Inside the nucleus
An atom is mostly empty space. Almost all its mass sits in a tiny centre, the nucleus, about 10⁻¹⁵ m across (100 000 times smaller than the atom).
The nucleus has protons (charge +1, mass about 1 u) and neutrons (no charge, mass about 1 u). Together they are called nucleons.
- Atomic (proton) number Z = number of protons. It decides the element.
- Mass (nucleon) number A = protons + neutrons. Neutrons N = A − Z.
- Notation: ᴬ_Z X, e.g. ¹⁴₆C has 6 protons and 8 neutrons.
Protons repel each other. They are held together by the strong nuclear force, which is very strong but acts only over about 3 × 10⁻¹⁵ m.
Isotopes
Isotopes are atoms of the same element (same Z) with different numbers of neutrons (different A). They react the same way chemically but have different masses, and some are unstable. Examples: hydrogen-1, deuterium (²H), tritium (³H); carbon-12 (stable) and carbon-14 (radioactive); uranium-235 and uranium-238.
Radioactive decay: alpha, beta, gamma
An unstable nucleus gives out radiation to become more stable. This is radioactive decay. It is random (we cannot predict when one nucleus decays) and spontaneous (heat or pressure do not change it).
| Type | What it is | Change | Stopped by | Ionising |
|---|---|---|---|---|
| Alpha α | ⁴₂He nucleus | A − 4, Z − 2 | paper, few cm of air | strong |
| Beta-minus β⁻ | fast electron | A same, Z + 1 | few mm aluminium | medium |
| Gamma γ | high-energy EM wave | no change in A or Z | thick lead / concrete (reduced) | weak |
Decay equations
A and Z must balance on both sides.
α: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
β⁻: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e (+ antineutrino)
β⁺ (positron) decay also exists: a proton becomes a neutron and Z falls by 1.
Background radiation comes from rocks (radon gas), cosmic rays, food and medical scans.
Half-life
The half-life is the time for half the unstable nuclei in a sample (or its activity) to decay. After n half-lives the fraction left is (½)ⁿ.
Activity is measured in becquerel (1 Bq = 1 decay per second). Half-lives range from fractions of a second to billions of years (uranium-238: 4.5 billion years; carbon-14: about 5 730 years; iodine-131: 8 days).
Particles and nuclear energy
Protons and neutrons are made of smaller particles called quarks (proton = up, up, down; neutron = up, down, down). Electrons and neutrinos are leptons. Every particle has an antiparticle with the same mass but opposite charge (the positron is the anti-electron).
In beta-minus decay a down quark changes to an up quark, so a neutron becomes a proton.
Big nuclei can split (fission) and small nuclei can join (fusion); both release huge energy because a little mass turns into energy (E = mc²). See the next lesson for details.
Safety and uses
Radiation can damage cells and DNA. Keep distance, reduce time and use shielding. Uses: medical imaging and therapy, sterilising, dating, smoke detectors, thickness gauges and power.
Try it
Toss 32 coins; remove all "heads". Repeat and count. The number halves each throw, just like nuclei per half-life.
Key formulas and definitions
- A = Z + N
- Alpha: ᴬ_Z X → ᴬ⁻⁴_{Z−2}Y + ⁴₂He
- Beta-minus: ᴬ_Z X → ᴬ_{Z+1}Y + ⁰₋₁e
- Gamma: no change in A or Z
- Fraction left after n half-lives = (½)ⁿ
- Activity in becquerel: 1 Bq = 1 decay per second
- Proton = uud, neutron = udd
Worked examples
1. How many protons, neutrons and nucleons are in ²³⁵₉₂U?
Protons Z = 92. Nucleons A = 235. Neutrons N = 235 − 92 = 143.
2. Radium-226 (Z = 88) gives off an alpha particle. What is formed?
A = 226 − 4 = 222, Z = 88 − 2 = 86. Z = 86 is radon: ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He.
3. Strontium-90 (Z = 38) is a beta-minus emitter. Write the product.
A stays 90, Z = 38 + 1 = 39 (yttrium): ⁹⁰₃₈Sr → ⁹⁰₃₉Y + ⁰₋₁e.
4. A sample has activity 800 Bq and half-life 3 hours. What is its activity after 12 hours?
12 ÷ 3 = 4 half-lives. 800 → 400 → 200 → 100 → 50 Bq.
5. A wooden tool has ¼ of the carbon-14 of living wood. Half-life = 5 730 years. How old is it?
¼ = (½)², so 2 half-lives = 2 × 5 730 = 11 460 years.
6. U-238 decays to Pb-206 (Z: 92 → 82) through α and β⁻ steps. How many alpha and beta decays?
A falls 238 − 206 = 32, and only alpha changes A: 32 ÷ 4 = 8 alphas. 8 alphas lower Z by 16 (to 76), but Z ends at 82, so 82 − 76 = 6 beta-minus decays.
Common mistakes
- Thinking the mass number changes in beta decay. In β⁻ decay A stays the same; only Z rises by 1.
- Saying after two half-lives nothing is left. It is ¼, not 0.
- Believing isotopes are different elements. Same Z means same element.
- Thinking gamma is a particle with mass that changes the nucleus. It is an EM wave carrying energy.