Nuclear Physics

• E = mc²; energy released in a reaction E = c²Δm.
• Mass defect: the difference between the total mass of separate nucleons and the mass of the nucleus. Binding energy: energy to separate a nucleus into its nucleons.
• Binding energy per nucleon peaks near iron-56; fusion of light nuclei and fission of heavy nuclei both increase it and release energy.
• Decay is spontaneous and random; A = λN; λ = 0.693/t_½.
• x = x₀e^−λt for activity, undecayed nuclei or count rate.

E = c²Δm

Mass and energy are equivalent: E = mc². Nuclear equations balance nucleon number (top) and proton number (bottom), for example ¹⁴₇N + ⁴₂He → ¹⁷₈O + ¹₁H.

The mass defect of a nucleus is the difference between the total mass of its separate protons and neutrons and the mass of the nucleus. The binding energy is the energy needed to separate a nucleus completely into its individual nucleons; it equals c² × mass defect.

The graph of binding energy per nucleon against nucleon number rises steeply for light nuclei, peaks at about 8.8 MeV near A = 56 (iron), then falls slowly. Higher binding energy per nucleon means a more stable nucleus. Fusion is the joining of two light nuclei into a heavier one; fission is the splitting of a heavy nucleus (usually after absorbing a neutron) into two lighter nuclei and a few neutrons. Both move towards the peak, so the products have greater total binding energy, less mass, and energy is released.

A = λN

Measured count rates fluctuate around an average: evidence that decay is random (you cannot predict which nucleus will decay next, or when). It is also spontaneous: it is not affected by external conditions such as temperature or pressure.

activity ⁻¹ decay constant half-life _½

₀ ^−λt _{0 ½}