AP Physics 2 · Unit 15 · Topic 5 of 5 · 6 min lesson

Nuclear Physics

A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.

Quiz this topic · 5 questions

The big idea

Unstable nuclei decay on their own, emitting alpha particles, beta particles or gamma rays. In every nuclear reaction, the mass number A and charge (atomic number Z) are conserved. Each isotope has a half-life, and missing mass becomes energy: E = Δmc².

1. Types of decay

Alpha (⁴₂He)A − 4, Z − 2

Beta-minus (e⁻)neutron → proton: A same, Z + 1

Beta-plus (e⁺)proton → neutron: A same, Z − 1

Gamma (photon)A and Z unchanged; nucleus loses energy

CheckA and Z add up on both sides

Notation: ^A_ZX. A counts protons + neutrons; Z counts protons and decides the element.

Example: ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He. Top: 226 = 222 + 4. Bottom: 88 = 86 + 2.

Beta: ¹⁴₆C → ¹⁴₇N + e⁻ (+ an antineutrino).

2. Half-life and mass-energy

After each half-life, half the remaining nuclei are left. Which particular nucleus decays next is random.

After n half-livesN = N₀(½)ⁿ

Half-lifesame no matter how much is left

E = Δmc²mass defect becomes energy

1 u ↔ 931 MeVshortcut for Δm in atomic mass units

3. Example, then try it

Example

In a nuclear reaction, the products have 0.0050 u less mass than the reactants. How much energy is released?

E = (0.0050 u)(931 MeV/u) ≈ 4.7 MeV, millions of times more than a chemical reaction releases per atom.

Try it · work it on paper first

Iodine-131 has a half-life of 8.0 days. A sample starts with 1600 undecayed nuclei. How many remain after 24 days? How long until only 50 remain?

24 days: 24 ÷ 8.0 = 3 half-lives: 1600 → 800 → 400 → 200.

Fraction left: (½)³ = 1/8.

Down to 50: 1600 ÷ 50 = 32 = 2⁵, so 5 half-lives: 5 × 8.0 = 40 days.

Answer: 200 after 24 days; 50 after 40 days.

4. Common mistakes

“After two half-lives, it’s all gone.”After two half-lives, ¼ is left.

Mixing up beta decay’s effect on Z.Beta-minus raises Z by 1; the mass number stays the same.

Unbalanced equations.Check that A and Z each add up on both sides.

Check yourself

Polonium-210 (Z = 84) undergoes alpha decay. What nucleus is produced?

Alpha decay removes ⁴₂He: A goes 210 → 206 and Z goes 84 → 82, which is lead.

Ready to practice?

5 questions on Nuclear Physics, each with a hint and an explanation for every wrong answer.

Quiz this topic All of Unit 15