Ionising Radiation and Nuclear Reactions

Nuclear Model of the Atom

  • The nuclear model has evolved over time.

  • Atoms are basic units of matter with a nucleus of protons and neutrons, surrounded by electrons.

  • Electrons are maintained by electrostatic forces.

Atomic Components

  • Nucleus: positively charged core containing protons and neutrons.

    • Proton: subatomic particle with +1 charge, same mass as neutron.

    • Electron: subatomic particle with -1 charge, lighter than proton.

    • Neutron: subatomic particle, same mass as proton, no charge (except Hydrogen).

  • Nucleons: protons and neutrons in the nucleus.

  • Nuclide: nucleus with specific number of protons and neutrons.

Atomic Representation

  • Elements: types of atoms (e.g., oxygen, helium, carbon).

    • Defined as a substance that cannot be broken down by chemical reactions.

  • Atomic number (Z): number of protons in an atom.

    • Determines element's position in the periodic table.

  • Increase in protons means increase in atomic number and mass.

  • A is the atomic mass (number of protons + number of neutrons)
    -X is the element symbol
    -Z is the atomic number

Elementary Charges and Ions

  • Elementary charge: electric charge of a single electron or proton.

    • More positive charges: atom is positive overall.

    • More negative charges: atom is negative overall.

    • Equal charges: atom is neutral.

  • Ion: atom that has lost or gained electrons.

    • Cation: positive ion (more positive charges).

    • Anion: negative ion (more negative charge).

Atomic Mass Unit (amu)

  • Defined as one-twelfth of the mass of a carbon-12 atom.

  • Used to express masses of subatomic particles.

Isotopes

  • Elements with same number of protons, different number of neutrons.

  • Same atomic number, different atomic mass.

  • Identical chemical properties, differing physical properties due to mass.

Nuclear Stability

  • In a stable nucleus, nucleons are tightly bound.

  • Electrostatic repulsion between protons is significant.

  • Electrostatic force varies inversely with separation distance.

Role of Neutrons

  • Add distance between protons to reduce repulsive force.

  • Act as nuclear 'glue' via strong nuclear force.

  • Strong force: short-ranged, attractive force between all nucleons.

  • Decreases rapidly as separation increases.

Ratio of Nuclear Stability

  • Smaller nuclei: neutron-to-proton (N/Z) ratio of 1:1.

  • As proton number increases, strong force weakens, electrostatic force strengthens.

  • N/Z ratio changes to maintain stability (see p. 139).

  • No stable nuclides above proton number 82.

Discovery of Nuclear Radioactivity

  • Radionuclides: unstable nuclides that undergo changes to their nucleus.

  • Radioactive: substances emitting radiation to reduce excess energy.

  • Radioactive decay: spontaneous emission of radiation.

Elementary Particles

  • Neutron discovered by James Chadwick (1932).

  • Positron discovered by Carl Anderson.

Types of Nuclear Radiation

  • Ionising radiation: radiation that removes electrons from atoms.

    • Includes gamma rays, X-rays, UV radiation, alpha and beta particles.

  • Nuclear radiation: radiation from the nucleus (alpha, beta, gamma).

Alpha Radiation ($\alpha$)

  • Helium nuclei (2 protons, 2 neutrons).

  • Emitted from the nucleus with a 2+ charge.

  • Transfer kinetic energy upon collision, creating ions.

  • Low penetrating ability (stopped by skin), but causes damage over short distances.

  • Deflected towards negatively charged plates in an electric field.

Beta Negative ($\beta^-$) Radiation

  • Electrons emitted from the nucleus at high speed.

  • Produces electron antineutrinos.

Beta Positive ($\beta^+$) Radiation

  • High-energy positrons emitted from the nucleus.

  • Produces neutrinos.

  • Higher penetrating ability than alpha particles, stopped by paper or plastic.

  • β+ deflects toward the negative plate.

  • β- deflects in the opposite direction.

Gamma Radiation ($\gamma$)

  • No charge, very high energy.

  • High penetration, causes least tissue damage over the same distance.

  • Transfers energy to molecules throughout the body.

  • No deflection in electric and magnetic fields.

Nuclear Shielding

  • Intensity: average power per unit area (Wm-2) or counts per second (cps).

  • Radiation spreads out spherically and is inversely proportional to radius squared.

  • I \propto \frac{1}{r^2}

  • I1 r1^2 = I2 r2^2

Intensity and Shielding

  • Penetration depends on type, matter, and density of radiation.

  • Lead as a good shield: high atomic mass and density

  • Intensity varies exponentially with thickness.

  • Half-value layer (HVL): thickness to reduce intensity by half.

Balancing Nuclear Equations

  1. Sum of mass numbers and total charge must be equal on both sides.

  2. Coefficients indicate multiple particles emitted.

Types of Radioactive Decay

  • Depends on nuclide instability (excess mass, neutrons, or protons).

    • Alpha Decay

    • Beta Negative (electron) Decay

    • Beta-positive (positron) Decay

Alpha Decay

  • Occurs when there is too much mass for the nuclear glue to hold it together.

  • Nucleus sheds protons and neutrons as packets.

    • Called transmutation, as the elements identity is changed.

  • Daughter nuclei release energy as gamma rays.

Neutrino

  • Elementary subatomic particle with no charge and a small mass.

  • Beta-negative decay: occurs with too many neutrons.

  • Parent emits an electron and electron antineutrino, daughter will have one more proton.

Beta-Positive Decay

  • Occurs when there are too many protons in the nucleus.

    • Also called positron decay.

  • A positron is a positive electron with same mass but opposite charge.

  • Positron emission occurs when the nucleus of an atom rearranges

  • Proton decays into a neutron, positron, and electron neutrino.

Gamma Decay

  • Electrons move from excited to ground state and release \gamma radiation.

  • No change in number of protons and neutrons, so no transmutation

Decay Series

  • Sequence of nucleides formed by successive radioactive decays until forming a stable decay product

Half-Life

  • The time taken for half of the atoms in a sample to decay

  • Amount of remaining nuclei: N = N_0 (\frac{1}{2})^n

  • n = \frac{Time Elapsed}{Half Life}

    • N_0 is the initial amount of substance.

Artificial Transmutation

  • Nuclear reactions induced artificially

  • Change of an isotope into another by bombardment with external particles

Mass Defect

  • Difference between the mass of a nucleus and the sum of the masses of its constituent particles

Binding Energy

  • The amount of energy required to break apart a nucleus into its individual protons and neutrons by overcoming the forces that hold it together.

Mass Equivalence Relationship

  • Einstein: mass and energy are equivalent.

  • \Delta E = \Delta mc^2
    - ΔE is the energy in joules
    - Δm is the mass defect in kilograms
    - c is the speed of light in a vacuum (3x108m/s)

Binding Energy in Joules/Nucleon

  • The binding energy divided by the number of nucleons in the nucleus of an atom

Binding Energy in Electron Volts (eV)

  • is one million eV and is a unit of energy defined as the work done on an electron to move it through an electric potential of 1volt or 1.6x10-19J
    - 1.6 \times 10^{-13} J = 1 MeV$$

Nuclear Fission

  • Fission reactions contain a lighter particle collides with a heavier parent nucleus, making it more unstable thus more energy is released

Neutron-Induced Nuclear Fission

  • It occurs when a neutron is fired at and absorbed within a U-235 nucleus to form U-236

    • Which will then split into two pieces.

Formula

-ΔE is the energy released or absorbed in J
-Δm is the change in mass or mass defect (in Kg) in a reaction.