Nuclear and radiochemistry

Atoms of the same element can have different numbers of neutrons; these are isotopes. Some isotopes have unstable nuclei that give out radiation to become more stable. This is radioactive decay, and it is random: you cannot predict when a particular nucleus will decay.

• Alpha (\alpha): a helium nucleus (two protons, two neutrons). Strongly ionising, but stopped by paper or a few centimetres of air.
• Beta (\beta): a fast electron, made when a neutron turns into a proton. Stopped by a few millimetres of aluminium.
• Gamma (\gamma): electromagnetic radiation from the nucleus. Weakly ionising; only thick lead or concrete stops most of it.

The half-life is the time for half the radioactive nuclei in a sample to decay, or for its activity (in becquerels) to halve. Iodine-131 has a half-life of about 8 days, so after 24 days one-eighth is left.

Smoke alarms use a weak alpha source, americium-241. Gamma rays sterilise surgical instruments. Medical tracers need short half-lives to limit the dose.

Fission splits a heavy nucleus such as uranium-235 after it absorbs a neutron, releasing energy and neutrons for a chain reaction. Fusion joins light nuclei, such as the hydrogen isotopes in the Sun.

Writing decay equations

Mass number A and atomic number Z must balance.

• \alpha decay: A falls by 4 and Z by 2. {}^{238}_{92}\mathrm{U} \rightarrow {}^{234}_{90}\mathrm{Th} + {}^{4}_{2}\alpha
• \beta^- decay: a neutron becomes a proton, so Z rises by 1 and A is unchanged. {}^{14}_{6}\mathrm{C} \rightarrow {}^{14}_{7}\mathrm{N} + {}^{0}_{-1}\mathrm{e} (plus an antineutrino).
• \beta^+ decay (positron emission) and electron capture turn a proton into a neutron, so Z falls by 1. Fluorine-18, used in PET scans, decays this way to oxygen-18.
• \gamma emission changes neither; the nucleus just sheds energy.

The decay mode follows from the neutron-to-proton ratio. Light stable nuclei have roughly equal numbers; heavier ones need extra neutrons to offset the repulsion between protons. Nuclei with too many neutrons undergo \beta^- decay, those with too few undergo \beta^+ decay or electron capture, and very heavy nuclei lose mass by \alpha decay.

Half-life calculations

After n half-lives the fraction left is (1/2)^n. Living things keep the same ^{14}C/^{12}C ratio as the atmosphere, but after death ^{14}C decays with t_{1/2} \approx 5730 years. A wooden bowl showing a quarter of the expected activity is two half-lives old, about 11 500 years. Beyond about 50 000 years too little ^{14}C remains to measure.

Where the energy comes from

In both fission and fusion the products have slightly less mass than the reactants, and the difference appears as energy, E = mc^2. Fission of one uranium-235 nucleus releases about 200 MeV, tens of millions of times more than burning one carbon atom.

Decay kinetics

Each nucleus has the same probability of decaying per unit time, so decay is first order:

Activity A = \lambda N (Bq) falls the same way. Worked example: ^{18}F has t_{1/2} \approx 110 min. A dose measured at 400 MBq at 09:00 has, at 11:45, 400 \times 2^{-165/110} = 400 \times 2^{-1.5} \approx 141 MBq.

Parent-daughter equilibria

When a longer-lived parent feeds a shorter-lived daughter, the daughter's activity grows until it tracks the parent's. The hospital technetium generator relies on this. Molybdate, ^{99}MoO_4^{2-} (t_{1/2} \approx 66 h), is held on an alumina column and decays to ^{99m}Tc (t_{1/2} \approx 6.0 h). Singly charged pertechnetate, TcO_4^-, binds weakly and is washed off with saline while the doubly charged molybdate stays behind. Daughter activity then regrows to a maximum after about 23 h. This is transient equilibrium; secular equilibrium is the limit where the parent's activity barely changes, as for ^{226}Ra and ^{222}Rn.

^{99m}Tc decays by isomeric transition, emitting a 140 keV \gamma-ray with no particle emission, which suits gamma cameras and keeps the dose low. Its chemistry is tailored to the target: reducing pertechnetate with tin(II) in the presence of the right ligand gives diphosphonate complexes that seek bone, or the Tc(I) hexakis(isonitrile) cation, sestamibi, that collects in heart muscle.

Binding energy

A ^4He nucleus has mass 4.001506 u; two free protons and two free neutrons total 4.031882 u. The 0.030376 u mass defect times 931.5 MeV u^{-1} gives 28.3 MeV, about 7.1 MeV per nucleon. Binding energy per nucleon peaks near iron and nickel, so fission of heavy nuclei and fusion of light ones both release energy.

Making radionuclides

Reactors make neutron-rich isotopes by neutron capture or fission (^{99}Mo is recovered from irradiated uranium targets). Cyclotrons make proton-rich ones: ^{18}O(p,n)^{18}F in ^{18}O-enriched water gives [^{18}F]fluoride, which is dried with potassium carbonate and Kryptofix 2.2.2 to make a naked, nucleophilic fluoride. S_\mathrm{N}2 displacement of triflate from a protected mannose derivative, then deprotection, gives [^{18}F]FDG. Synthesis, purification and quality control must all fit within a couple of half-lives.

Nuclear medicine is moving from imaging alone to theranostics, where one targeting molecule carries a diagnostic isotope to find disease and a therapeutic one to treat it. PSMA ligands labelled with the positron emitter ^{68}Ga select prostate-cancer patients by PET, and the matching ^{177}Lu compound (a \beta^- emitter, t_{1/2} about 6.6 days) delivers the dose; [^{177}Lu]Lu-PSMA-617 was approved in 2022.

Targeted alpha therapy goes further. Alpha particles dump their energy within a few cell diameters, so they kill tumour cells with less damage to neighbours. ^{223}RaCl_2 treats bone metastases simply because radium behaves like calcium. ^{225}Ac needs a chelator that holds a large, weakly Lewis-acidic +3 ion under mild conditions, where DOTA performs poorly; macrocycles such as macropa were designed for this. A deeper problem is recoil: each \alpha emission kicks the daughter nucleus out of any chelate, and the free radioactive daughters redistribute in the body.

Radiofluorination has broadened. Classical ^{18}F chemistry needed electron-poor arenes or aliphatic leaving groups. Copper-mediated fluorination of aryl boronic esters and stannanes, and iodonium ylide precursors, now allow late-stage labelling of electron-rich arenes, opening many drug candidates to PET studies.

Supply is a research problem in its own right. Most ^{99}Mo comes from a few ageing reactors, and outages have caused shortages, so accelerator and low-enriched-uranium routes are being developed; ^{225}Ac supply is limited by small stocks of its parent, ^{229}Th.

In the fuel cycle, separating americium and curium from lanthanides in spent fuel is hard because their +3 ions are so alike. Soft N-donor extractants such as bis-triazinyl pyridines exploit slightly greater covalency in actinide bonding. How far 5f orbitals take part in bonding remains debated, tested by X-ray spectroscopy and relativistic calculations.