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Particle and Nuclear Physics

Balanced Equations
  • α-decay: 42α
    • Nucleon number decreases by 4
    • Proton number decreases by 2
  • β-decay: 0-1β
    • Proton number increases by 1
  • β+-decay: 0+1β+
    • Proton number decreases by 1
  • γ-decay: 00γ
    • Proton and nucleon number are unchanged
Mass-Energy Equivalence
  • Einstein’s Mass-energy relation: E = mc². “Mass of a system increases when energy is supplied to it”
    • where c is the velocity of light in free space
  • Mass Defect (ΔM): The difference between the total mass of the individual, separate nucleons and the mass of the nucleus.
  • Binding Energy (ΔE): The minimum external energy required to separate all the neutrons and protons of a nucleus. It is also the energy released when the nucleus is assembled from its constituent nucleons
    • The binding energy of a nucleus is a measure of how tightly the nucleus is bound and hence how stable it is
    • Binding Energy per Nucleon of a nucleus is the ratio of the total binding energy to tits nucleon number
    • The higher the binding energy per nucleon, the most stable the atom is
Atomic Mass Unit
  • 1u is defined as 1/12 of the mass of a neutral atom of carbon-12 — approximately equal to
    1.661 × 10-27 kg
  • Mass excess = mass (in u) – nucleon number
Nuclear Fission and Fusion

  • Fission is a process in which a massive nucleus splits to form two smaller fragments
    • The large nucleus has a lower binding energy per nucleon so splits into fission fragments which have higher binding energy per nucleon, therefore, more stable
  • Fusion is a process by which two very light nuclei join together to form a heavier nucleus
    • Two light nuclei fuse so the final binding energy per nucleon will be greater than the original value
  • In general, if energy is released in a nuclear reaction, then it shows that the binding energy of the product nuclei is greater than that of the reactants
Spontaneous and Random Nature
  • Radioactive processes are random and spontaneous
  • Random: Impossible to predict and each nucleus has the same probability of decaying per unit time
  • Spontaneous: Not affected by external factors such as the presence of other nuclei, temperature and pressure
  • Evidence on a graph:
    • Random: The graph will have fluctuations in count rate
    • Spontaneous: The graph has the same shape even at different temperatures, pressures ,etc.
Radioactive Decay
  • The rate of decay of a given nuclide at any time is proportional to the number (N) of nuclei present at that time
    • dN/dt = -λN
  • The activity (A) of a radioactive sample is the rate at which nuclei decay or disintegrate
  • the decay constant (λ) is the probability that an individual nucleus will decay per unit time interval
    • A = λN
  • The above relationship can also be written as:
    • x = x0e-λt
      • where x could represent activity, number of undecayed nuclei or received count
Exponential Nature

  • The activity of a radioactive substance represents an exponential decay
  • The half-life (t½) of a radioactive substance is the mean time taken for half of the active nuclei in a sample to decay
    • Assuming the initial activity is 1, at half-life, the activity would be ½, so:
      • ½ = (1)e-λt
      • Take ln of both sides: ln(½) = -λt½
      • Calculate and rearrange: λ = 0.693/t½
  • Thus, decay constant is inversely proportional to its half-life
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