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 (Engineering) · Physics · Modern and nuclear physics. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.
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
Practice questions
Try each one, then open the answer.
1. In the fusion reaction 2H + 3H → 4He + X, the particle X is
- Aa proton
- Ban α-particle
- Can electron
- Da neutron
Show answer
Answer: D. Mass numbers: 2 + 3 = 4 + 1; charge numbers: 1 + 1 = 2 + 0. So X has A = 1 and Z = 0: a neutron. This deuterium–tritium fusion releases about 17.6 MeV.
2. Energy is released both when a heavy nucleus splits (fission) and when light nuclei join (fusion), because in each case
- Athe total number of nucleons decreases
- Bthe products have a greater binding energy per nucleon
- Cthe products have a smaller binding energy per nucleon
- Dneutrons are turned completely into energy
Show answer
Answer: B. Binding energy per nucleon is greatest near iron-56. Splitting heavy nuclei or fusing light ones moves towards this peak, so the products are more tightly bound; the mass lost is released as energy. The number of nucleons does not change.
3. A radioactive nuclide has a half-life of 693 s. Its decay constant is
- A1.4 × 10−3 s−1
- B1.0 × 103 s−1
- C1.0 × 10−3 s−1
- D4.8 × 102 s−1
Show answer
Answer: C. λ = 0.693/T½ = 0.693/693 = 1.0 × 10−3 s−1. 1.4 × 10−3 s−1 is 1/T½, which leaves out the 0.693 (ln 2).
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