Atoms and Nuclei

The One Thing

Atomic structure is explained by quantized electron energy levels surrounding a dense nucleus, while nuclear stability and reactions are governed by binding energy, radioactive decay, and mass–energy conversion.

Reactions, Processes and Experiments

Key Terms

• Thomson atomic model: An early model in which electrons are embedded in a uniform sphere of positive charge; it could not explain scattering results.
• Rutherford nuclear model: A model proposing that nearly all atomic mass and positive charge are concentrated in a very small nucleus, with electrons around it.
• Bohr model: A model in which electrons occupy permitted stationary orbits with quantized angular momentum and emit or absorb radiation only during transitions between energy levels.
• Stationary orbit: An allowed electron orbit in the Bohr model in which the electron does not continuously radiate energy.
• Quantization of angular momentum: Bohr's condition that electron angular momentum is restricted to values L = nh/(2π), where n is a positive integer.
• Energy levels: Discrete allowed energies of an electron in an atom; for hydrogen, E_n = -13.6/n² eV.
• Atomic spectrum: The characteristic set of wavelengths or frequencies emitted or absorbed by an atom when electrons change energy levels.
• Rydberg formula: The wavelength relation for hydrogen spectral lines: 1/λ = R(1/n₁² - 1/n₂²), where n₂ > n₁ and R is the Rydberg constant.
• Ionisation energy: The minimum energy required to remove an electron completely from an atom in its ground state.
• Nucleus: The central part of an atom containing protons and neutrons and carrying positive charge.
• Nucleon: A particle found in the nucleus: either a proton or a neutron.
• Atomic number: The number of protons in a nucleus, represented by Z; it identifies the element.
• Mass number: The total number of protons and neutrons, represented by A, so A = Z + N.
• Isotopes: Atoms of the same element having the same atomic number but different mass numbers because they contain different numbers of neutrons.
• Nuclear radius: The approximate radius of a nucleus, given by R = R₀A^(1/3), where R₀ is about 1.2 fm.
• Mass defect: The difference between the total mass of separate nucleons and the actual mass of the bound nucleus.
• Binding energy: The energy required to separate a nucleus completely into its individual protons and neutrons; it equals the mass defect multiplied by c².
• Binding energy per nucleon: The average binding energy of each nucleon, used to compare nuclear stability; greater values generally indicate greater stability.
• Strong nuclear force: A very strong, short-range attractive force between nucleons that helps hold the nucleus together.
• Radioactivity: The spontaneous disintegration of unstable nuclei accompanied by the emission of nuclear radiation.
• Alpha decay: A decay process in which a helium nucleus is emitted; A decreases by 4 and Z decreases by 2.
• Beta decay: A decay involving conversion between neutrons and protons, with emission of an electron or positron and a neutrino or antineutrino.
• Gamma decay: The emission of high-energy electromagnetic radiation from an excited nucleus without changing A or Z.
• Decay constant: The probability per unit time that a particular unstable nucleus will decay, represented by λ.
• Half-life: The time required for half the radioactive nuclei in a sample to decay, given by T₁/₂ = 0.693/λ.
• Mean life: The average lifetime of radioactive nuclei, given by τ = 1/λ.
• Nuclear fission: The splitting of a heavy nucleus into lighter nuclei, usually releasing energy and additional neutrons.
• Nuclear fusion: The combination of light nuclei to form a heavier nucleus, releasing energy when the products have greater binding energy per nucleon.

Easily Confused

• Thomson atomic model and Rutherford nuclear model: Thomson distributed positive charge throughout the atom, whereas Rutherford concentrated nearly all positive charge and mass in a small nucleus.
• Ground state and excited state: The ground state has n = 1, whereas an excited state has an electron in a higher permitted energy level.
• Atomic number and mass number: Atomic number Z counts protons and identifies the element; mass number A counts protons and neutrons.
• Alpha, beta and gamma radiation: Alpha particles are helium nuclei, beta particles are fast electrons or positrons, and gamma rays are uncharged electromagnetic waves.
• Alpha decay and beta decay: Alpha decay changes A by −4 and Z by −2; beta decay changes Z by one while leaving A unchanged.
• Half-life and mean life: Half-life is T₁/₂ = 0.693/λ, whereas mean life is τ = 1/λ.
• Mass defect and binding energy: Mass defect is a mass difference; binding energy is the corresponding energy obtained by multiplying the mass defect by c².
• Fission and fusion: Fission splits a heavy nucleus, whereas fusion combines light nuclei.
• Activity and decay constant: Activity is the decay rate of a sample, A_activity = λN; the decay constant λ is the probability per unit time that one particular unstable nucleus will decay.
• Ionising power and penetrating power: Alpha radiation has relatively high ionising power but low penetrating power, whereas gamma radiation has very high penetrating power.

What Gets Asked

• Explain Rutherford's gold-foil experiment: state that most alpha particles passed through while a small number were strongly deflected, and connect this to an atom that is mostly empty space with a small, dense nucleus.
• State or apply Bohr's postulates: use stationary states, L = nh/(2π), and hν = E_i - E_f; confusing continuous classical radiation with discrete transitions loses marks.
• Calculate hydrogen-like atomic quantities: apply r_n = a₀n²/Z and E_n = -13.6Z²/n² eV, identifying n = 1 as the ground state and higher n as excited states.
• Interpret nuclear notation and composition: for ^A_ZX, identify Z, A, and N = A - Z; confusing proton number with nucleon number changes the element or isotope.
• Complete nuclear decay equations: use the specific alpha, beta-minus, and beta-plus equations and conserve charge and nucleon number; beta decay must include the appropriate neutrino or antineutrino.
• Solve radioactive-decay problems: use N = N₀e^(-λt), T₁/₂ = 0.693/λ, τ = 1/λ, A_activity = λN, or N = N₀(1/2)^n; do not treat individual decay times as predictable.
• Explain fission and fusion energy release: relate both processes to movement toward greater binding energy per nucleon, while noting that fission may produce a chain reaction and fusion requires extremely high temperature and pressure.