The atomic nucleus: protons, neutrons and isotopes
Almost all of an atom's mass sits in its nucleus, a cluster of protons and neutrons about 100,000 times smaller across than the atom itself. The number of protons decides which element it is; the number of neutrons decides which isotope, and whether the nucleus is stable or radioactive.
The short version
- Protons and neutrons are together called nucleons.
- Atomic number (Z) = number of protons. Mass number (A) = protons + neutrons. Neutrons = A − Z.
- Isotopes have the same Z but different A: carbon-12, carbon-13 and carbon-14 all have 6 protons.
- The strong nuclear force holds nucleons together against the electric repulsion of the protons, but only over about 10⁻¹⁵ m.
- Unstable nuclei decay by alpha, beta or gamma emission, each at a characteristic half-life.
How small, how dense
A nucleus has a radius of roughly 10⁻¹⁵ m; a whole atom is roughly 10⁻¹⁰ m. That is a factor of about 100,000. Scale an atom up to a 100-meter sports stadium and the nucleus is about 1 millimeter across (100 m ÷ 100,000 = 0.001 m): a grain of sand at the center spot. The electrons occupy the rest of the space.
Because nearly all the mass is packed into that tiny volume, nuclear matter is extraordinarily dense: about 1.8 × 10¹⁴ grams per cubic centimeter, compared with 1 g/cm³ for water. Compressed to nuclear density, the whole Earth would be only about 200 meters in radius.
Numbers that name a nucleus
A nucleus (a nuclide) is written with the mass number at upper left and the atomic number at lower left of the symbol, for example ¹⁴₆C for carbon-14. In everyday writing it is simply "carbon-14" or "C-14", since the element name already tells you Z.
| Isotope | Z (protons) | A (mass number) | Neutrons (A − Z) | Stable? |
|---|---|---|---|---|
| Hydrogen-1 | 1 | 1 | 0 | Yes |
| Hydrogen-2 (deuterium) | 1 | 2 | 1 | Yes |
| Hydrogen-3 (tritium) | 1 | 3 | 2 | No |
| Carbon-12 | 6 | 12 | 6 | Yes |
| Carbon-13 | 6 | 13 | 7 | Yes |
| Carbon-14 | 6 | 14 | 8 | No |
Isotopes of an element behave almost identically in chemistry, because chemistry is about electrons and the electron count matches the proton count. They differ in mass and in nuclear behavior: some are radioactive, and some (like hydrogen-1 and carbon-13) have the nuclear spin that makes NMR and MRI possible.
The strong force and binding energy
Protons repel each other electrically, and at nuclear distances that push is enormous. What holds the nucleus together is the strong nuclear force, which attracts protons and neutrons to each other. It is stronger than the electric force at very short range but fades to almost nothing beyond about 10⁻¹⁵ m, which is why nuclei are so small. Neutrons add strong-force "glue" without adding repulsion, so heavier nuclei need proportionally more neutrons: light stable nuclei have about equal numbers, while lead-207 has about 1.5 neutrons per proton. Of the thousands of known nuclides, only about 250 are stable.
A nucleus weighs less than its separate parts. For helium-4, two protons and two neutrons weigh 4.0331 atomic mass units (amu) apart, but the nucleus measures 4.0026 amu. The missing 0.0305 amu, the mass defect, has become binding energy through E = mc²: about 28.4 MeV for the nucleus, or about 7.1 MeV per nucleon. That is millions of times more than the energy of a chemical bond, which is why nuclear reactions release so much energy.
Binding energy per nucleon rises from light nuclei to a peak of about 8.8 MeV near mass number 56 to 62 (iron and nickel), then slowly falls. Fusing very light nuclei, or splitting very heavy ones, moves toward that peak and releases energy.
Radioactive decay and half-life
An unstable nucleus changes toward a more stable arrangement by emitting radiation. The three classic types:
| Type | What leaves the nucleus | Change in Z | Change in A | Example | Stopped by |
|---|---|---|---|---|---|
| Alpha (α) | A helium-4 nucleus (2 protons + 2 neutrons) | −2 | −4 | Polonium-210 → lead-206 | A sheet of paper or the outer layer of skin |
| Beta minus (β⁻) | An electron (a neutron becomes a proton) | +1 | 0 | Iodine-131 → xenon-131 | Clothing or a thin layer of aluminum |
| Beta plus (β⁺) | A positron (a proton becomes a neutron) | −1 | 0 | Oxygen-15 → nitrogen-15 | Similar to β⁻; the positron soon annihilates with an electron |
| Gamma (γ) | A high-energy photon from an excited nucleus | 0 | 0 | Excited cobalt-60 → cobalt-60 | Several inches of lead or feet of concrete to reduce it greatly |
Alpha emitters are harmless outside the body but dangerous if swallowed or inhaled, because all their energy is deposited in a tiny volume of tissue. Beta decay also emits a neutrino (or antineutrino), which escapes almost without interacting.
Half-life
The half-life is the time for half of the radioactive nuclei in a sample to decay. You cannot predict when one particular nucleus will decay, but a large sample follows the rule exactly. Start with 1,000 atoms of cobalt-60 (half-life 5.27 years):
- after 5.27 years: 500 left
- after 10.54 years: 250 left
- after 15.81 years: 125 left
Half-lives range from fractions of a second to billions of years. Carbon-14 has a half-life of about 5,730 years, which is why it is used to date once-living material up to roughly tens of thousands of years old. Iodine-131, used in thyroid medicine, has a half-life of about 8 days.
Memory aid
"Z is the Zip code, A is the All-in count." The proton number (Z) tells you which element "address" you are at; the mass number (A) counts all the nucleons. Neutrons are what is left over: A − Z.
For decay, picture three visitors leaving a crowded house. Alpha is a heavy guest who takes four bags and two badges (A − 4, Z − 2) and stumbles at the first doormat (paper). Beta is a quick messenger who changes a neutron's badge into a proton's (Z + 1) without carrying any bags out (A unchanged). Gamma is just a flash of light: nothing changes but energy, and it passes through most materials.
A verse to remember it
Check yourself
Uranium-238 has Z = 92. How many neutrons does it have, and what does it become after one alpha decay?
238 − 92 = 146 neutrons. Alpha decay removes 2 protons and 2 neutrons: Z = 90, A = 234, which is thorium-234.
What is the difference between carbon-12 and carbon-14?
Both have 6 protons (so both are carbon). Carbon-12 has 6 neutrons and is stable; carbon-14 has 8 neutrons and is radioactive.
A sample starts with 80 g of a radioactive isotope with a half-life of 2 days. How much is left after 6 days?
6 days is three half-lives: 80 → 40 → 20 → 10 g.
Why do heavy stable nuclei have more neutrons than protons?
Neutrons add strong-force attraction without adding electric repulsion. As the number of protons grows, extra neutrons are needed to hold the nucleus together.