Nuclear physics (A-level only)

Explanation

• Rutherford scattering changed the atomic model through linked observations and inferences. Most alpha particles crossed thin metal foil with little deflection, showing that atoms are mostly empty space.
• Some deflected through small angles because positive alpha particles were repelled by positive charge. Very few scattered through large angles or backwards, requiring a strong force concentrated in a tiny region.
• The nuclear model therefore places nearly all atomic mass and all positive charge in a nucleus far smaller than the atom.
• A diffuse positive-charge model could not provide the intense local force needed to reverse an alpha particle.
• Explanations must connect each observation to its specific inference.

Explanation

• Alpha is strongly ionising with short range and low penetration; beta has intermediate ionisation and is absorbed by thin aluminium; gamma is weakly ionising but highly penetrating and needs thick dense shielding. Absorption experiments identify radiation and support thickness control: beta suits paper or aluminium foil, while gamma can monitor steel.
• For a point gamma source, $I=k/x^2$, using source-to-detector distance and background-corrected count rate.
• Required practical 12 tests this by plotting corrected rate against $1/x^2$.
• Background originates from sources including cosmic rays and rocks and must be measured separately.
• Safe handling balances time, distance and shielding, while medical uses require a justified risk–benefit comparison.

Explanation

• Radioactive decay is random for one nucleus, but every nucleus of an isotope has the same constant probability per unit time, the decay constant $\lambda$. Hence $\Delta N/\Delta t=-\lambda N$, $N=N_0e^{-\lambda t}$ and $A=\lambda N=A_0e^{-\lambda t}$, where $1\,\text{Bq}=1\,\text{s}^{-1}$.
• Half-life satisfies $T_{1/2}=\ln2/\lambda$. It can be found from repeated halving on a decay curve or from the gradient $-\lambda$ of a $\ln A$ or $\ln N$ graph.
• Models may use dice or experimental data.
• Calculations can require molar mass and Avogadro’s constant.
• Applications include dating and radioactive-waste storage.

Explanation

• On an $N$–$Z$ graph, light stable nuclei lie near $N=Z$, while stable heavy nuclei need more neutrons than protons. A neutron-rich nucleus may undergo $\beta^-$ decay, giving $N-1$ and $Z+1$.
• A proton-rich nucleus may undergo $\beta^+$ decay or electron capture, each giving $N+1$ and $Z-1$. Alpha decay reduces $N$ and $Z$ by $2$ each.
• Nuclear excited states lose energy by gamma emission without changing $N$, $Z$ or $A$; technetium-99m is used as a gamma source in diagnosis.
• Energy-level diagrams may represent transitions.
• Nuclear equations must conserve nucleon number and charge.

Explanation

• Nuclear radii are typically of order $10^{-15}\,\text{m}$. Closest approach estimates an upper limit by equating an alpha particle’s initial kinetic energy to Coulomb electric potential energy at closest separation.
• Electron diffraction gives radius more directly: the angular intensity pattern and its minima depend on nuclear size. Experimental data support $R=R_0A^{1/3}$.
• Since spherical volume is proportional to $R^3$, nuclear volume is proportional to $A$; nuclear mass is also approximately proportional to $A$, so nuclear density is approximately constant.
• Calculations require femtometre conversion, order-of-magnitude reasoning and the Coulomb equation.
• The intensity-against-angle shape for electron diffraction should be recognised.

Explanation

• Every energy change has an equivalent mass change through $E=mc^2$. Binding energy is the energy required to separate a nucleus into free nucleons, and the mass defect between separated constituents and the nucleus represents that energy.
• For masses in atomic mass units, $1\,\text{u}=931.5\,\text{MeV}$. Average binding energy per nucleon measures nuclear stability.
• Its graph rises steeply for light nuclei, peaks near medium nucleon number and falls slowly for heavy nuclei.
• Fusion of light nuclei and fission of heavy nuclei release energy because products move towards higher binding energy per nucleon.
• Calculations should show initial mass, final mass, mass difference and a consistent unit conversion.

Explanation

• A fissile nucleus absorbs a slow thermal neutron, becomes unstable and splits, releasing energy and more neutrons. A chain reaction is critical when one neutron per fission, on average, causes another fission; critical mass is the minimum arrangement able to sustain it.
• A moderator slows fast neutrons by elastic collisions, working best with light nuclei and low neutron absorption; water or graphite can be used. Control rods such as boron or cadmium absorb neutrons and regulate reaction rate.
• Coolant removes thermal energy and needs suitable heat capacity, flow behaviour, stability and low neutron absorption.
• Material choices follow these functions.
• A mechanical collision model explains efficient neutron energy transfer to light moderator nuclei.

Explanation

• Nuclear safety combines suitable fuel containment, remote handling, shielding and emergency shutdown. Remote tools increase distance from intense sources; shielding reduces external exposure and containment limits contamination.
• Rapid insertion of neutron-absorbing rods stops the fission chain reaction, but radioactive products continue producing decay heat, so cooling remains essential.
• Waste production, remote handling and storage depend on activity and half-life: highly active waste needs shielding, secure containment and long-term management.
• Time, distance and shielding reduce exposure but do not substitute for contamination controls.
• A balanced judgement compares specific accident, waste and radiation risks with benefits such as reliable low-carbon electricity, rather than claiming either zero risk or no benefit.