Step into the atom's heart. Scroll down and the live panel on the right brings each idea to life — protons and neutrons packing the nucleus, radiation racing through paper, aluminium and lead, half-lives ticking away, and the very furnace of the Sun lit by E = mc².
1 — The nucleus: Z, A & isotopes
Almost all of an atom is empty space. At its centre is the nucleus — a dense cluster of protons (positive) and neutrons (neutral), together called nucleons. The electrons swarm far outside.
- Atomic number Z — the number of protons; it fixes which element you have.
- Mass number A — the number of nucleons, so A = Z + N (N = neutrons).
- Isotopes — same Z, different N (and A): carbon-12 and carbon-14 are both carbon, but ¹⁴C has two extra neutrons.
Nuclide notationZAX · e.g. 612C has 6 protons, 6 neutrons
isotopes of carbon: 612C · 613C · 614C
Exam point: Z names the element; isotopes share chemistry but differ in mass and nuclear stability.
2 — Nuclear size & density
The atom is about 10⁻¹⁰ m across; the nucleus only about 10⁻¹⁴ m — ten thousand times smaller. Yet over 99.9% of the atom's mass is crammed into that speck.
Nuclear radiusR = R₀ A^(1/3), R₀ ≈ 1.2 × 10⁻¹⁵ m (1.2 fm)
density ρ ≈ 2.3 × 10¹⁷ kg/m³ — the same for every nucleus
- Unimaginably dense — a single matchbox of nuclear matter would weigh billions of tonnes.
- Constant density — bigger nuclei just hold more nucleons at the same packing, so ρ stays fixed.
Picture it: if the atom were a cricket stadium, the nucleus would be a grain of rice on the centre spot — but a grain heavier than the whole stadium.
3 — Radioactivity: α, β, γ
An unstable nucleus sheds energy as radiation. There are three kinds, and they differ enormously in mass, charge and how far they punch through matter.
- Alpha (α) — a helium nucleus (24He), +2 charge, heavy and slow. Stopped by a sheet of paper.
- Beta (β) — a fast electron from the nucleus, −1 charge, light. Stopped by a few mm of aluminium.
- Gamma (γ) — a high-energy photon, no charge, no mass. Only thick lead or concrete cuts it down.
| Ray | What it is | Charge | Stopped by |
|---|
| α | He nucleus | +2 | paper |
| β | electron | −1 | aluminium |
| γ | photon | 0 | lead |
Ionising power is the reverse: α ionises most (most dangerous if swallowed); γ least but reaches furthest.
4 — Decay equations & transmutation
When a nucleus decays it becomes a different element — true transmutation. The trick to every equation is that the totals of A (top) and Z (bottom) must balance on both sides.
Alpha decay (A −4, Z −2)92238U → 90234Th + 24He
Beta-minus decay (A same, Z +1)614C → 714N + −10e
inside: a neutron → proton + electron
worked — balancing
What is X in 88226Ra → X + 24He?
A: 226 − 4 = 222 · Z: 88 − 2 = 86 → X = 86222Rn (radon)
Gamma emission carries off only energy — A and Z are unchanged; the nucleus simply drops to a lower energy state.
5 — Half-life & exponential decay
You cannot predict which nucleus decays next — it is pure chance, like popcorn kernels popping at random. But for a huge number, a steady fraction decays each second. The half-life T½ is the time for half the sample to decay.
Exponential decayN = N₀ (½)^(t / T½) · after n half-lives, fraction left = (½)ⁿ
activity A = λN (λ = decay constant), A in becquerels (Bq)
- After 1 T½ — ½ remains; after 2 T½ — ¼; after 3 T½ — ⅛.
- Random but reliable — one nucleus is unpredictable; a billion together obey a smooth curve.
worked — three half-lives
T½ = 5 years. Fraction left after 15 years?
15 / 5 = 3 half-lives → (½)³ = ⅛ = 12.5%
6 — Mass defect & binding energy
Strange but true: a nucleus weighs less than the protons and neutrons that make it. That missing mass, the mass defect Δm, was converted into the energy that glues the nucleus together — the binding energy.
Einstein's mass–energyE = Δm c² · c = 3 × 10⁸ m/s
1 atomic mass unit (u) = 931.5 MeV of energy
- Mass defect Δm — (mass of separate nucleons) − (mass of the nucleus).
- Binding energy — the energy you must supply to pull the nucleus completely apart.
worked — helium-4
Δm = 0.0304 u for ⁴He. Binding energy?
E = 0.0304 × 931.5 = ≈ 28.3 MeV
7 — B.E. per nucleon: fission & fusion
The most useful quantity is binding energy per nucleon — how tightly each nucleon is held. Plot it against mass number and the curve rises steeply, peaks near iron-56 (the most stable nucleus), then slowly falls.
The key ideamoving toward the iron peak = nucleons more tightly bound = energy released
light nuclei → fuse (climb left side) · heavy nuclei → split (climb right side)
- Fusion — joining light nuclei (H → He) climbs the steep left side: huge energy per kilogram.
- Fission — splitting heavy nuclei (U → fragments) climbs the gentle right side toward iron.
Why both work: iron-56 sits at the bottom of the energy valley. Everything "wants" to roll toward it — so both fusion of the light and fission of the heavy give out energy.
8 — Fission (reactors) & fusion (the Sun)
- Nuclear fission — a slow neutron splits a ²³⁵U nucleus into two fragments plus 2–3 fast neutrons. Those neutrons split more nuclei: a chain reaction, controlled in a reactor by moderators and control rods.
- Nuclear fusion — light nuclei merge. In the Sun's core hydrogen fuses to helium at ~15 million K, the source of all sunlight and the fuel of the stars.
Typical reactionsfission: 01n + 92235U → 56141Ba + 3692Kr + 301n + energy
fusion: 12H + 13H → 24He + 01n + 17.6 MeV
Per kilogram, fusion beats fission and leaves far less radioactive waste — which is why the world is racing to build a working fusion reactor.
9 — Recap, uses & hazards
- Medicine — cobalt-60 γ-rays treat cancer; technetium-99m tracers image organs; iodine-131 targets the thyroid.
- Carbon dating — living things hold steady ¹⁴C; after death it decays with T½ = 5730 years, dating wood, bone and cloth.
- Energy — fission reactors generate electricity; fusion promises clean power.
- Hazards — ionising radiation damages cells; shield with distance, time and lead, and measure dose in sieverts.
- Nucleus = protons + neutrons; Z names the element, A = Z + N; isotopes share Z.
- R = R₀A^⅓; the nucleus is tiny but holds nearly all the mass — fixed huge density.
- α (paper), β (aluminium), γ (lead); ionising power runs α > β > γ.
- α decay: A −4, Z −2; β⁻ decay: Z +1; balance A and Z every time.
- N = N₀(½)^(t/T½) — each half-life halves what's left.
- Δm → binding energy by E = Δm c²; 1 u = 931.5 MeV.
- B.E./nucleon peaks at iron-56 → fusion (light) and fission (heavy) both release energy.