8.2 Problems 439
8.40 The following plot (Fig. 8.7) shows the average binding energy per nucleon
for stable nuclei as a function of mass number.
Explain how the mass of a nucleus can be calculated from this plot and esti-
mate the mass of^23592 U.
Briefly describe the main features of the plot in the context of nuclear
models such as the liquid Drop Model, the Fermi Gas Model and the Nuclear
Shell Model.
In terms of the Liquid Drop Model, explain why nuclear fission and fusion
are possible and estimate the energy released when a nucleus of^23592 U under-
goes fission into the fragments^8735 Br and^14557 La with the release of three prompt
neutrons.
[University of Cambridge, Tripos 2004]
Fig. 8.7B/A versus A plot
8.41 Investigate using liquid drop model, theβstability of the isobars^12753 I and
127
54 Xe given that
127
51 Sb→β
−+ 127
52 Te+^1 .60 MeV
127
55 Cr→β++ 127
54 Xe+^1 .06 MeV
[University of London 1969]8.42 The empirical mass formula is
A
ZM=^0 .99198 A−^0 .000841 Z+^0 .01968 A
2 / (^3) + 0 .0007668 Z (^2) A− 1 / 3
- 0 .09966(Z−A/2)^2 A−^1 −δ
in atomic mass units, whereδ=± 0 .01204 A−^1 /^2 or 0.
Determine whether or not the nuclide^2712 Mg is stable toβdecay.
[University of Newcastle 1966]
8.2.9 Optical Model ....................................
8.43 Show that the imaginary part of the complex potentialV=−(U+iW)inthe
optical model has the effect of removing particle flux from the elastic channel.