Concepts: Radioactivity, fission and fusion

4.1 Radioactivity

Some nuclei are unstable and transform into other nuclei by emitting particles or radiation. The three emissions are named for their nature. Alpha particles are helium nuclei, beta particles are electrons, and gamma rays are electromagnetic radiation with wavelengths shorter than X-rays. In each case the parent nucleus changes its atomic number, its mass number or both, so the emission is also a transmutation.

Stability is governed mainly by the balance between neutrons and protons. For light nuclei the stable ratio is about one to one; for heavy nuclei it rises to about three neutrons for every two protons, because extra neutrons help offset the Coulomb repulsion. Nuclei away from this balance are unstable and radioactive, and only about ten per cent of known isotopes are stable. The unstable ones are produced artificially by bombarding stable targets, or are observed in astronomical sources.

4.2 The decay law

Radioactive decay is random at the level of a single nucleus, but the number of decays in a sample follows an exact law. If a sample has N nuclei at time t and a decay constant λ, the number surviving after that instant is governed by

N = N0 e to the power -λt

The half-life is the time in which half the nuclei decay:

T one-half = 0.693/λ

The mean life, the time by which the population has dropped to 1/e of its initial value, is τ = 1/λ. Activity is the number of decays per second, R = λN, measured in becquerels; one curie is 3.7 × 10 to the 10 becquerels. Because N falls exponentially, the activity falls the same way.

4.3 Fission

When a heavy nucleus such as uranium-235 absorbs a neutron, it can split into two medium-mass fragments and release a few neutrons. A typical reaction produces antimony-133 and niobium-99 along with four neutrons. Because the fragments lie in the tightly bound middle region of the binding energy curve, the reaction releases energy, of the order of 200 MeV per fission. Two points matter for the numerical questions: the Q value comes from the mass difference on the two sides, and the fragments are more tightly bound than the parent, which is why the energy appears.

4.4 Fusion

When two light nuclei combine, the product lies higher on the binding energy curve and energy is released. The proton-proton chain in the sun does this on an enormous scale, turning hydrogen into helium. A laboratory example is the fusion of two deuterium nuclei to give helium-3 and a neutron, releasing 3.27 MeV. The difficulty is that the two positively charged nuclei repel each other, so fusion needs very high temperature to bring them close enough for the short-range nuclear force to take over; this is why fusion power is hard to achieve on earth even though it is the sun's ordinary business.

4.5 What each emission does to the nucleus

An alpha emission removes two protons and two neutrons, so the mass number falls by four and the atomic number by two. A beta emission changes a neutron into a proton inside the nucleus, so the mass number stays the same while the atomic number rises by one. Gamma emission changes neither A nor Z; it carries away excess energy from an excited nucleus. Writing these three changes correctly is usually enough to balance a decay equation, and the balance is checked by making the total A and total Z match on the two sides.

4.6 Activity and its units

Activity is a rate, so it is measured in decays per second. One becquerel is one decay per second, a very small unit; the curie, equal to 3.7 × 10 to the 10 becquerels, was defined from the activity of one gram of radium. Since activity is λN and N falls exponentially, the activity also falls by half in every half-life. A sample that is one day old and has a half-life of hours has already lost a measurable fraction of its activity, which is the basis of radioactive dating methods.

4.7 Why fission fragments are also radioactive

The two fragments produced in fission usually have too many neutrons for their new proton numbers, so they are unstable and decay by beta emission until they reach a stable ratio. That is why the products of fission keep emitting radiation after the splitting event. The released neutrons, meanwhile, can trigger further fissions if the material and geometry allow it, which is the basis of a self-sustaining chain.