Nuclear & Particle Physics

Rutherford scattering, nuclear radius, radioactive decay, binding energy, fission, fusion, and conservation laws.

Spec Points Covered
  • I can describe Rutherford's alpha-particle scattering experiment and explain how the results led to the nuclear model.
  • I can estimate nuclear radius from closest-approach calculations using $\frac{1}{2}$mv^2 = $\frac{Qq}{4\pi\epsilon_0 r}$.
  • I can use the empirical relationship r = r_0 $A^{1/3}$ to calculate nuclear radius.
  • I can explain how electron diffraction provides evidence for nuclear radius and use $R \approx$$\frac{0.61\lambda}{\sin\theta}$.
  • I can explain what is meant by the strong nuclear force and describe its key properties.
  • I can define mass defectThe difference between the total mass of the individual nucleons and the actual mass of the nucleus. This mass is converted to binding energyThe capacity to do work. Measured in joules (J).. and binding energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). required to completely separate a nucleus into its individual protons and neutrons. Equal to the mass defectThe difference between the total mass of the individual nucleons and the actual mass of the nucleus. This mass is converted to binding energy. multiplied by c²., and calculate them from atomic mass data.
  • I can use $E = mc^2$ to convert between mass and energy units.
  • I can interpret a binding energy per nucleonThe binding energyThe energy required to completely separate a nucleus into its individual protons and neutrons. Equal to the mass defectThe difference between the total mass of the individual nucleons and the actual mass of the nucleus. This mass is converted to binding energy. multiplied by c². of a nucleus divided by its nucleon number (mass number). Higher values indicate greater nuclear stability. curve and use it to explain fission and fusion.
  • I can describe the processes of nuclear fissionThe splitting of a heavy nucleus into two smaller nuclei of roughly equal mass, releasing energy and neutrons. and fusion and explain the energy release in each.
  • I can use the radioactive decayThe spontaneous and random disintegration of an unstable nucleus, emitting radiation (alpha, beta, or gamma) to become more stable. equation N = N_0 $e^{-\lambda t}$and relate decay constantThe probability of decay of a nucleus per unit time. Measured in s⁻¹. to half-lifeThe time taken for half the number of radioactive nuclei in a sample to decay, or for the activityThe number of nuclear decays per unit time. Measured in becquerels (Bq), where 1 Bq = 1 decay per second. to halve..
  • I can define activityThe number of nuclear decays per unit time. Measured in becquerels (Bq), where 1 Bq = 1 decay per second. and use A = $\lambda$N.
  • I can apply conservation of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C)., baryon numberA quantum number conserved in all interactions. Baryons (protons, neutrons) have baryon number +1, antibaryons have -1, and mesons/leptons have 0., and lepton numberA quantum number conserved in all interactions. Leptons (electrons, neutrinos) have lepton number +1, antileptons have -1, and hadrons have 0. to nuclear reactions.
Notes
01 Geiger and Marsden fired alpha particles at thin gold foil and observed the scattering pattern → 02 The nuclear radius can be estimated from the closest approach of an alpha particle: at the $r = r_0 A^{1/3}$ → 03 Mass defect (Δm) Mass defect (Δm) → 04 The graph of binding energy per nucleon against nucleon number (A) rises steeply for light → 05 Radioactive decay Radioactive decay → 06 Alpha (α) → 07 Nuclear fission Nuclear fission → 08 In every nuclear reaction → 09 Binding energy → 10 Radioactive decay →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
$$r = r_0 A^{1/3}$$
$$E = \Delta m \cdot c^2$$
$$N = N_0 e^{-\lambda t}$$
$$t_{1/2} = \frac{\ln 2}{\lambda}$$
$$A = \lambda N$$
$$\frac{1}{2}mv^2 = \frac{Qq}{4\pi\epsilon_0 r}$$