Points to Ponder

The density of nuclear matter is roughly constant across all nuclei — it does not depend on the mass number $A$. In contrast, the mass density of the whole atom (including the electron cloud) varies with atomic size, so it does not share this constancy.

The nuclear radius measured by electron scattering differs slightly from that measured by alpha-particle scattering. Electrons probe the charge distribution of the nucleus, while alpha particles (and similar projectiles) interact with the nuclear matter itself, so they sense a slightly different boundary.

After Einstein’s mass-energy equivalence $E = mc^2$, mass and energy are no longer conserved separately. Instead, we have a single law: conservation of mass–energy. Nuclear physics provides the strongest evidence for this principle, and it is essential for understanding nuclear energy. The $Q$-value of a nuclear process (decay or reaction) can therefore be written in terms of the initial and final masses.

The binding energy per nucleon curve shows that energy can be released (exothermic reactions) in two ways: when two very light nuclei fuse together, or when a very heavy nucleus splits (fission) into nuclei of intermediate mass.

For fusion to occur, the light nuclei must have enough initial kinetic energy to overcome the Coulomb repulsion barrier between them. This is why fusion requires extremely high temperatures.

Although the binding energy per nucleon curve is generally smooth and slowly varying, it shows distinct peaks at nuclides like $^4\text{He}$, $^{16}\text{O}$, etc. These peaks are taken as evidence of a shell-like structure inside the nucleus, analogous to atomic electron shells.

An electron and a positron form a particle–antiparticle pair. They have identical mass, and their charges are equal in magnitude but opposite in sign. When an electron and a positron meet, they annihilate each other, converting their entire mass into energy in the form of gamma-ray photons. …