Page 317 - Radiochemistry and nuclear chemistry

300 Radiochemistry and Nuclear Chemistry

certainly have some idea about what is going to happen. It is indeed our enjoyment in
developing models which causes us to experiment in science. We also want to be able to
make quantitative predictions based on our models which we therefore formulate in
mathematical terms. To allow tractable calculations most models involves simplifications
of the "real world'. Of course, since man is fallible some models may turn out to be wrong
but as new data accumulate, wrong or naive models are replaced by better ones.
We have already shown how one model for the nuclear structure, the liquid drop model,
has helped us to explain a number of nuclear properties, the most important being the shape
of the stability valley. But the liquid drop model fails to explain other important properties.
In this chapter we shall try to arrive at a nuclear model which takes into account the
quantum mechanical properties of the nucleus.

11.1. Requirements of a nuclear model

Investigation of light emitted by excited atoms (J. Rydberg 1895) led N. Bohr to suggest
the quantizeA model for the atom, which became the foundation for explaining the chemical
properties of the elements and justifying their ordering in the periodic system. From studies
of molecular spectra and from theoretical quantum and wave mechanical calculations, we
are able to interpret many of the most intricate details of chemical bonding.
In a similar manner, patterns of nuclear stability, results of nuclear reactions and
spectroscopy of radiation emitted by nuclei have yielded information which helps us develop
a picture of nuclear structure. But the situation is more complicated for the nucleus than for
the atom. In the nucleus there are two kinds of particles, protons and neutrons, packed
close together, and there are two kinds of forces - the electrostatic force and the short
range strong nuclear force. This more complex situation has caused slow progress in
developing a satisfactory model, and no single nuclear model has been able to explain all
the nuclear phenomena.

11.1.1. Some general nuclear properties

Let us begin with a summary of what we know about the nucleus, and see where that
leads us.
In Chapter 3 we observed that the binding energy per nucleon is almost constant for the
stable nuclei (Fig. 3.3) and that the radius is proportional to the cube root of the mass
number. We have interpreted this as reflecting fairly uniform distribution of charge and
mass throughout the volume of the nucleus. Other experimental evidence supports this
interpretation (Fig. 3.4). This information was used to develop the liquid drop model,
which successfully explains the valley of stability (Fig. 3.1). This overall view also supports
the assumption of a strong, short range nuclear force.
A more detailed consideration of Figures 3.1 and 3.3 indicates that certain mass numbers
seem to be more stable, i.e. nuclei with Z- or N-values of 2, 8, 20, 28, 50, and 82 (see also
Table 3.1). There is other evidence for the uniqueness of those numbers. For example, if
either the probability of capturing a neutron (the neutron capture cross-section) or the
energy required to release a neutron is plotted for different elements, it is found that