _{-1}^{0}\beta \rightarrow _{94}^{239}Pu
  • Americium (Am): _{94}^{239}Pu \rightarrow _{95}^{243}Am
  • Curium (Cm): _{94}^{239}Pu + _{2}^{4}\alpha \rightarrow _{96}^{242}Cm + _{0}^{1}n

Nuclear Fission

• Nuclear fission is the process in which a heavy nucleus splits into two or more lighter nuclei, releasing a large amount of energy.

Fission Reaction

• Example:
  _{92}^{235}U + _{0}^{1}n \rightarrow _{38}^{90}Sr + _{54}^{143}Xe + 3 _{0}^{1}n + \text{Energy}
• Energy released per ^{235}U atom:
  • \text{Energy} = [\text{mass } ^{235}U + \text{mass } n - (\text{mass } ^{90}Sr + \text{mass } ^{143}Xe + 3 \times \text{mass } n)] \times c^2
    \text{Energy} = 3.3 \times 10^{-11} \text{ J per }^{235}U = 2.0 \times 10^{13} \text{ J per mole }^{235}U

Comparison with Combustion

• Combustion of 1 ton of coal releases approximately 5 \times 10^{7} J of energy.
• Nuclear fission releases significantly more energy per mass compared to combustion.

Nuclear Chain Reaction

• A nuclear chain reaction is a self-sustaining sequence of nuclear fission reactions.

Critical Mass

• The critical mass is the minimum amount of fissionable material required to sustain a nuclear chain reaction.

Nuclear Reactor

Components of a Nuclear Reactor

• Uranium fuel: Provides the fissionable material.
• Control rods: Absorb neutrons to control the rate of the chain reaction.
• Water: Acts as a moderator to slow down neutrons and as a coolant to remove heat.
• Shield: Protects workers from radiation.

Process

• The heat generated by nuclear fission is used to produce steam, which drives a turbine to generate electricity.

Waste Production

Natural Fission Reactor

• Oklo, Gabon: Site of a natural nuclear fission reactor that operated about 2 billion years ago.
• The natural uranium had a higher concentration of U-235 than current natural uranium.
• Natural Uranium
  • 0.7202 \% U-235
  • 99.2798\% U-238
• Measured at Oklo
  • 0.7171 \% U-235

Nuclear Fusion

• Nuclear fusion is the process in which two light nuclei combine to form a heavier nucleus, releasing a large amount of energy.

Fusion Reactions

• Examples:
  _1^2H + _1^2H \rightarrow _1^3H + _1^1H (6.3 x 10-13 J)
  _1^2H + _1^3H \rightarrow _2^4He + _0^1n (2.8 x 10-12 J)
  _3^6Li + _1^2H \rightarrow 2 _2^4He (3.6 x 10-12 J)

Tokamak

• Tokamak devices use magnetic fields to confine plasma at high temperatures for fusion reactions.

Radioisotopes in Medicine

• Radioisotopes are used in various medical applications, including:
  • Tracers to study blood flow and organ function
  • Imaging agents for diagnostic purposes
  • Therapeutic agents for cancer treatment

Common Radioisotopes

• ^{24}Na: t1/2 = 14.8 hr, β emitter, blood-flow tracer
• ^{131}I: t1/2 = 14.8 hr, β emitter, thyroid gland activity
• ^{123}I: t1/2 = 13.3 hr, γ-ray emitter, brain imaging
• ^{18}F: t1/2 = 1.8 hr, β+ emitter, positron emission tomography (PET)
• ^{99m}Tc: t1/2 = 6 hr, γ-ray emitter, imaging agent

Production of ^{99m}Tc

• _{42}^{98}Mo + _{0}^{1}n \rightarrow _{42}^{99}Mo
• _{92}^{235}U + _{0}^{1}n \rightarrow _{42}^{99}Mo + \text{other fission products}
• _{42}^{99}Mo \rightarrow _{43}^{99m}Tc + _{-1}^{0}\beta + \nu
• _{43}^{99m}Tc \rightarrow _{43}^{99}Tc + \gamma\text{-ray}
• ^{99}Mo has a half-life of 66 hours and is used to produce ^{99m}Tc, which has a half-life of 6 hours.

Radiation Detection

Geiger-Müller Counter

• A Geiger-Müller counter is a device used to detect ionizing radiation.
• It consists of a tube filled with argon gas, with a central anode and a cathode.
• Ionizing radiation enters the tube through a window, ionizing the argon gas and creating a cascade of electrons that produce an electrical signal.

Biological Effects of Radiation

Units of Radiation

• Radiation absorbed dose (rad): 1 rad = 1 \times 10^{-5} \text{ J/g} of material
• Roentgen equivalent for man (rem): 1 rem = 1 rad x Q (Quality Factor)

Quality Factors

• γ-ray: Q = 1
• β particle: Q = 1
• α particle: Q = 20

Food Irradiation

Dosage and Effects

• Up to 100 kilorads:
  • Inhibits sprouting of potatoes, onions, garlic.
  • Inactivates trichinae in pork.
  • Kills or prevents insects from reproducing in grains, fruits, and vegetables.
  • 100 – 1000 kilorads:
    • Delays spoilage of meat poultry and fish.
    • Reduces salmonella.
    • Extends shelf life of some fruit.
  • 1000 to 10,000 kilorads:
    • Sterilizes meat, poultry and fish.
    • Kills insects and microorganisms in spices and seasoning.