Radioactivity and Nuclear Reactions

Radioactivity

• Radioactivity is the emission of subatomic particles at high energy by nuclei (radioactive)
• Isotopes are atoms of the same element with different numbers of neutrons
• Isotope notation is written as ^A_ZX, where A is mass number, Z is atomic number and X is the element symbol.
• 1p = proton, 1n = neutron, 0e = electron, 0β = positron.
• 4₂α or ⁴₂He = alpha particle

N/Z ratio

• N/Z ratio (proton/neutron) affects nuclear stability
• Stable N/Z ratio ranges from ~1 to ~1.5 depending on atomic number (Z)
• Nuclei with high or low N/Z may be unstable.
• Nuclei above Z=83 are unstable.

Nuclear Fission & Fusion

• Nuclear fission is the splitting of a large nucleus into smaller ones, releasing energy.
• Nuclear fusion is the combining of small nuclei into a larger one, also releasing energy.
• Critical mass is the amount of isotope needed to start a fission reaction.

Energy from Fission

• Energy is released during a fission reaction due to mass defect.
• Einstein's equation (E = mc²) links mass and energy.
• 1 MeV = 1.602 x 10^-13 J
• 1 amu of mass defect = 931.5 MeV.
• Mass defect = difference between the nucleus's mass and the sum of masses of separated constituent particles.

Decay Types

• Alpha decay: Unstable nuclei emit alpha particles (⁴₂He). Low penetration power and high ionizing power.
• Beta decay: Unstable nuclei emit electrons. Higher penetration power, lower ionizing power than alpha decay.
• Gamma emission: High-energy radiation emitted from unstable nuclei. Highest penetration power, least ionizing power.
• Positron emission: Unstable nuclei emit positrons.
• Electron capture: Inner orbital electron is absorbed by the nucleus resulting into proton converting into neutron.

Ionizing & Penetrating Power

• Ionizing power is the ability of radiation to ionize molecules/atoms
• Penetrating power is the ability of radiation to penetrate matter.
• Gamma rays have the highest penetration and lowest ionization powers, followed by Beta and then Alpha.

Parent & Daughter Nuclides

• Parent nuclide decays into a daughter nuclide.
• Example: ²³⁸₉₂U decays into ²³⁴₉₀Th +⁴₂He

Radioactive Decay Rate

• Radioactive decay follows first-order kinetics.
• Rate = k * N (where k is the decay constant and N is the number of nuclei)
• Half-life (t_1/2) = 0.693/k, the time it takes for half of the parent nuclide to decay.

Magic Numbers

• Magic numbers are specific numbers of protons or neutrons that result in exceptionally stable nuclides. (e.g. 2,8,20,28,50,82 for protons, 126 for neutrons).

Particle Accelerators

• Linear accelerator: Tube shaped device used for accelerating particles.
• Cyclotron: Ring-shaped device used for accelerating charged particles.