Quick summary
Nuclear chemistry deals with changes in the nucleus of an atom. This topic covers nuclear particles and forces, mass defect and binding energy, the n/p ratio and stability, radioactive decay (α, β, γ), the rate of decay and half-life, artificial transmutation, nuclear fission and fusion, and applications such as radiocarbon dating and radioisotopes in medicine and agriculture.
Key points
- The nucleus contains protons and neutrons (nucleons). Mass number A = protons + neutrons; atomic number Z = protons.
- Isotopes: same Z, different A (¹²C, ¹⁴C). Isobars: same A, different Z (⁴⁰Ar, ⁴⁰Ca). Isotones: same number of neutrons.
- Nucleons are held by the very strong, short-range nuclear force.
- Mass defect (Δm): the mass of a nucleus is less than the total mass of its separate nucleons. This missing mass appears as binding energy (E = Δmc²).
- Binding energy per nucleon is highest near iron (Fe-56, about 8.8 MeV), so medium nuclei are the most stable. Heavy nuclei gain stability by fission, light nuclei by fusion.
- n/p ratio: stable light nuclei have n/p ≈ 1; heavier stable nuclei need more neutrons (up to about 1.5). Nuclei above the stability belt emit β⁻; those below emit positrons or capture electrons.
- α decay: loses ⁴₂He → A decreases by 4, Z by 2. β⁻ decay: a neutron changes to a proton → Z increases by 1, A unchanged. γ emission: energy only, no change in A or Z.
- Group displacement law (Soddy and Fajans): α emission moves the element two places left in the periodic table; β emission moves it one place right.
- Radioactive decay is a first-order process: rate does not depend on temperature or pressure.
- Nuclear fission: a heavy nucleus (U-235) splits into two medium nuclei when hit by a slow neutron, releasing about 200 MeV and 2–3 neutrons; this can start a chain reaction (used in reactors and atom bombs).
- Nuclear fusion: light nuclei (isotopes of hydrogen) combine to form a heavier nucleus; it powers the Sun and needs very high temperature.
- Applications: C-14 dating of old organic material, Co-60 in cancer therapy, I-131 for thyroid study and treatment, P-32 as a tracer in agriculture, irradiation of food.
Important terms
- Radioactivity (किरणोत्सर्ग) – spontaneous emission of radiation by unstable nuclei, discovered by Henri Becquerel (1896).
- Half-life (t½) – time for half of the radioactive nuclei to decay.
- Decay constant (λ) – fraction of nuclei decaying per unit time.
- Chain reaction – a self-sustaining series of fissions caused by released neutrons.
- Critical mass – minimum mass of fissile material needed to sustain a chain reaction.
Formulas
- E = Δmc²; 1 amu (u) ≡ 931.5 MeV
- Δm = [Z mₚ + (A − Z) mₙ] − M(nucleus)
- N = N₀ e^(−λt); λ = (2.303/t) log (N₀/N)
- t½ = 0.693/λ; average life τ = 1/λ
- After n half-lives: N = N₀ (½)ⁿ
- C-14 dating: t = (2.303/λ) log (N₀/N), t½ of C-14 ≈ 5730 years
5 important questions
Q1. Define mass defect and binding energy.
Mass defect is the difference between the total mass of free protons and neutrons and the actual mass of the nucleus. Binding energy is the energy equivalent of this mass defect (E = Δmc²); it is the energy needed to break the nucleus into its nucleons.
Q2. ²³⁸₉₂U emits one α and two β particles. Find the product.
α: A = 238 − 4 = 234, Z = 92 − 2 = 90. Two β⁻: Z = 90 + 2 = 92, A stays 234. Product is ²³⁴₉₂U, an isotope of uranium.
Q3. Calculate the binding energy of ⁴₂He. (mₚ = 1.00728 u, mₙ = 1.00867 u, mass of He nucleus = 4.00151 u)
- Mass of nucleons = 2 × 1.00728 + 2 × 1.00867 = 2.01456 + 2.01734 = 4.03190 u
- Δm = 4.03190 − 4.00151 = 0.03039 u
- BE = 0.03039 × 931.5 = 28.31 MeV
- BE per nucleon = 28.31/4 ≈ 7.08 MeV
Q4. A wooden sample has 25% of the C-14 activity of fresh wood. Find its age (t½ = 5730 years).
- N/N₀ = 0.25 = (½)², so 2 half-lives have passed.
- Age = 2 × 5730 = 11,460 years
- Check: λ = 0.693/5730 = 1.209 × 10⁻⁴ per year; t = (2.303/λ) log 4 = (2.303 × 0.602)/1.209 × 10⁻⁴ ≈ 11,460 years ✓
Q5. Distinguish between nuclear fission and nuclear fusion.
- Fission: heavy nucleus splits; fusion: light nuclei join.
- Fission starts with slow neutrons at ordinary temperature; fusion needs millions of degrees.
- Fission gives radioactive waste; fusion products are mostly not radioactive.
- Fusion gives more energy per unit mass.
- Fission is used in nuclear power stations; fusion powers the Sun and stars (controlled fusion is still under research).
Exam tip
For decay problems, balance both A and Z on each side. For half-life questions, first check if the fraction is a simple power of ½ — it saves time.