Flashcards · IB Diploma Programme Physics · Topic 5

E. Nuclear and quantum physics flashcards

40 cards on Topic 5, subtopics E.1 to E.5. Pick a subtopic or study them all.

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E.1 Structure of the atom

Geiger–Marsden–Rutherford scattering: observations and conclusions: Nearly all alpha particles go straight through: mostly empty space. A few deflect through large angles; very few bounce back: a tiny, massive, positive nucleus.
Nucleon number, proton number and neutron number: A: protons + neutrons. Z: protons. N = A − Z. A neutral atom has Z electrons.
Continuous, emission and absorption spectra: Continuous: all wavelengths (hot, dense solid). Emission: bright lines (excited gas, electrons falling). Absorption: dark lines on a continuous spectrum (cool gas absorbing matching photons).
What do line spectra show about atoms?: Energy levels are discrete. A photon emitted or absorbed has energy equal to the gap between two levels: E = hf, λ = hc/ΔE.
Levels at −8.0, −3.0 and −1.0 eV. Is a 4.0 eV photon absorbed from the ground state?: No: the gaps are 5.0, 7.0 and 2.0 eV, and none equals 4.0 eV.
The electronvolt: 1 eV = 1.60 × 10⁻¹⁹ J, the energy gained by charge e moved through 1 V.
Nuclear radius and nuclear density: R = R₀A^(1/3) (R₀ ≈ 1.2 fm). The volume is proportional to A, so all nuclei have about the same density. (HL only)
Distance of closest approach of an alpha particle to a nucleus: All the kinetic energy becomes electric potential energy: Ek = k(2e)(Ze)/d, so d = 2kZe²/Ek. (HL only)
Bohr model energy levels of hydrogen, and the n = 3 to n = 2 photon: E = −13.6/n² eV (with mvr = nh/2π). 3 → 2: 13.6 × (1/4 − 1/9) = 1.89 eV, about 658 nm. (HL only)

E.2 Quantum physics (HL only)

Threshold frequency and work function: Threshold frequency f₀: the lowest frequency that releases photoelectrons from a given metal. Work function Φ: the least energy needed to free an electron at the surface. hf₀ = Φ. (HL only)
Einstein’s photoelectric equation: Emax = hf − Φ. One photon gives all its energy to one electron; Φ is used to free it and the rest is kinetic energy. (HL only)
Three photoelectric observations that wave theory cannot explain: A threshold frequency, whatever the intensity; Emax rises with frequency but not intensity; emission with no measurable delay, even in faint light. (HL only)
Graph of stopping potential against frequency: A straight line: gradient h/e, horizontal intercept f₀, vertical intercept −Φ/e. All metals give parallel lines. (HL only)
360 nm light needs a stopping potential of 0.80 V. Work function?: Photon energy = hc/λ = 5.52 × 10⁻¹⁹ J = 3.45 eV, so Φ = 3.45 − 0.80 = 2.65 eV. (HL only)
De Broglie wavelength, and the evidence for matter waves: λ = h/p. Electrons (and neutrons, atoms) diffract, and diffraction is a wave property. For an electron accelerated through V, p = √(2meV). (HL only)
Compton scattering: A photon scatters from an electron with a longer wavelength: Δλ = (h/mₑc)(1 − cos θ), h/mₑc = 2.43 × 10⁻¹² m. It shows photons carry momentum. (HL only)

E.3 Radioactive decay

Mass defect and binding energy: Mass defect: mass of the separated nucleons minus the mass of the nucleus. Binding energy: its energy equivalent, the energy needed to separate the nucleus into free nucleons. 1 u = 931.5 MeV/c².
Shape of the binding energy per nucleon curve: Rises steeply for light nuclides (high point at helium-4), broad peak near A = 56 to 62 at about 8.8 MeV per nucleon, then falls slowly to about 7.6 MeV at uranium.
Strong nuclear force: An attractive force between nucleons acting over only a few femtometres.
Alpha, beta-minus, beta-plus and gamma decay: α: He-4 nucleus, A − 4, Z − 2. β⁻: electron + antineutrino, Z + 1. β⁺: positron + neutrino, Z − 1. γ: photon, no change to A or Z.
Random and spontaneous decay: Random: which nucleus decays next, and when, cannot be predicted. Spontaneous: not triggered or changed by outside conditions such as temperature or pressure.
Activity vs count rate, and correcting for background: Activity: decays per unit time in the source (Bq). Count rate: what the detector registers. Subtract the background count rate before halving or plotting.
A source of 1280 Bq has a half-life of 20 min. Activity after 1.0 h?: 60 ÷ 20 = 3 half-lives, so 1280 ÷ 8 = 160 Bq
Radioactive decay law and the decay constant: N = N₀e^(−λt), A = λN, T½ = ln 2 / λ. λ is the probability per unit time that a nucleus decays. (HL only)
Why does the continuous beta spectrum show a neutrino exists?: Beta electrons have a range of energies up to a maximum, so a third particle (the neutrino or antineutrino) must share the energy. (HL only)

E.4 Fission

Spontaneous vs neutron-induced fission: Spontaneous: no trigger needed; rare. Neutron-induced: the nucleus (such as uranium-235) absorbs a neutron and then splits into two fragments, usually releasing two or three neutrons.
Why does fission release energy?: The fragments have a higher binding energy per nucleon than the parent, so the products have less mass. Energy released = Δm c², mostly as kinetic energy of the fragments.
U-235 + n → Xe-140 + Sr-94 + 2n loses 0.198264 u. Energy released?: 0.198264 × 931.5 = 185 MeV (2.96 × 10⁻¹¹ J)
Subcritical, critical and supercritical chain reactions: k = average number of neutrons per fission causing another fission. k < 1: dies away. k = 1: steady (a power plant). k > 1: grows.
Role of the moderator vs the control rods: Moderator: slows fast neutrons by elastic collisions so they can cause fission. Control rods: absorb neutrons to keep k = 1, or below 1 to shut down.
Role of the heat exchanger and of shielding: Heat exchanger: passes thermal energy from the radioactive primary coolant to a second circuit that makes steam. Shielding: absorbs neutrons and gamma rays from the core.
Why is there a critical mass, and why is uranium enriched?: Bigger pieces lose a smaller fraction of neutrons through the surface. Natural uranium is only about 0.7% uranium-235; enrichment raises this fraction.

E.5 Fusion and stars

Why is a main sequence star stable?: Outward pressure from hot gas and radiation balances inward gravity at every layer. If the core cools the star contracts and heats; if it heats it expands and cools.
Conditions needed for fusion in a star: High temperature, so nuclei can overcome their electric repulsion, and high density, so collisions are frequent.
Four hydrogen atoms (1.007825 u each) fuse to helium-4 (4.002603 u). Energy released?: Mass lost = 0.028697 u, so 0.028697 × 931.5 = 26.7 MeV (about 0.7% of the mass).
Hertzsprung–Russell diagram: axes and main regions: Luminosity up, temperature across (increasing to the left). Main sequence: diagonal band. Red giants: upper right. Super giants: top. White dwarfs: bottom left.
Parallax distance, with an example: d (pc) = 1 / p (arc-second). p = 0.0125″ gives 80 pc (about 261 ly). 1 pc = 3.26 ly = 3.09 × 10¹⁶ m.
Evolution of a low-mass star and of a high-mass star: Low mass: main sequence → red giant → outer layers shed → white dwarf. High mass: main sequence → super giant → supernova → neutron star or black hole.
Two stars have the same luminosity; one has half the surface temperature. Compare radii.: L = 4πσR²T⁴, so R ∝ 1/T² at fixed L: the cooler star has four times the radius.
Why does a star leave the main sequence?: Core hydrogen runs out, core fusion falls, gravity wins, the core contracts and heats, fusion continues in a shell, and the outer layers expand and cool.