Nuclear physics flashcards

3.8.1 Radioactivity

Rutherford scattering: observations and conclusions

Most α pass straight through → the atom is mostly empty space. Some deflect through large angles → a small, concentrated positive charge. Very few rebound → the nucleus holds most of the mass.

α, β⁻ and γ: ionising ability and what stops them

α: strongly ionising, a few cm in air, stopped by paper. β⁻: less ionising, about a metre in air, stopped by a few mm of aluminium. γ: weakly ionising, reduced by thick lead; obeys I = k/x² in air.

Required practical 12: testing the inverse-square law for γ

Measure background first and subtract it. Record count rates at several distances d. A graph of 1/√C against d is a straight line if I ∝ 1/x².

Decay constant λ, activity, and half-life

λ is the probability of a nucleus decaying per unit time. Activity A = λN (Bq, with λ in s⁻¹). N = N₀e^(−λt). T½ = ln 2/λ.

Graph of ln A against t for a radioactive sample

ln A = ln A₀ − λt: a straight line with gradient −λ and intercept ln A₀.

Which decay for an unstable nucleus with too many neutrons, too many protons, or very heavy?

Too many neutrons (above the stability line): β⁻. Too many protons: β⁺ or electron capture. Very heavy: α.

Nuclear radius equation, and the radius for A = 64 with R₀ = 1.2 fm

R = R₀A^(1/3). R = 1.2 × 64^(1/3) = 1.2 × 4 = 4.8 fm.

Why is nuclear density roughly constant?

Volume ∝ R³ ∝ A and mass ∝ A, so density is the same for all nuclei, about 10¹⁷ kg m⁻³.

Why does α closest approach give only an estimate of nuclear radius?

It overestimates R (the α never touches the nucleus), and the α can be affected by the strong force near the nucleus. Electron diffraction is better: electrons feel no strong force.

Atomic mass unit

1 u is one-twelfth of the mass of a carbon-12 atom (1.661 × 10⁻²⁷ kg); 1 u = 931.5 MeV.

Binding energy and mass difference

Binding energy: the energy needed to separate the nucleus into its nucleons. Mass difference: mass of the separate nucleons minus mass of the nucleus.

Binding energy per nucleon curve: where is the peak, and why do fission and fusion release energy?

The peak is near A ≈ 56 (about 8.8 MeV). Fusion of light nuclei and fission of heavy nuclei both increase the binding energy per nucleon, so both release energy.

Moderator vs control rods in a thermal reactor

Moderator (water, graphite): slows neutrons by elastic collisions. Control rods (boron, cadmium): absorb neutrons, to keep one further fission per fission.

Critical mass

The minimum mass of fuel for a self-sustaining chain reaction.