Atoms, nuclei and radiation

The Nuclear Atom

• Atoms consist of a tiny, dense nucleus surrounded by electrons in orbit.

• The nucleus contains protons (positively charged) and neutrons (neutral).
• Electrons are negatively charged and much less massive than nucleons.

Rutherford α-Particle Scattering Experiment

• High-energy α-particles (helium nuclei) were directed at thin gold foil.

• Most passed through with little deflection, but a few were deflected at large angles.
• This showed that:
  • Most of the atom is empty space.
  • The positive charge and most mass are concentrated in a very small nucleus.

Atomic and Nuclear Notation

• Each atom is described by:
  • Proton number ($Z$): number of protons (defines the element).
  • Nucleon number ($A$): total number of protons and neutrons.
• Nuclide notation: $^A_Z X$, where $X$ is the chemical symbol.

Isotopes

• Isotopes are atoms of the same element (same $Z$) but different numbers of neutrons (different $A$).
• Isotopes have identical chemical properties but different physical properties (e.g., mass, stability).

Conservation Laws in Nuclear Reactions

• In all nuclear processes:
  • Nucleon number ($A$) is conserved.
  • Proton number ($Z$) (i.e., charge) is conserved.

Types of Nuclear Radiation

Alpha ($\alpha$) Radiation

• Consists of helium nuclei ($^4_2 \text{He}$): 2 protons, 2 neutrons.
• Mass: 4 u; Charge: +2e.
• Low penetration, high ionising power.

Beta ($\beta$) Radiation

• Two types:
  • $\beta^-$: Electron ($e^-$), charge $-e$, mass $\approx 0.00055$ u.
  • $\beta^+$: Positron ($e^+$), charge $+e$, mass $\approx 0.00055$ u.
• Moderate penetration, moderate ionising power.

Gamma ($\gamma$) Radiation

• Electromagnetic wave (photon), no mass, no charge.
• High penetration, low ionising power.

Neutrinos and Antineutrinos in Beta Decay

• In $\beta^-$ decay: a neutron turns into a proton, emitting an electron and an antineutrino ($\bar{\nu}_e$).
• In $\beta^+$ decay: a proton turns into a neutron, emitting a positron and a neutrino ($\nu_e$).

Energy of Emitted Particles

• $\alpha$-particles have discrete (fixed) energies.
• $\beta$-particles have a continuous range of energies because energy is shared with the (anti)neutrino.

Radioactive Decay Equations

• General form for $\alpha$-decay: $$^A_Z X \rightarrow ^{A-4}_{Z-2} Y + ^4_2 \alpha$$
• General form for $\beta^-$-decay: $$^A_Z X \rightarrow ^A_{Z+1} Y + \beta^- + \bar{\nu}_e$$
• General form for $\beta^+$-decay: $$^A_Z X \rightarrow ^A_{Z-1} Y + \beta^+ + \nu_e$$

Atomic Mass Unit

• The unified atomic mass unit (u) is a standard unit of mass:
  • $1~\text{u} = 1.66 \times 10^{-27}~\text{kg}$
  • 1 u is defined as $\frac{1}{12}$ the mass of a carbon-12 atom.

---

Summary:

• Atoms have a small, dense nucleus containing protons and neutrons.
• Isotopes have the same number of protons but different numbers of neutrons.
• Nuclear reactions conserve nucleon number and charge.
• $\alpha$, $\beta$, and $\gamma$ radiation have different properties.
• Antiparticles have the same mass but opposite charge to their particles.
• Neutrinos/antineutrinos are involved in beta decay.
• Use nuclide notation and atomic mass unit in calculations.