Nuclear Chemistry

Nuclear chemistry studies reactions that change the composition of atomic nuclei. A nucleus is characterized by its atomic number (Z, the number of protons) and its mass number (A, the total number of protons and neutrons). Protons and neutrons are collectively called nucleons.

Not all combinations of protons and neutrons produce stable nuclei. The band of stability is the region on a plot of neutron number versus proton number where stable nuclides exist. Light stable nuclei have roughly equal numbers of protons and neutrons (n:p ≈ 1), but heavier stable nuclei require increasingly more neutrons than protons (n:p up to ∼1.5) because additional neutrons help offset the electrostatic repulsion between protons.

Nuclei that fall outside the band of stability are radioactive — they undergo spontaneous decay to move toward a more stable neutron-to-proton ratio.

Radioactive decay is the spontaneous emission of particles or energy from an unstable nucleus. The main types are:

Alpha and beta decay change the identity of the element. Gamma emission releases energy without changing the nuclide’s composition. Positron emission and electron capture both convert a proton to a neutron, lowering Z by 1.

In nuclear equations, both mass number (A) and atomic number (Z) must be conserved — the sums on each side of the arrow must be equal.

Example of alpha decay: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Check: A = 238 = 234 + 4 ✓, Z = 92 = 90 + 2 ✓.

Example of beta decay: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e. A neutron converts to a proton, emitting an electron. A stays at 14, Z goes from 6 to 7.

To predict the product of a nuclear reaction, use conservation rules to find the missing A and Z values, then identify the element from the periodic table. This is the key skill: if you know the parent nuclide and the type of decay, you can always determine the daughter nuclide.

Radioactive decay is a first-order kinetic process. The half-life (t_1/2) is the time required for half the radioactive atoms in a sample to decay. After n half-lives, the fraction remaining is (1/2)ⁿ.

The quantitative relationship: N = N₀ · (1/2)^t/t_1/2, or equivalently N = N₀ · e^−λt, where the decay constant λ = 0.693 / t_1/2.

Half-lives vary enormously: ^99mTc (used in medical imaging) has t_1/2 = 6 hours, ¹⁴C (used in radiocarbon dating) has t_1/2 = 5730 years, and ²³⁸U has t_1/2 = 4.5 billion years. The half-life is a fixed property of each nuclide — it cannot be changed by temperature, pressure, or chemical environment.

Radiocarbon dating uses the known half-life of ¹⁴C (5730 years) to determine the age of organic materials. Living organisms continuously exchange carbon with their environment, maintaining a constant ¹⁴C/¹²C ratio. Once an organism dies, ¹⁴C decays without being replenished, so the ratio decreases predictably over time.

By measuring the remaining ¹⁴C/¹²C ratio and comparing it to the ratio in living organisms, you can calculate how many half-lives have elapsed and thus the age of the sample. This technique is reliable for materials up to about 50,000 years old (roughly 9 half-lives).

Other dating methods use isotopes with longer half-lives for geological timescales: uranium-lead dating (²³⁸U → ²⁰⁶Pb, t_1/2 = 4.5 × 10⁹ years) can date rocks billions of years old.

Nuclear fission is the splitting of a heavy nucleus into two lighter fragments, triggered by absorption of a neutron. The process releases enormous energy and additional neutrons.

The classic example: ²³⁵U absorbs a neutron and splits into two mid-mass nuclei (such as ⁹²Kr and ¹⁴¹Ba) plus 2–3 additional neutrons. These released neutrons can trigger further fission events, creating a chain reaction.

A chain reaction becomes self-sustaining when the critical mass of fissile material is present — enough material that, on average, each fission event triggers at least one more. In nuclear power plants, the chain reaction is controlled using neutron-absorbing rods. The energy released per fission event is roughly a million times greater than the energy released by a typical chemical reaction.

Nuclear fusion is the combining of light nuclei to form a heavier nucleus, releasing even more energy per gram than fission. The Sun is powered by fusion, primarily the conversion of hydrogen into helium.

Fusion requires extremely high temperatures (~10⁷–10⁸ K) to overcome the electrostatic repulsion between positively charged nuclei. This is why controlled fusion for power generation remains a major engineering challenge.

Both fission and fusion release energy because the products have higher nuclear binding energy per nucleon than the reactants. Binding energy is calculated from the mass defect (Δm) — the difference between the mass of the individual nucleons and the mass of the assembled nucleus — using Einstein’s equation E = Δmc². Iron-56 has the highest binding energy per nucleon, which is why fission of elements heavier than iron and fusion of elements lighter than iron both release energy.

A systematic approach to nuclear chemistry problems:

1. Identify the type of decay from the particle emitted: alpha (⁴₂He), beta (⁰_-1e), positron (⁰₊₁e), or gamma (γ, no mass or charge change).
2. Balance both mass number and atomic number in every nuclear equation. The sum of mass numbers and the sum of atomic numbers must be equal on both sides.
3. For half-life calculations: use the relationship N = N₀ × (½)^t/t½. Count the number of half-lives elapsed, then halve the starting amount that many times.
4. Distinguish nuclear from chemical: nuclear reactions change the identity of the element (transmutation), involve enormous energy changes, and are unaffected by temperature, pressure, or catalysts.

Common mistakes: not balancing both mass number and atomic number independently, confusing beta decay (neutron → proton + electron) with electron capture (proton + electron → neutron), misapplying the half-life formula by using elapsed time without dividing by the half-life period, and thinking that chemical conditions (temperature, bonding) affect nuclear decay rates.