Definition
Rutherford's alpha-particle scattering experiment fired alpha particles at thin gold foil. Most passed straight through, but a small fraction deflected at large angles, and a very few bounced almost straight back — revealing that an atom's mass and positive charge are concentrated in a tiny, dense central nucleus, with the rest of the atom being mostly empty space occupied by orbiting electrons.
The nucleus contains protons (positive charge) and neutrons (no charge), together called nucleons. Its two main characteristics are its charge (from the protons) and its mass (from protons and neutrons together, since electrons contribute negligible mass).
Atomic number () number of protons, which determines the element's identity and chemical properties, since chemical behaviour depends on the arrangement of electrons, which in a neutral atom equals the number of protons.
Isotopes are atoms of the same element (same number of protons, so same chemical properties) with different numbers of neutrons — this different neutron count changes the atom's mass and nuclear stability without changing how it bonds chemically, which is why isotopes share chemical behaviour but differ in physical properties like mass and radioactivity.
Remember
Even though an atom is mostly empty space, solid objects still feel solid and we don't fall through walls because the electrons in our atoms and in the wall's atoms strongly repel each other (like charges) as they get close, well before the nuclei themselves could ever meet — it's electric repulsion between electron clouds, not the atoms 'touching', that keeps solid matter apart.
Example 1 — protons and neutrons in a nuclide
Find the number of protons and neutrons in .
- The subscript () is the atomic number = number of protons.
- The superscript () is the mass number = protons + neutrons.
- Neutrons .
Answer: protons, neutrons
Definition
Radioactive decay is the process by which an unstable nucleus emits radiation and transforms into a more stable nucleus.
Alpha radiation: positively charged, consisting of protons and neutrons (a helium nucleus) — the heaviest and most strongly charged of the three, so it's stopped by just a sheet of paper or a few cm of air, but is the most damaging if it does get inside the body.
Beta radiation: a fast-moving electron emitted from the nucleus (when a neutron converts to a proton) — lighter and more penetrating than alpha, stopped by a few mm of aluminium.
Gamma radiation: high-energy electromagnetic radiation, carrying no mass and no charge, so it changes neither the proton nor neutron count of the nucleus — yet it's still dangerous because, as pure high-energy radiation, it penetrates deep into the body and can ionize (damage) cells and DNA along its entire path, unlike alpha and beta which mostly do their damage very locally.
Example 2 — writing an alpha decay equation
Americium-241 () undergoes alpha decay. Write the equation and name the resulting nucleus.
- Alpha decay releases a particle, reducing mass number by and atomic number by .
- New mass number ; new atomic number .
- Atomic number is neptunium (Np).
Answer: — the resulting nucleus is neptunium-237
Definition
Half-life is the time taken for half of a radioactive sample's nuclei to decay — a fixed, constant property of a given isotope, unaffected by temperature, pressure, or chemical state.
Remember
Scientists can estimate the half-life of a newly discovered radioactive element without waiting thousands of years by measuring its activity (decay rate, e.g. decays detected per second) right now and tracking how that rate falls over a short, practical observation period — since the decay follows a predictable exponential pattern, even a small, short-term drop in activity is enough to calculate the full half-life mathematically.
Example 3 — mass remaining after several half-lives
A g sample has a half-life of years. How much remains after years?
- Number of half-lives .
- Remaining fraction .
- Remaining mass .
Answer: g
Example 4 — finding half-life from a fraction remaining
A substance has a half-life of months. In how much time will one-eighth remain?
- , so half-lives have passed.
- Time .
Answer: months
Example 5 — finding half-life from time and fraction
In days, one-eighth of a polonium sample remains. Find its half-life.
- , so half-lives days.
- Half-life .
Answer: days
Example 6 — half-life from a decayed fraction
Three-fourths of a sample decays in one hour. Find the half-life in minutes.
- If has decayed, remains.
- , so half-lives have passed in minutes.
- Half-life .
Answer: minutes
Definition
Carbon dating estimates the age of once-living material using carbon-14, a radioactive isotope formed continuously in the atmosphere and taken up by living organisms at a roughly constant ratio to ordinary carbon-12. Once an organism dies, it stops absorbing new carbon-14, and the carbon-14 already present decays at its known half-life ( years) — comparing the remaining carbon-14 to the original expected amount gives the time since death.
Remember
If carbon-14 stopped forming in the atmosphere today, future carbon dating of anything that died after that point would become unreliable, since the technique depends on knowing the constant starting ratio of carbon-14 to carbon-12 at the time of death — without ongoing formation, that assumed starting ratio would no longer hold true for newer samples.
Example 7 — age of a fossil from carbon-14
A fossil has of the carbon-14 of a living sample. Find its age (half-life of carbon-14 years).
- , so half-lives have passed.
- Age .
Answer: years
Definition
Nuclear fission: a heavy nucleus splits into two lighter nuclei (usually after absorbing a neutron), releasing a large amount of energy — the process used in nuclear power stations.
Nuclear fusion: two light nuclei combine to form a heavier nucleus, releasing energy — e.g. hydrogen nuclei fusing into helium. This is the primary energy source of the Sun and other stars, where immense gravitational pressure and temperature force nuclei together despite their mutual electrical repulsion.
Key difference: fission splits heavy nuclei, fusion joins light nuclei; both release energy because the resulting nuclei have slightly less total mass than the starting material, with that missing mass converted into energy.
( m/s) — explains that mass and energy are equivalent and interconvertible; even a tiny amount of mass converts into an enormous amount of energy, since is such a huge number.
Example 8 — energy from mass conversion
In a nuclear reaction, of mass converts into energy. Find the energy released.
- kg.
- .
Answer: J
Definition
Practical applications of nuclear radiation include medical diagnosis and cancer treatment (radiotherapy), sterilizing medical equipment, carbon dating, and power generation via nuclear fission.
Ionizing radiation can damage biological tissue by knocking electrons out of the molecules that make up cells (including DNA), which can kill cells outright or cause mutations — this is why radiation exposure needs to be carefully controlled and shielded against, even for radiation types (like gamma) that don't leave any residue behind.
Quick Recap
- ●Rutherford's experiment: mass and positive charge concentrated in a tiny nucleus, atom mostly empty space
- ●Atomic number = protons; isotopes = same protons, different neutrons (same chemistry, different physical properties)
- ●Alpha (, weak penetration), beta (electron, medium), gamma (EM wave, no mass/charge, most penetrating)
- ●Half-life: constant time for half a sample to decay; remaining fraction for half-lives
- ●Carbon dating: compares remaining C-14 to expected starting ratio, using C-14's known half-life
- ●Fission: heavy nucleus splits. Fusion: light nuclei combine (powers the Sun). Both release energy via
