Atomic Nuclei & Isotopes

What an Atomic Nucleus Is Made Of

Almost the entire mass of an atom — more than 99.9% — is packed into its nucleus, even though the nucleus occupies only about a ten-trillionth of the atom's total volume. The nucleus consists of two kinds of nucleons: positively charged protons and electrically neutral neutrons. Both have almost identical mass (around 1.67 · 10⁻²⁷ kg) and are themselves each built from three quarks.

The number of protons — the atomic number Z — determines which chemical element it is: any atom with exactly 6 protons is carbon, any with 79 protons is gold. Change the proton count and you change the element. The neutron number N, however, can vary for the same element — and that variation is exactly what gives rise to isotopes.

Protons repel each other electromagnetically — neutrons add extra strong attraction without contributing any charge of their own. That's why heavier nuclei need disproportionately more neutrons than protons to stay stable.

What Makes an Isotope

Isotopes are atoms of the same element — meaning they share the same proton number Z — that differ in their neutron number N. Because the neutron count has almost no effect on chemical behavior (which is determined almost entirely by the electrons), isotopes of an element behave nearly identically in chemical terms. Their nuclei, however, can differ fundamentally: some remain stable for eternity, others decay within seconds.

The notation mass number A (the sum of protons and neutrons, written as a left superscript) and atomic number Z (written as a left subscript) in front of the element symbol uniquely identifies a nuclide. Carbon occurs naturally in three isotopes:

The Valley of Stability

If you plot the neutron number N against the proton number Z for every known nuclide, a narrow band of stable nuclei emerges — the valley of stability. For light elements, the optimum lies close to N = Z (equal numbers of protons and neutrons). As the proton number grows, the band increasingly shifts toward a neutron surplus, because additional neutrons are needed to offset the growing Coulomb repulsion among an ever-larger number of protons — without themselves adding to that repulsion.

Nuclei outside this valley are unstable and decay in ways that move them closer to it: a neutron surplus is usually corrected by β⁻ decay (a neutron turns into a proton), a proton surplus by β⁺ decay or electron capture. Very heavy nuclei beyond lead often eject entire helium nuclei — alpha decay. The exact decay modes and their kinematics are explored in more depth on the particle physics page on radioactive decays.

Binding Energy per Nucleon

The mass of an atomic nucleus is always smaller than the sum of the masses of its individual nucleons — the difference is called the mass defect and, by Einstein's E = mc², corresponds exactly to the energy that would be released in assembling the nucleus: the binding energy. Dividing this by the number of nucleons gives the binding energy per nucleon — a direct measure of how tightly a nucleus holds together.

Plotting this value against the mass number A produces a curve with a maximum in the region of iron-56 and nickel-62 — the most tightly bound nuclei in the entire periodic table. (The exact peak actually belongs to nickel-62, by a razor-thin margin over iron-56; but since iron-56 is by far the more common nuclide in this region and gives the peak its familiar name, it serves here as the reference point.) This explains why both the fission of heavy elements and the fusion of light elements release energy: both processes move along the curve toward this maximum.

Why Iron, of All Elements?

The reason for this particular maximum lies in a competition between two forces with very different ranges. The strong nuclear force is extremely short-ranged — each nucleon only "feels" its immediate neighbors, no matter how large the nucleus as a whole is. As the nucleon count grows, this contribution to the binding energy per nucleon therefore cannot keep rising indefinitely — it saturates. The electric repulsion between protons (the Coulomb force), by contrast, acts across the entire nucleus and grows ever faster with the proton number, since every proton repels every other proton in the nucleus. Up to about mass number 56, the gain from additional nucleon bonds outweighs the still-moderate Coulomb repulsion — each additional nucleon makes the nucleus, on average, more tightly bound. Beyond iron, the balance tips: additional protons contribute more repulsive than attractive energy, and the curve turns back down. Iron-56, nickel-62, and cobalt-59 sit almost exactly at the point where the saturation of the nuclear force and the growth of Coulomb repulsion balance each other out — somewhere within this narrow group lies the maximum binding energy per nucleon in the entire periodic table (precise measurements place it minutely at nickel-62, not at iron-56 itself).

What Isotopes Are Used for in Practice

Because isotopes behave almost identically in chemical terms but are physically distinguishable — whether by mass or by radioactivity — they can be used as markers in processes that would otherwise be impossible to observe.