A radioactive sample has a half-life of 8 days and a mass of 80 g of the active nuclide. How much of the nuclide is left after 24 days?
- Number of half-lives: n = 24/8 = 3.
- Fraction left = (½)3 = 1/8.
- Mass left = 80 × 1/8 = 10 g.
Answer: 10 g
Nuclear physics
NUST NET Physics · Physics · Modern and nuclear physics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
A nucleus is written with its nucleon number A and proton number Z. In every nuclear equation both numbers balance on the two sides, which is how you identify an unknown particle or the product of a decay chain.
The mass of a nucleus is less than the total mass of its separate protons and neutrons. This mass defect, turned into energy by E = mc2, is the binding energy that holds the nucleus together. Nuclei near iron have the most binding energy per nucleon, so both fission of heavy nuclei and fusion of light nuclei release energy.
Radioactive decay is random, but a large sample halves in a fixed time called the half-life.
Rules to remember
- In any nuclear equation the total A and the total Z are the same on both sides
- α decay: A falls by 4, Z falls by 2. β− decay: A unchanged, Z rises by 1. γ emission: A and Z unchanged
- Mass defect: Δm = Z × mp + (A − Z) × mn − mnucleus
- Binding energy = Δm × c2; with Δm in u, binding energy = Δm × 931 MeV
- Half-life: fraction left after n half-lives = (½)n, with n = t/T½; decay constant λ = 0.693/T½; activity = λN
- Ionising power: α > β > γ. Penetrating power: γ > β > α
- Cloud chamber tracks: α thick, straight and short; β thin and winding; γ faint and scattered
Common mistake
Lowering Z for β− decay. A neutron turns into a proton, so Z goes up by 1 while A stays the same.
Worked example
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