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 (t_½) 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) = -λt_½
    • Calculate and rearrange: λ = ^0.693/_t½
• Thus, decay constant is inversely proportional to its half-life