E: Nuclear and Atomic physics

Describe Rutherford's scattering experiment, including the three main observations and conclusions about the structure of the atom.

In Rutherford's gold‐foil experiment, most α‐particles passed through undeflected (atom is mostly empty space), some were deflected by small angles (positive charge concentrated in a tiny nucleus), and a very few bounced back (nucleus is very small, dense, and contains most mass).

Describe the structure and approximate size of an atom.

An atom has a central nucleus (~10⁻¹⁵ m radius) of protons and neutrons, surrounded by an electron cloud extending to ~10⁻¹⁰ m; electrons occupy quantized orbitals around the nucleus.

Distinguish between an atom's atomic number and mass number, and be able to use notation to distinguish between them.

Atomic number Z is the number of protons (defines element); mass number A is total protons + neutrons. Notation: ⁽ᴬ⁾₍Z₎X (e.g. ²³₁₁Na for sodium‐23).

Understand that the absorption and emission spectra for each element are unique.

Each element's electrons have specific energy level spacings, so they absorb and emit photons only at characteristic wavelengths, producing unique spectral "fingerprints."

Explain how spectral lines are evidence for the existence of discrete energy levels.

Spectral lines appear only at specific wavelengths corresponding to energy differences ΔE = h f between quantized electron levels, proving that electrons occupy discrete energy states.

Describe how emissions and absorption spectra are produced.

Emission lines arise when excited electrons drop to lower levels, emitting photons of specific energies. Absorption lines occur when ground‐state electrons absorb photons to jump to higher levels, removing those wavelengths from a continuous spectrum.

Calculate the frequency (or wavelength) of released or absorbed photons using the energy difference between energy levels in an atom.

Use ΔE = h f to find f = ΔE/h and then λ = c/f. Input known energy levels (in J or eV) and Planck's constant.

Explain how the results of Rutherford's experiment change when higher‐energy alpha particles are used.

Higher‐energy α‐particles probe closer to the nucleus before deflection, causing larger‐angle scattering and yielding more detailed information on nuclear size and charge distribution.

Describe the discrete energy levels in the Bohr model for the hydrogen atom and understand the terms of the quantisation of angular momentum.

In Bohr's hydrogen model, electrons occupy orbits with quantized angular momentum L = n h/2π, radii rₙ ∝ n², and energies Eₙ = -13.6 eV/n²; transitions produce the observed spectral lines.

Describe a photon as a packet of energy

A photon is a quantum of electromagnetic energy with E = h f and momentum p = h/λ, exhibiting both wave‐like and particle‐like behavior.

Discuss the photoelectric effect and explain why the classical theory of light means a wave cannot be explained by the photoelectric effect.

In the photoelectric effect, electrons are emitted only if light frequency exceeds a threshold, regardless of intensity. Classical waves predict that any frequency should eject electrons given enough intensity or time, contrary to observations, requiring quantized light.

Define the work function and threshold frequency.

The work function Φ is the minimum energy needed to remove an electron from a metal. The threshold frequency f₀ is the minimum light frequency such that h f₀ = Φ; no electrons are emitted for f < f₀ at any intensity.

Interpret the following graphs relating to the photoelectric effect:

Kinetic energy vs frequency: KE_max = h f - Φ, linearly rising above f₀ with slope h. Photo‐current vs intensity: current ∝ intensity for f > f₀, zero for f < f₀. Stopping potential vs frequency: V_s intercept at f₀, slope h/e.

Recognise that matter can have wave‐like properties (wave-particle duality)

de Broglie hypothesis: particles have wavelength λ = h/p, confirmed by electron diffraction and interference experiments.

Describe the experiment where electrons can be accelerated and diffracted through a thin graphite film, thus proving the wave nature of electrons.

In the Davisson-Germer experiment, electrons scattered from a nickel crystal produced diffraction patterns matching Bragg's law, confirming electrons have wave‐like wavelengths λ = h/p.

Explain how the Compton scattering of photons off electrons with increased wavelength is additional evidence of the particle nature of light.

In Compton scattering, X‐ray photons collide with electrons and emerge with longer wavelengths Δλ = (h/m_e c)(1 - cosθ), consistent with photon momentum transfer as discrete particles.

Describe an isotope

Isotopes are atoms of the same element (same Z) that differ in neutron number (different A), having nearly identical chemical properties but different nuclear stability.

Define the mass-energy equivalence as given by E = m c² in nuclear reactions

Mass-energy equivalence states that mass defect Δm in nuclear reactions converts to energy E = Δm c², explaining large energy releases in fission and fusion.

Recall the definition for binding energy and binding energy per nucleon

Binding energy is the energy required to separate a nucleus into its constituent nucleons; binding energy per nucleon = total BE divided by A, indicating nucleus stability.

Explain why nuclei can be unstable and how the strong force keeps nuclei together

Nuclei are unstable when electrostatic repulsion between protons overcomes the short‐range strong nuclear force; the strong force binds nucleons at distances <2 fm, dominating at very short range.

Describe radioactive decay and how it is measured

Radioactive decay is spontaneous emission of α, β, or γ radiation following N(t) = N₀ e^(-λ t). It is measured by detectors (Geiger-Müller, scintillation) counting decay events over time.

Define activity

Activity A is the decay rate, A = -dN/dt = λ N, measured in becquerels (Bq, decays per second).

Describe the properties of alpha, beta, and gamma radiation.

α: helium nuclei, heavy, +2 charge, low penetration, high ionization. β: electrons (or positrons), lighter, moderate penetration and ionization. γ: high‐energy photons, no charge, high penetration, low ionization per unit path length.

Define half‐life in radioactive decay

Half‐life t₁/₂ is time for half the radioactive nuclei to decay: t₁/₂ = ln2/λ.

Describe the origins of background radiation and understand the effect of background radiation on the count rate

Background radiation arises from cosmic rays, terrestrial isotopes (uranium, thorium), and human sources (medical, industrial). It adds a constant count rate that must be subtracted from measurements.

Describe evidence for the strong nuclear force

Existence of bound nuclei despite proton repulsion, saturation of binding energy per nucleon around iron, and nuclear scattering experiments revealing short‐range attractive forces.

Understand the role of the ratio of neutrons to protons for stability of nuclides

Stable nuclei lie near the valley of stability where N/Z ≈1 for light elements, increasing to ~1.5 for heavy elements; deviations lead to β decay to restore stability.

State that the spectrum of alpha and gamma radiations provides evidence for discrete nuclear energy levels

γ‐ray spectra show sharp lines from quantized nuclear transitions; α particles emitted at discrete energies correspond to specific nuclear decays.

State the continuous spectrum of beta decay as evidence for the neutrino

The continuous energy distribution of β electrons implies missing energy carried by an undetected neutral particle (neutrino), conserving energy and momentum.

Define the decay constant

Decay constant λ is the probability per unit time a nucleus will decay, related to half‐life by λ = ln2/t₁/₂.

Describe how energy is released in spontaneous and neutron‐induced fission

In spontaneous fission, heavy nuclei split into fragments with mass defect releasing E = Δm c². In neutron‐induced fission, absorption of a neutron triggers splitting into two fragments plus neutrons, releasing ~200 MeV per event.

Describe the role of chain reactions in nuclear fission reactions

In fission, released neutrons cause further fissions if the reproduction factor k ≥1, sustaining a self‐amplifying chain reaction in reactors or bombs.

Explain the role of control rods, moderators, heat exchangers, and shielding in a nuclear power plant

Control rods absorb excess neutrons to regulate the reaction; moderators (water, graphite) slow neutrons to thermal energies; heat exchangers transfer reactor heat to turbines; shielding (lead, concrete) protects against radiation.

Describe the properties of the products of nuclear fission and their management, including the impact of long‐term storage

Fission products are radioactive isotopes with varied half‐lives emitting β and γ. They require cooling, shielding, and isolation in secure dry casks or geological repositories to protect environment and health.

Describe fusion as the source of energy in stars, the conditions required for fusion to occur, and the basic fusion reactions present in stars on the main‐sequence

Stars fuse hydrogen into helium via proton-proton chain or CNO cycle at T ≥10⁷ K and high pressures; mass defect Δm yields energy E = Δm c² sustaining stellar luminosity.

Describe the equilibrium between radiation pressure and gravity in stars—how the star then achieves stellar equilibrium

Hydrostatic equilibrium is maintained when outward radiation/gas pressure from fusion balances inward gravitational pressure, keeping the star stable over its main‐sequence lifetime.

Sketch and interpret HR diagrams, including the location of main sequence stars, red giants, supergiants, white dwarfs, the instability strip, and lines of constant radius

The HR diagram plots luminosity vs. surface temperature: main sequence runs from hot‐bright to cool‐dim; red giants/supergiants lie above right; white dwarfs below left; instability strip crosses mid‐regions; constant radius lines slope diagonally.

Define the parsec

Parsec (pc) is distance at which 1 AU subtends 1 arcsecond; 1 pc = 3.09×10¹⁶ m ≈3.26 ly.

Arcsecond

A unit of angular measure equal to 1/3600 of a degree.

Parsec

The distance at which a star's parallax is one arcsecond, used to measure astronomical distances.

Describe the method to determine the distance to stars using parallax. Understand the limitations of this method as the distance increases.

Stellar parallax measures apparent shift p (in arcseconds) over Earth's orbit; distance d (in parsecs) = 1/p. At large distances p becomes too small to measure accurately, requiring other distance indicators.

Explain how surface temperature may be obtained from a star's spectrum, using intensity‐wavelength graphs and/or Wien's Displacement Law

Wien's law: λ_max T = 2.9×10⁻³ m·K; the peak wavelength of a star's blackbody‐like spectrum gives its surface temperature T = 2.9×10⁻³/λ_max.

Explain how the chemical composition of a star may be determined from the star's spectrum, using the absorption spectrum of light received from the star

Absorption lines at characteristic wavelengths correspond to electronic transitions of elements; by matching line patterns and strengths to laboratory spectra, elemental abundances in stellar atmospheres are determined.