Nuclear physics embraces that area of physics devoted to the study of various atomic nuclei, their interactions, dynamics and especially their use in specific nuclear models which help to describe how nuclear energy (whether by fission or fusion) is produced. It is especially important to grasp the basics if we are to go on to discuss the possible use of nuclear energy as an accompaniment to alternative sources (e.g. solar. wind, geothermal etc.) and thereby reduce significantly the use of fossil fuels.
1.The Liquid Drop modelNuclear models occur under a set of hypotheses, each of which explains some aspect of nuclear behavior. The most basic is perhaps the “liquid drop model” which is used to account for nuclear fission, radioactivity. This is illustrated in Fig, 1 below:
This model is premised on the exceedingly short range of nuclear forces which requires that nearest neighbor attractions predominate. This is somewhat similar to the type of attraction between the molecules of a liquid which leads to the property of its surface tension. Thus, in a liquid drop nucleus each nucleon shares its total binding energy with every nucleon.
As the simplified model diagram (for U 235 fission) shows, we expect a spherical configuration in the minimum energy or unexcited state. The unstable (compound) nucleus then yields two “daughter nuclei” : La 139 and Mo 95, with two additional neutrons released.
E(B) = E(s) + (E(v) + E(c)
A reduction in any one or all of these constituent energies reduces the overall binding energy and hence the bonding energy between any pair of nucleons. To account for energy release in the fission of heavy nuclei we need only represent the nucleus as a liquid drop and its transition from the unexcited to the excited state as shown in Fig. 1.
(1) fo(Z, A) = 1.008142Z + 1.008982 (A – Z)
Evaluate the terms of the semi-empirical mass formula for the U 238 nucleus, if A = 238 and Z = 92. From this obtain the mass deficiency DM, where:
DM = ( Z) m p + (A- Z) m n - M(Z,A)
Where m p is the proton mass and m n the neutron mass
the binding energy Eb = DM c2 , and also the binding energy per nucleon Eb / A