Nuclear Structure and Decay

James Richard Fromm

Chemists usually consider nuclear reactions to lie more in the domain of physics than in the domain of chemistry. However, nuclear reactions have major implications for many issues which are both chemically and technologically significant. Chemists both contribute to and make use of techniques related to the decay of radioactive nuclei, which is the subject of this and the following sections.

In all earlier sections, the atomic nucleus has been considered to contain the protons and neutrons, the subatomic particles of the nucleus, while the electrons lying outside the nucleus have been the objects of primary chemical concern. This understanding is somewhat naive, because atomic nuclei can also produce other subatomic particles, such as mesons and neutrinos, when nuclear reactions take place. However, it is still sufficient for most chemical purposes.

Certain combinations of neutrons and protons form atomic nuclei which have no observable tendency to dissociate, or decay, spontaneously. These nuclei, which generally have a neutron/proton ratio near one to one, make up the stable isotopes. Nuclei of other combinations of neutrons and protons do tend to decay spontaneously, and they are referred to as radioactive isotopes. A small number of very long-lived radioactive isotopes, particularly 235U and 232Th, together with the shorter-lived daughter isotopes which arise from their decay, are found naturally on Earth. All other radioactive isotopes are produced artificially.

Artificially produced radioactive isotopes are generally created in uranium-based nuclear reactors, which will be taken up in later sections, or in large nuclear accelerators which use electric and magnetic fields to cause nuclei to collide at sufficient speed to overcome the mutual repulsion of their electrons and actually engage in nuclear reactions.

The law of conservation of energy applies to nuclear reactions just as it does to ordinary chemical reactions. Energy is involved in nuclear reactions just as energy is involved in ordinary chemical reactions. This energy must appear somewhere: as binding energy of nuclei, as the energy of photons of electromagnetic radiation, or as kinetic energy of the nuclei. The energy which appears in the form of photons or kinetic energy can often produce secondary nuclear reactions, and is more than sufficient to produce chemical reactions.

Binding Energy

If an atom is considered to be made up of electrons, neutrons, and protons, one would expect the mass of an atom to be simply the sum of the masses of the total particles which make it up. As it turns out, this is not exactly true. The mass of an atom as measured by mass spectrometry is always found to be slightly less than the mass of the total number of subatomic particles which make it up. The energy equivalent to this mass difference according to the Einstein equation E = mc2 is called the binding energy of the atom (or, if the calculation is made for the nucleus alone, of the nucleus).

Example. An atom of the element fluorine has nine protons, ten neutrons, and ten electrons. The atomic mass of fluorine is 18.99840 g/mol. We can calculate the binding energy of the fluorine atom as follows. The atomic masses of the constituent particles are:

9 x (1.0072697) = 9.0654273 g/mol
10 x (1.0086650) = 10.0866500 g/mol
10 x (0.0005486) = 0.0054860 g/mol

These add up to 19.1575633 g/mol which is 0.1591601 g/mol larger than the actual mass of the fluorine atom. The binding energy of the atom is given by the Einstein equation as (0.1591601 g/mol)(299792458 m/s)2 = 1.43 x 10+16 g-m2/mol-s2 (or 1.43 x 10+13 kg-m2/mol-s2 which is also 1.43 x 10+13 J/mol). This amount of energy is much greater than the normal energies which are involved in the formation of chemical bonds, a few to a few hundred kJ/mol.

The binding energy of the atom is also the binding energy of the nucleus since the mass of the nucleus is the mass of the atom less the mass of its electrons.

Copyright 1997 James R. Fromm