Particles and radiation

Explanation

• The simple atom contains protons and neutrons in the nucleus with electrons outside it. A proton has charge $+e$ and relative mass $1$, a neutron has zero charge and relative mass $1$, and an electron has charge $-e$ and relative mass about $1/1836$; SI masses and charges may also be required.
• In ${}^{A}_{Z}X$, $Z$ is proton number, $A$ is nucleon number and neutron number is $A-Z$.
• Isotopes share $Z$ but have different neutron numbers.
• Specific charge is net charge divided by total mass in $\text{C kg}^{-1}$.
• Examiners expect ion charge, nuclear composition and sign to be handled separately.

Explanation

• The strong nuclear force stabilises nuclei: it is attractive over separations up to about $3\,\text{fm}$ but repulsive below about $0.5\,\text{fm}$, preventing collapse. Unstable nuclei undergo alpha or beta decay.
• Alpha emission lowers nucleon number by $4$ and proton number by $2$.
• In $\beta^-$ decay a neutron becomes a proton, so $A$ is unchanged and $Z$ rises by $1$; the equation includes an electron and electron antineutrino.
• The neutrino was proposed because the continuous beta-energy distribution otherwise conflicted with energy conservation.
• Examiners expect balanced $A$ and $Z$, the correct neutrino and the strong-force range stated with femtometre scale.

Explanation

• Every particle has a corresponding antiparticle with the same mass and rest energy but opposite charge and additive quantum numbers. Required pairs include electron-positron, proton–antiproton, neutron–antineutron and neutrino–antineutrino.
• Electromagnetic radiation is modelled as photons with $E=hf=hc/\lambda$.
• Annihilation converts a particle–antiparticle pair into photons, while pair production requires at least the pair’s combined rest energy and a nearby body for momentum conservation.
• A slow electron and positron usually produce two $0.511\,\text{MeV}$ photons, relevant to PET.
• Examiners expect energy to be shared correctly, wavelength and frequency units to be consistent, and neutral antiparticles not automatically to be treated as identical.

Explanation

• The four fundamental interactions are gravitational, electromagnetic, weak and strong. Exchange particles describe force transfer between elementary particles.
• The electromagnetic interaction uses virtual photons. At this level, weak interactions include $\beta^-$ and $\beta^+$ decay, electron capture and electron-proton collisions, using $W^+$ or $W^-$ bosons; gluons, $Z^0$ and gravitons are not tested.
• Simple interaction diagrams must identify incoming and outgoing particles and the exchanged particle while conserving charge at each vertex.
• For $\beta^-$ decay, $n\rightarrow p+W^-$ followed by $W^-\rightarrow e^-+\bar{\nu}_e$.
• Examiners expect the interaction and exchange particle, not merely a named decay.

Explanation

• Hadrons experience the strong interaction. Baryons and antibaryons have baryon number $+1$ and $-1$; required examples are proton, neutron and their antiparticles.
• Mesons, including pions and kaons, have baryon number zero. The proton is the only stable baryon, the pion mediates the strong nuclear force, and kaons can decay into pions.
• Leptons do not experience the strong interaction; required families are electron, electron neutrino, muon and muon neutrino with antiparticles, and family lepton numbers are conserved separately.
• Strange particles are pair-produced by strong interactions with strangeness conserved, then decay weakly with change $0$, $+1$ or $-1$.
• Examiners expect classification plus relevant quantum numbers.

Explanation

• Only up, down and strange quarks and their antiquarks are required. Their charges are $+\tfrac23e$, $-\tfrac13e$ and $-\tfrac13e$; antiquarks have opposite charge and quantum numbers.
• Each quark has baryon number $+\tfrac13$, each antiquark $-\tfrac13$; strange quark has strangeness $-1$ and antistrange $+1$. Required baryons are $p=uud$ and $n=udd$, with corresponding three-antiquark antibaryons.
• Mesons are quark–antiquark pairs, including pions and kaons.
• Neutron beta decay changes a down quark to an up quark.
• Examiners expect charge, baryon number and strangeness to be obtained by adding the constituent values.

Explanation

• Charge, baryon number, electron-family lepton number, muon-family lepton number, energy and momentum are conserved in particle interactions. Strangeness is conserved in strong interactions but may change by $0$, $+1$ or $-1$ in weak interactions.
• In $\beta^-$ decay a down quark changes to an up quark; in $\beta^+$ decay an up quark changes to a down quark.
• A reaction satisfying charge conservation alone may still be forbidden.
• Data are supplied for particles outside the required set.
• Examiners expect initial and final totals to be tabulated for each relevant quantum number and energy–momentum feasibility to be considered rather than inferred from one successful check.

Explanation

• In the photon model, one photon transfers all its energy $hf$ to one surface electron.
• Emission occurs only when $hf\geq\phi$, where $\phi$ is work function, so threshold frequency is $f_0=\phi/h$.
• Above threshold, $E_{k,\max}=hf-\phi$ and stopping potential satisfies $eV_s=E_{k,\max}$.
• Raising frequency increases maximum kinetic energy; raising intensity at fixed frequency increases photon arrival rate and therefore emission rate, but not maximum kinetic energy.
• Examiners expect work function converted consistently between eV and J, immediate emission explained by one-photon transfer, and a negative calculated kinetic energy interpreted as no emission.

Explanation

• Excitation raises an atomic electron to a higher bound level, while ionisation removes it from the atom.
• In an inelastic collision, the incident electron must transfer an allowed discrete excitation energy or at least the ionisation energy; remaining energy stays as kinetic energy.
• An electron accelerated through potential difference $V$ gains $eV$, numerically $V\,\text{eV}$.
• In a fluorescent tube, accelerated electrons excite mercury atoms; de-excitation produces ultraviolet photons that excite the coating, whose later de-excitation emits visible light.
• Examiners expect excitation to remain bound, ionisation to produce a free electron, eV–J conversion, and collision energy to be shared without inventing a partly allowed atomic transition.

Explanation

• Atomic electrons occupy discrete energy levels. A line emission spectrum is evidence that only particular downward transitions and photon energies occur.
• For a transition from higher $E_1$ to lower $E_2$, $hf=E_1-E_2$; the positive energy gap may also be used in $\lambda=hc/\Delta E$.
• Upward absorption requires a photon whose energy exactly matches an available gap, rather than partial absorption of an intermediate energy.
• Energy levels may be quoted in joules or electronvolts.
• Examiners expect the correct initial and final levels, a positive gap converted to joules before using $h$, and each spectral line linked to one permitted transition.

Explanation

• Electron diffraction shows that matter particles possess wave properties, while the photoelectric effect shows particle-like photon transfer by electromagnetic radiation.
• The de Broglie wavelength is $\lambda=h/p=h/(mv)$ for a non-relativistic particle.
• Increasing momentum shortens wavelength and reduces diffraction for unchanged crystal spacing or aperture.
• For an electron accelerated from rest through potential $V$, energy $eV$ gives momentum $\sqrt{2meV}$ and hence $\lambda=h/\sqrt{2meV}$.
• Examiners expect momentum in $\text{kg m s}^{-1}$, voltage converted through $eV$ rather than treated as joules, and evidence to be evaluated as scientific models change through peer review and community validation.