Question bank — Fusion — solar fusion, tokamak (concept)

False — higher $B/A$ means more energy per nucleon is needed to pull it apart, so it is more tightly bound and more stable.

False — only for light nuclei below iron on the $B/A$ curve. Fusing two nuclei heavier than iron would move you down the curve and cost energy.

True in effect — the products are genuinely lighter than the reactants; that missing rest-mass reappeared as kinetic energy and radiation. Mass and energy are two accounts of one quantity.

False — $\sim 1.5\times 10^7$ K is far too cold to beat the Coulomb barrier by brute force; fusion proceeds only through quantum tunnelling through that barrier.

False — the magnetic force $q\vec{v}\times \vec{B}$ is perpendicular to $\vec{v}$, so it does zero work and cannot change speed. Heating comes from currents, RF waves, and neutral beams.

False — it needs a higher temperature (~$10^8$ K), precisely because we lack the Sun's crushing gravity to compress and confine the fuel.

False — plasma has electrons stripped off, so it is a soup of free ions and electrons; being charged, it responds strongly to magnetic and electric fields, which ordinary gas does not.

False — in the p–p chain neutrinos carry only about 2% of the ~26.7 MeV; the rest emerges as photons and kinetic energy that eventually becomes sunlight.

True — this is the unifying idea. Light nuclei fuse upward toward iron; heavy nuclei split downward toward iron. Iron is the valley you fall into from both sides.

Error: fusion joins light nuclei, it does not split anything. Only fission (of heavy nuclei) splits. They share the direction (toward iron), not the mechanism.

Error: it is $\Delta m{c}^2$, not $\Delta mc$. The squared speed of light is the huge conversion factor that turns a tiny mass into a large energy.

Error: the first step ($p+p\to {}^2\text{D}$) is extremely slow (weak-interaction bottleneck). The Sun is bright because it contains an astronomical number of protons, not because any one reaction is quick.

Error: on Earth we cannot supply the Sun's gravity, so we use magnetic confinement instead — bending field lines into a torus so charged particles spiral along them without hitting the wall.

Error: mass is not exactly conserved — the helium nucleus is lighter than four protons, and that mass defect ($\approx 26.7$ MeV worth) becomes energy.

Error: particles spiral along field lines but drift off the ends of a straight field. You must close the loop into a torus, and even then you need a twisted (helical) field to cancel vertical drifts.

Error: it is a triple product $nT{\tau }_E$. Density, temperature, and confinement time must jointly be large; being blazingly hot but too thin or too leaky still fails.

Because the [[Binding Energy per Nucleon Curve|$B/A$ curve]] rises below iron and falls above it. Combining light nuclei climbs the curve (products more tightly bound → energy out); combining heavy nuclei would descend it (energy in).

Because [[Mass-Energy Equivalence (E=mc^2)|$E=m{c}^2$]] is the exact exchange rate between mass and energy; $c^2\approx 9\times 10^{16}{\text{m}}^2/{\text{s}}^2$ is enormous, which is why a mass loss of a fraction of a u yields millions of eV.

Both nuclei are positively charged and repel via the Coulomb force. High temperature means high kinetic energy, letting nuclei approach close enough for the short-range strong force (and tunnelling) to bind them.

D–T has the largest reaction cross-section at the lowest temperature and releases 17.6 MeV, so it ignites most easily — worth the trouble even though tritium is radioactive.

A charged particle spirals along a field line (gyration). A closed loop has no ends to leak out of, so the particle circulates endlessly instead of escaping.

Because $\vec{F}=q\vec{v}\times \vec{B}$ is perpendicular to velocity and does zero work — it steers particles but never speeds them up. The energy for fusion must come from separate heating.

The rate-limiting first step of the p–p chain relies on the slow weak interaction and rare tunnelling, so the fuel burns gradually. Its self-gravity also stabilises it against runaway.

Nothing useful — iron sits at the peak of the $B/A$ curve, so any fusion or fission of it moves downhill and absorbs energy rather than releasing it.

No — the triple product $nT{\tau }_E$ would still be ~zero because $n\to 0$. A perfect but empty trap fuses nothing; all three factors must be large together.

With no $q\vec{v}\times \vec{B}$ to redirect them, the charged particles fly straight, strike the chamber wall, cool instantly, and the fusion conditions collapse — a disruption.

No — break-even ($Q=1$) merely means output equals input; useful net power (and ignition, $Q\to \infty$, where the reaction self-heats) requires exceeding it.

Effectively zero classically — with no kinetic energy they cannot approach through the Coulomb barrier at all; only finite energy plus tunnelling gives a nonzero chance.

No — neutral atoms feel no Lorentz force ($q=0$), so a magnetic field could not steer or trap them. Ionisation is exactly what makes magnetic confinement possible.

The temperature must keep enough nuclei above the tunnelling threshold to sustain reactions faster than energy leaks out. Below that, losses win, the plasma cools, and fusion quenches — which is why D–T's low ignition temperature is prized.